LMFDB - Galois group: 36T28

Show commands: Magma

magma:G := TransitiveGroup(36, 28);

Group invariants

Abstract group:	$C_3\times D_{12}$	magma:IdentifyGroup(G);
Order:	$72=2^{3} \cdot 3^{2}$	magma:Order(G);
Cyclic:	no	magma:IsCyclic(G);
Abelian:	no	magma:IsAbelian(G);
Solvable:	yes	magma:IsSolvable(G);
Nilpotency class:	not nilpotent	magma:NilpotencyClass(G);

Group action invariants

Degree $n$ :	$36$	magma:t, n := TransitiveGroupIdentification(G); n;
Transitive number $t$ :	$28$	magma:t, n := TransitiveGroupIdentification(G); t;
Parity:	$-1$	magma:IsEven(G);
Primitive:	no	magma:IsPrimitive(G);
$\card{\Aut(F/K)}$ :	$6$	magma:Order(Centralizer(SymmetricGroup(n), G));
Generators:	$(1,36)(2,35)(3,34)(4,33)(7,8)(9,14)(10,13)(11,15)(12,16)(17,18)(21,26)(22,25)(23,28)(24,27)(29,30)$ , $(1,32,11,3,29,9,2,31,12,4,30,10)(5,22,13,7,24,16,6,21,14,8,23,15)(17,33,26,19,35,27,18,34,25,20,36,28)$	magma:Generators(G);

Low degree resolvents

$\card{(G/N)}$ Galois groups for stem field(s)
$2$ : $C_2$ x 3
$3$ : $C_3$
$4$ : $C_2^2$
$6$ : $S_3$ , $C_6$ x 3
$8$ : $D_{4}$
$12$ : $D_{6}$ , $C_6\times C_2$
$18$ : $S_3\times C_3$
$24$ : $D_{12}$ , $D_4 \times C_3$
$36$ : $C_6\times S_3$

Resolvents shown for degrees $\leq 47$

$\card{(G/N)}$	Galois groups for stem field(s)
$2$ :	$C_2$ x 3
$3$ :	$C_3$
$4$ :	$C_2^2$
$6$ :	$S_3$ , $C_6$ x 3
$8$ :	$D_{4}$
$12$ :	$D_{6}$ , $C_6\times C_2$
$18$ :	$S_3\times C_3$
$24$ :	$D_{12}$ , $D_4 \times C_3$
$36$ :	$C_6\times S_3$

Subfields

Degree 2: $C_2$
Degree 3: $C_3$ , $S_3$
Degree 4: $D_{4}$
Degree 6: $C_6$ , $D_{6}$
Degree 9: $S_3\times C_3$
Degree 12: $D_{12}$ , $D_4 \times C_3$
Degree 18: $S_3 \times C_6$

