↑

Learn more

Note: Search results may be incomplete due to uncomputed quantities: Rational (116441 objects)

Refine search

Order Exponent Nilpotency class Nilpotent
Center Commutator Central quotient Abelianization
Abelian Cyclic Solvable Simple
Perfect Direct product Semidirect product Wreath product
Automorphism group Automorphisms Transitive degree Permutation degree
Minimal degree of $\C$-irrep Minimal degree of $\Q$-irrep Minimal degree of $\C$-rep Minimal degree of $\Q$-rep
Outer aut. group Outer automorphisms Metabelian Metacyclic
Almost simple Quasisimple A-group Z-group
Frattini subgroup Derived length Rank Schur multiplier
Supersolvable Monomial Rational
Number of subgroups Number of normal subgroups Number of conjugacy classes
Number of characteristic subgroups Number of autjugacy classes Number of divisions
Order statistics Order factorization Commutator length
Sort order Select

Results (1-50 of 5577 matches)

Next   displayed columns for results
Label Name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
2.1 $C_2$ $2$ $2$ $2$ $C_2$ $C_1$ $C_1$ $C_{2}$ Cyclic
4.2 $C_2^2$ $2^{2}$ $2$ $4$ $C_2^2$ $C_1$ $C_1$ $C_{2}^{2}$ Abelian - 2
6.1 $S_3$ $2 \cdot 3$ $2 \cdot 3$ $3$ $C_1$ $S_3$ $C_3$ $C_{2}$ Solvable - 2
8.3 $D_4$ $2^{3}$ $2^{2}$ $5$ $C_2$ $C_2^2$ $C_2$ $C_{2}^{2}$ Nilpotent - 2
8.4 $Q_8$ $2^{3}$ $2^{2}$ $5$ $C_2$ $C_2^2$ $C_2$ $C_{2}^{2}$ Nilpotent - 2
8.5 $C_2^3$ $2^{3}$ $2$ $8$ $C_2^3$ $C_1$ $C_1$ $C_{2}^{3}$ Abelian - 3
12.4 $D_6$ $2^{2} \cdot 3$ $2 \cdot 3$ $6$ $C_2$ $S_3$ $C_3$ $C_{2}^{2}$ Solvable - 2
16.11 $C_2\times D_4$ $2^{4}$ $2^{2}$ $10$ $C_2^2$ $C_2^2$ $C_2$ $C_{2}^{3}$ Nilpotent - 2
16.12 $C_2\times Q_8$ $2^{4}$ $2^{2}$ $10$ $C_2^2$ $C_2^2$ $C_2$ $C_{2}^{3}$ Nilpotent - 2
16.14 $C_2^4$ $2^{4}$ $2$ $16$ $C_2^4$ $C_1$ $C_1$ $C_{2}^{4}$ Abelian - 4
18.4 $C_3:S_3$ $2 \cdot 3^{2}$ $2 \cdot 3$ $6$ $C_1$ $C_3:S_3$ $C_3^2$ $C_{2}$ Solvable - 2
24.12 $S_4$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ $5$ $C_1$ $S_4$ $A_4$ $C_{2}$ Solvable - 3
24.14 $C_2\times D_6$ $2^{3} \cdot 3$ $2 \cdot 3$ $12$ $C_2^2$ $S_3$ $C_3$ $C_{2}^{3}$ Solvable - 2
32.27 $C_2^2\wr C_2$ $2^{5}$ $2^{2}$ $14$ $C_2^2$ $C_2^3$ $C_2^2$ $C_{2}^{3}$ Nilpotent - 2
32.34 $C_4:D_4$ $2^{5}$ $2^{2}$ $14$ $C_2^2$ $C_2^3$ $C_2^2$ $C_{2}^{3}$ Nilpotent - 2
32.35 $C_4:Q_8$ $2^{5}$ $2^{2}$ $14$ $C_2^2$ $C_2^3$ $C_2^2$ $C_{2}^{3}$ Nilpotent - 2
32.43 $D_8:C_2$ $2^{5}$ $2^{3}$ $11$ $C_2$ $C_2\times D_4$ $C_4$ $C_{2}^{3}$ Nilpotent - 3
32.44 $Q_{16}:C_2$ $2^{5}$ $2^{3}$ $11$ $C_2$ $C_2\times D_4$ $C_4$ $C_{2}^{3}$ Nilpotent - 3
32.46 $C_2^2\times D_4$ $2^{5}$ $2^{2}$ $20$ $C_2^3$ $C_2^2$ $C_2$ $C_{2}^{4}$ Nilpotent - 2
32.47 $C_2^2\times Q_8$ $2^{5}$ $2^{2}$ $20$ $C_2^3$ $C_2^2$ $C_2$ $C_{2}^{4}$ Nilpotent - 2
32.49 $D_4:C_2^2$ $2^{5}$ $2^{2}$ $17$ $C_2$ $C_2^4$ $C_2$ $C_{2}^{4}$ Nilpotent - 2
32.50 $C_4.C_2^3$ $2^{5}$ $2^{2}$ $17$ $C_2$ $C_2^4$ $C_2$ $C_{2}^{4}$ Nilpotent - 2