Low degree siblings

24T67, 36T28
Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

Label	Cycle Type	Size	Order	Index	Representative
1A	$1^{36}$	$1$	$1$	$0$	$()$
2A	$2^{18}$	$1$	$2$	$18$	$( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)$
2B	$2^{15},1^{6}$	$6$	$2$	$15$	$( 1,36)( 2,35)( 3,34)( 4,33)( 7, 8)( 9,14)(10,13)(11,15)(12,16)(17,18)(21,26)(22,25)(23,28)(24,27)(29,30)$
2C	$2^{18}$	$6$	$2$	$18$	$( 1, 4)( 2, 3)( 5,35)( 6,36)( 7,33)( 8,34)( 9,17)(10,18)(11,19)(12,20)(13,16)(14,15)(21,32)(22,31)(23,30)(24,29)(25,27)(26,28)$
3A1	$3^{12}$	$1$	$3$	$24$	$( 1,15,25)( 2,16,26)( 3,13,28)( 4,14,27)( 5,20,32)( 6,19,31)( 7,17,29)( 8,18,30)( 9,24,33)(10,23,34)(11,22,36)(12,21,35)$
3A-1	$3^{12}$	$1$	$3$	$24$	$( 1,25,15)( 2,26,16)( 3,28,13)( 4,27,14)( 5,32,20)( 6,31,19)( 7,29,17)( 8,30,18)( 9,33,24)(10,34,23)(11,36,22)(12,35,21)$
3B	$3^{12}$	$2$	$3$	$24$	$( 1, 7,35)( 2, 8,36)( 3, 6,34)( 4, 5,33)( 9,14,20)(10,13,19)(11,16,18)(12,15,17)(21,25,29)(22,26,30)(23,28,31)(24,27,32)$
3C1	$3^{12}$	$2$	$3$	$24$	$( 1,17,21)( 2,18,22)( 3,19,23)( 4,20,24)( 5, 9,27)( 6,10,28)( 7,12,25)( 8,11,26)(13,31,34)(14,32,33)(15,29,35)(16,30,36)$
3C-1	$3^{12}$	$2$	$3$	$24$	$( 1,21,17)( 2,22,18)( 3,23,19)( 4,24,20)( 5,27, 9)( 6,28,10)( 7,25,12)( 8,26,11)(13,34,31)(14,33,32)(15,35,29)(16,36,30)$
4A	$4^{9}$	$2$	$4$	$27$	$( 1, 4, 2, 3)( 5, 8, 6, 7)( 9,11,10,12)(13,15,14,16)(17,20,18,19)(21,24,22,23)(25,27,26,28)(29,32,30,31)(33,36,34,35)$
6A1	$6^{6}$	$1$	$6$	$30$	$( 1,26,15, 2,25,16)( 3,27,13, 4,28,14)( 5,31,20, 6,32,19)( 7,30,17, 8,29,18)( 9,34,24,10,33,23)(11,35,22,12,36,21)$
6A-1	$6^{6}$	$1$	$6$	$30$	$( 1,16,25, 2,15,26)( 3,14,28, 4,13,27)( 5,19,32, 6,20,31)( 7,18,29, 8,17,30)( 9,23,33,10,24,34)(11,21,36,12,22,35)$
6B	$6^{6}$	$2$	$6$	$30$	$( 1,36, 7, 2,35, 8)( 3,33, 6, 4,34, 5)( 9,19,14,10,20,13)(11,17,16,12,18,15)(21,30,25,22,29,26)(23,32,28,24,31,27)$
6C1	$6^{6}$	$2$	$6$	$30$	$( 1,22,17, 2,21,18)( 3,24,19, 4,23,20)( 5,28, 9, 6,27,10)( 7,26,12, 8,25,11)(13,33,31,14,34,32)(15,36,29,16,35,30)$
6C-1	$6^{6}$	$2$	$6$	$30$	$( 1,18,21, 2,17,22)( 3,20,23, 4,19,24)( 5,10,27, 6, 9,28)( 7,11,25, 8,12,26)(13,32,34,14,31,33)(15,30,35,16,29,36)$
6D1	$6^{5},3^{2}$	$6$	$6$	$29$	$( 1,22,15,36,25,11)( 2,21,16,35,26,12)( 3,23,13,34,28,10)( 4,24,14,33,27, 9)( 5,32,20)( 6,31,19)( 7,30,17, 8,29,18)$
6D-1	$6^{5},3^{2}$	$6$	$6$	$29$	$( 1,11,25,36,15,22)( 2,12,26,35,16,21)( 3,10,28,34,13,23)( 4, 9,27,33,14,24)( 5,20,32)( 6,19,31)( 7,18,29, 8,17,30)$
6E1	$6^{6}$	$6$	$6$	$30$	$( 1,27,15, 4,25,14)( 2,28,16, 3,26,13)( 5,21,20,35,32,12)( 6,22,19,36,31,11)( 7,24,17,33,29, 9)( 8,23,18,34,30,10)$
6E-1	$6^{6}$	$6$	$6$	$30$	$( 1,14,25, 4,15,27)( 2,13,26, 3,16,28)( 5,12,32,35,20,21)( 6,11,31,36,19,22)( 7, 9,29,33,17,24)( 8,10,30,34,18,23)$
12A1	$12^{3}$	$2$	$12$	$33$	$( 1, 6,36, 4, 7,34, 2, 5,35, 3, 8,33)( 9,15,19,11,14,17,10,16,20,12,13,18)(21,28,30,24,25,31,22,27,29,23,26,32)$
12A5	$12^{3}$	$2$	$12$	$33$	$( 1,34, 8, 4,35, 6, 2,33, 7, 3,36, 5)( 9,17,13,11,20,15,10,18,14,12,19,16)(21,31,26,24,29,28,22,32,25,23,30,27)$
12B1	$12^{3}$	$2$	$12$	$33$	$( 1,14,26, 3,15,27, 2,13,25, 4,16,28)( 5,18,31, 7,20,30, 6,17,32, 8,19,29)( 9,22,34,12,24,36,10,21,33,11,23,35)$
12B-1	$12^{3}$	$2$	$12$	$33$	$( 1,27,16, 3,25,14, 2,28,15, 4,26,13)( 5,30,19, 7,32,18, 6,29,20, 8,31,17)( 9,36,23,12,33,22,10,35,24,11,34,21)$
12C1	$12^{3}$	$2$	$12$	$33$	$( 1,19,22, 4,17,23, 2,20,21, 3,18,24)( 5,12,28, 8, 9,25, 6,11,27, 7,10,26)(13,30,33,15,31,36,14,29,34,16,32,35)$
12C-1	$12^{3}$	$2$	$12$	$33$	$( 1,31,11, 4,29,10, 2,32,12, 3,30, 9)( 5,21,13, 8,24,15, 6,22,14, 7,23,16)(17,34,26,20,35,28,18,33,25,19,36,27)$
12C5	$12^{3}$	$2$	$12$	$33$	$( 1,23,18, 4,21,19, 2,24,17, 3,22,20)( 5,25,10, 8,27,12, 6,26, 9, 7,28,11)(13,36,32,15,34,30,14,35,31,16,33,29)$
12C-5	$12^{3}$	$2$	$12$	$33$	$( 1,10,30, 4,12,31, 2, 9,29, 3,11,32)( 5,15,23, 8,14,21, 6,16,24, 7,13,22)(17,28,36,20,25,34,18,27,35,19,26,33)$