32.51 $C_2^5$ $2^{5}$ $2$ $32$ $C_2^5$ $C_1$ $C_1$ $C_{2}^{5}$ Abelian - 5
36.10 $S_3^2$ $2^{2} \cdot 3^{2}$ $2 \cdot 3$ $9$ $C_1$ $S_3^2$ $C_3^2$ $C_{2}^{2}$ Solvable - 2
36.13 $C_6:S_3$ $2^{2} \cdot 3^{2}$ $2 \cdot 3$ $12$ $C_2$ $C_3:S_3$ $C_3^2$ $C_{2}^{2}$ Solvable - 2
48.38 $S_3\times D_4$ $2^{4} \cdot 3$ $2^{2} \cdot 3$ $15$ $C_2$ $C_2\times D_6$ $C_6$ $C_{2}^{3}$ Solvable - 2
48.40 $S_3\times Q_8$ $2^{4} \cdot 3$ $2^{2} \cdot 3$ $15$ $C_2$ $C_2\times D_6$ $C_6$ $C_{2}^{3}$ Solvable - 2
48.48 $C_2\times S_4$ $2^{4} \cdot 3$ $2^{2} \cdot 3$ $10$ $C_2$ $S_4$ $A_4$ $C_{2}^{2}$ Solvable - 3
48.51 $C_2^2\times D_6$ $2^{4} \cdot 3$ $2 \cdot 3$ $24$ $C_2^3$ $S_3$ $C_3$ $C_{2}^{4}$ Solvable - 2
54.14 $C_3^2:S_3$ $2 \cdot 3^{3}$ $2 \cdot 3$ $15$ $C_1$ $C_3^2:S_3$ $C_3^3$ $C_{2}$ Solvable - 2
64.134 $D_4:D_4$ $2^{6}$ $2^{3}$ $16$ $C_2$ $C_2^2\wr C_2$ $C_2\times C_4$ $C_{2}^{3}$ Nilpotent - 3
64.137 $D_4.D_4$ $2^{6}$ $2^{3}$ $16$ $C_2$ $C_2^2\wr C_2$ $C_2\times C_4$ $C_{2}^{3}$ Nilpotent - 3
64.138 $C_2\wr C_2^2$ $2^{6}$ $2^{2}$ $16$ $C_2$ $C_2^2\wr C_2$ $C_2^3$ $C_{2}^{3}$ Nilpotent - 3
64.177 $C_8:D_4$ $2^{6}$ $2^{3}$ $16$ $C_2^2$ $C_2\times D_4$ $C_2\times C_4$ $C_{2}^{3}$ Nilpotent - 3
64.178 $C_8.D_4$ $2^{6}$ $2^{3}$ $16$ $C_2^2$ $C_2\times D_4$ $C_2\times C_4$ $C_{2}^{3}$ Nilpotent - 3
64.182 $C_8:Q_8$ $2^{6}$ $2^{3}$ $16$ $C_2^2$ $C_2\times D_4$ $C_2\times C_4$ $C_{2}^{3}$ Nilpotent - 3
64.202 $C_2^3:D_4$ $2^{6}$ $2^{2}$ $28$ $C_2^3$ $C_2^3$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.211 $C_4^2:C_2^2$ $2^{6}$ $2^{2}$ $28$ $C_2^3$ $C_2^3$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.212 $C_4^2.C_2^2$ $2^{6}$ $2^{2}$ $28$ $C_2^3$ $C_2^3$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.215 $C_2^3:D_4$ $2^{6}$ $2^{2}$ $22$ $C_2^2$ $C_2^4$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.216 $C_4^2:C_2^2$ $2^{6}$ $2^{2}$ $22$ $C_2^2$ $C_2^4$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.217 $C_4^2.C_2^2$ $2^{6}$ $2^{2}$ $22$ $C_2^2$ $C_2^4$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.218 $C_2^2.C_2^4$ $2^{6}$ $2^{2}$ $22$ $C_2^2$ $C_2^4$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.224 $C_2^3:Q_8$ $2^{6}$ $2^{2}$ $22$ $C_2^2$ $C_2^4$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.225 $C_4^2.C_2^2$ $2^{6}$ $2^{2}$ $22$ $C_2^2$ $C_2^4$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.226 $D_4^2$ $2^{6}$ $2^{2}$ $25$ $C_2^2$ $C_2^4$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.230 $D_4\times Q_8$ $2^{6}$ $2^{2}$ $25$ $C_2^2$ $C_2^4$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.239 $Q_8^2$ $2^{6}$ $2^{2}$ $25$ $C_2^2$ $C_2^4$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.241 $C_4^2:C_2^2$ $2^{6}$ $2^{2}$ $19$ $C_2^2$ $C_2^4$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
64.242 $C_4^2:C_2^2$ $2^{6}$ $2^{2}$ $19$ $C_2^2$ $C_2^4$ $C_2^2$ $C_{2}^{4}$ Nilpotent - 2
Next   displayed columns for results