Malle's constant $a(G)$ : $1/15$

magma:ConjugacyClasses(G);

Character table

		1A	2A	2B	2C	3A1	3A-1	3B	3C1	3C-1	4A	6A1	6A-1	6B	6C1	6C-1	6D1	6D-1	6E1	6E-1	12A1	12A5	12B1	12B-1	12C1	12C-1	12C5	12C-5
	Size	1	1	6	6	1	1	2	2	2	2	1	1	2	2	2	6	6	6	6	2	2	2	2	2	2	2	2
	2 P	1A	1A	1A	1A	3A-1	3A1	3B	3C-1	3C1	2A	3A1	3A-1	3B	3C1	3C-1	3A1	3A-1	3A1	3A-1	6B	6B	6A1	6A-1	6C1	6C-1	6C-1	6C1
	3 P	1A	2A	2B	2C	1A	1A	1A	1A	1A	4A	2A	2A	2A	2A	2A	2B	2B	2C	2C	4A	4A	4A	4A	4A	4A	4A	4A
	Type
72.28.1a	R	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
72.28.1b	R	$1$	$1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$
72.28.1c	R	$1$	$1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$
72.28.1d	R	$1$	$1$	$1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$1$	$1$	$1$	$1$	$1$	$1$	$1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$	$- 1$
72.28.1e1	C	$1$	$1$	$1$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$
72.28.1e2	C	$1$	$1$	$1$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$
72.28.1f1	C	$1$	$1$	$- 1$	$- 1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$
72.28.1f2	C	$1$	$1$	$- 1$	$- 1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$ζ_{3}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$
72.28.1g1	C	$1$	$1$	$- 1$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$- 1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}^{- 1}$	$- ζ_{3}^{- 1}$	$- 1$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$- ζ_{3}$	$- 1$	$- ζ_{3}$	$- ζ_{3}^{- 1}$
72.28.1g2	C	$1$	$1$	$- 1$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$- 1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}$	$- ζ_{3}$	$- 1$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$- ζ_{3}^{- 1}$	$- 1$	$- ζ_{3}^{- 1}$	$- ζ_{3}$
72.28.1h1	C	$1$	$1$	$1$	$- 1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$- 1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$- ζ_{3}^{- 1}$	$- 1$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$- ζ_{3}$	$- 1$	$- ζ_{3}$	$- ζ_{3}^{- 1}$
72.28.1h2	C	$1$	$1$	$1$	$- 1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$	$- 1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$ζ_{3}^{- 1}$	$ζ_{3}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$- ζ_{3}$	$- 1$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$- ζ_{3}^{- 1}$	$- 1$	$- ζ_{3}^{- 1}$	$- ζ_{3}$
72.28.2a	R	$2$	$2$	$0$	$0$	$2$	$2$	$- 1$	$- 1$	$- 1$	$2$	$2$	$2$	$- 1$	$- 1$	$- 1$	$0$	$0$	$0$	$0$	$- 1$	$- 1$	$2$	$2$	$- 1$	$- 1$	$- 1$	$- 1$
72.28.2b	R	$2$	$- 2$	$0$	$0$	$2$	$2$	$2$	$2$	$2$	$0$	$- 2$	$- 2$	$- 2$	$- 2$	$- 2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
72.28.2c	R	$2$	$2$	$0$	$0$	$2$	$2$	$- 1$	$- 1$	$- 1$	$- 2$	$2$	$2$	$- 1$	$- 1$	$- 1$	$0$	$0$	$0$	$0$	$1$	$1$	$- 2$	$- 2$	$1$	$1$	$1$	$1$
72.28.2d1	C	$2$	$2$	$0$	$0$	$2 ζ_{3}^{- 1}$	$2 ζ_{3}$	$- 1$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$2$	$2 ζ_{3}$	$2 ζ_{3}^{- 1}$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$- 1$	$0$	$0$	$0$	$0$	$- ζ_{3}^{- 1}$	$- 1$	$2 ζ_{3}^{- 1}$	$2 ζ_{3}$	$- ζ_{3}$	$- 1$	$- ζ_{3}$	$- ζ_{3}^{- 1}$
72.28.2d2	C	$2$	$2$	$0$	$0$	$2 ζ_{3}$	$2 ζ_{3}^{- 1}$	$- 1$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$2$	$2 ζ_{3}^{- 1}$	$2 ζ_{3}$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$- 1$	$0$	$0$	$0$	$0$	$- ζ_{3}$	$- 1$	$2 ζ_{3}$	$2 ζ_{3}^{- 1}$	$- ζ_{3}^{- 1}$	$- 1$	$- ζ_{3}^{- 1}$	$- ζ_{3}$
72.28.2e1	R	$2$	$- 2$	$0$	$0$	$2$	$2$	$- 1$	$- 1$	$- 1$	$0$	$- 2$	$- 2$	$1$	$1$	$1$	$0$	$0$	$0$	$0$	$- ζ_{12}^{- 1} - ζ_{12}$	$- ζ_{12}^{- 1} - ζ_{12}$	$0$	$0$	$- ζ_{12}^{- 1} - ζ_{12}$	$ζ_{12}^{- 1} + ζ_{12}$	$ζ_{12}^{- 1} + ζ_{12}$	$ζ_{12}^{- 1} + ζ_{12}$
72.28.2e2	R	$2$	$- 2$	$0$	$0$	$2$	$2$	$- 1$	$- 1$	$- 1$	$0$	$- 2$	$- 2$	$1$	$1$	$1$	$0$	$0$	$0$	$0$	$ζ_{12}^{- 1} + ζ_{12}$	$ζ_{12}^{- 1} + ζ_{12}$	$0$	$0$	$ζ_{12}^{- 1} + ζ_{12}$	$- ζ_{12}^{- 1} - ζ_{12}$	$- ζ_{12}^{- 1} - ζ_{12}$	$- ζ_{12}^{- 1} - ζ_{12}$
72.28.2f1	C	$2$	$- 2$	$0$	$0$	$2 ζ_{3}^{- 1}$	$2 ζ_{3}$	$2$	$2 ζ_{3}^{- 1}$	$2 ζ_{3}$	$0$	$- 2 ζ_{3}$	$- 2 ζ_{3}^{- 1}$	$- 2 ζ_{3}$	$- 2 ζ_{3}^{- 1}$	$- 2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
72.28.2f2	C	$2$	$- 2$	$0$	$0$	$2 ζ_{3}$	$2 ζ_{3}^{- 1}$	$2$	$2 ζ_{3}$	$2 ζ_{3}^{- 1}$	$0$	$- 2 ζ_{3}^{- 1}$	$- 2 ζ_{3}$	$- 2 ζ_{3}^{- 1}$	$- 2 ζ_{3}$	$- 2$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$	$0$
72.28.2g1	C	$2$	$2$	$0$	$0$	$2 ζ_{3}^{- 1}$	$2 ζ_{3}$	$- 1$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$- 2$	$2 ζ_{3}$	$2 ζ_{3}^{- 1}$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$- 1$	$0$	$0$	$0$	$0$	$ζ_{3}^{- 1}$	$1$	$- 2 ζ_{3}^{- 1}$	$- 2 ζ_{3}$	$ζ_{3}$	$1$	$ζ_{3}$	$ζ_{3}^{- 1}$
72.28.2g2	C	$2$	$2$	$0$	$0$	$2 ζ_{3}$	$2 ζ_{3}^{- 1}$	$- 1$	$- ζ_{3}$	$- ζ_{3}^{- 1}$	$- 2$	$2 ζ_{3}^{- 1}$	$2 ζ_{3}$	$- ζ_{3}^{- 1}$	$- ζ_{3}$	$- 1$	$0$	$0$	$0$	$0$	$ζ_{3}$	$1$	$- 2 ζ_{3}$	$- 2 ζ_{3}^{- 1}$	$ζ_{3}^{- 1}$	$1$	$ζ_{3}^{- 1}$	$ζ_{3}$
72.28.2h1	C	$2$	$- 2$	$0$	$0$	$- 2 ζ_{12}^{2}$	$2 ζ_{12}^{4}$	$- 1$	$ζ_{12}^{2}$	$- ζ_{12}^{4}$	$0$	$- 2 ζ_{12}^{4}$	$2 ζ_{12}^{2}$	$ζ_{12}^{4}$	$- ζ_{12}^{2}$	$1$	$0$	$0$	$0$	$0$	$- ζ_{12} - ζ_{12}^{3}$	$ζ_{12}^{- 1} + ζ_{12}$	$0$	$0$	$- ζ_{12} + 2 ζ_{12}^{3}$	$- ζ_{12}^{- 1} - ζ_{12}$	$ζ_{12} - 2 ζ_{12}^{3}$	$ζ_{12} + ζ_{12}^{3}$
72.28.2h2	C	$2$	$- 2$	$0$	$0$	$2 ζ_{12}^{4}$	$- 2 ζ_{12}^{2}$	$- 1$	$- ζ_{12}^{4}$	$ζ_{12}^{2}$	$0$	$2 ζ_{12}^{2}$	$- 2 ζ_{12}^{4}$	$- ζ_{12}^{2}$	$ζ_{12}^{4}$	$1$	$0$	$0$	$0$	$0$	$- ζ_{12} + 2 ζ_{12}^{3}$	$ζ_{12}^{- 1} + ζ_{12}$	$0$	$0$	$- ζ_{12} - ζ_{12}^{3}$	$- ζ_{12}^{- 1} - ζ_{12}$	$ζ_{12} + ζ_{12}^{3}$	$ζ_{12} - 2 ζ_{12}^{3}$
72.28.2h3	C	$2$	$- 2$	$0$	$0$	$- 2 ζ_{12}^{2}$	$2 ζ_{12}^{4}$	$- 1$	$ζ_{12}^{2}$	$- ζ_{12}^{4}$	$0$	$- 2 ζ_{12}^{4}$	$2 ζ_{12}^{2}$	$ζ_{12}^{4}$	$- ζ_{12}^{2}$	$1$	$0$	$0$	$0$	$0$	$ζ_{12} + ζ_{12}^{3}$	$- ζ_{12}^{- 1} - ζ_{12}$	$0$	$0$	$ζ_{12} - 2 ζ_{12}^{3}$	$ζ_{12}^{- 1} + ζ_{12}$	$- ζ_{12} + 2 ζ_{12}^{3}$	$- ζ_{12} - ζ_{12}^{3}$
72.28.2h4	C	$2$	$- 2$	$0$	$0$	$2 ζ_{12}^{4}$	$- 2 ζ_{12}^{2}$	$- 1$	$- ζ_{12}^{4}$	$ζ_{12}^{2}$	$0$	$2 ζ_{12}^{2}$	$- 2 ζ_{12}^{4}$	$- ζ_{12}^{2}$	$ζ_{12}^{4}$	$1$	$0$	$0$	$0$	$0$	$ζ_{12} - 2 ζ_{12}^{3}$	$- ζ_{12}^{- 1} - ζ_{12}$	$0$	$0$	$ζ_{12} + ζ_{12}^{3}$	$ζ_{12}^{- 1} + ζ_{12}$	$- ζ_{12} - ζ_{12}^{3}$	$- ζ_{12} + 2 ζ_{12}^{3}$

magma:CharacterTable(G);

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Label	36T28

Degree	$36$
Order	$72$
Cyclic	no
Abelian	no
Solvable	yes
Primitive	no
$p$ -group	no
Group:	$C_3\times D_{12}$