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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

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Results (1-50 of 873 matches)

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Label	Name	Order	Exponent	Nilp. class	Der. length	Comp. length	Rank	$\card{\mathrm{conj}(G)}$	Subgroups	Subgroup classes	Normal subgroups	Center	Central quotient	Commutator	Abelianization	$\card{\mathrm{Aut}(G)}$	$\card{\mathrm{Out}(G)}$	Tr. deg	Perm. deg	$\C$-irrep deg	$\R$-irrep deg	$\Q$-irrep deg	$\C$-rep deg	$\R$-rep deg	$\Q$-rep deg	Type - length
2.1	$C_2$	$2$	$2$	$1$	$1$	$1$	$1$	$2$	$2$	$2$	$2$	$C_2$	$C_1$	$C_1$	$C_{2}$	$1$	$1$	$2$	$2$	$1$	$1$	$1$	$1$	$1$	$1$	Cyclic
3.1	$C_3$	$3$	$3$	$1$	$1$	$1$	$1$	$3$	$2$	$2$	$2$	$C_3$	$C_1$	$C_1$	$C_{3}$	$2$	$2$	$3$	$3$	$1$	$2$	$2$	$1$	$2$	$2$	Cyclic
5.1	$C_5$	$5$	$5$	$1$	$1$	$1$	$1$	$5$	$2$	$2$	$2$	$C_5$	$C_1$	$C_1$	$C_{5}$	$2^{2}$	$2^{2}$	$5$	$5$	$1$	$2$	$4$	$1$	$2$	$4$	Cyclic
7.1	$C_7$	$7$	$7$	$1$	$1$	$1$	$1$	$7$	$2$	$2$	$2$	$C_7$	$C_1$	$C_1$	$C_{7}$	$2 \cdot 3$	$2 \cdot 3$	$7$	$7$	$1$	$2$	$6$	$1$	$2$	$6$	Cyclic
11.1	$C_{11}$	$11$	$11$	$1$	$1$	$1$	$1$	$11$	$2$	$2$	$2$	$C_{11}$	$C_1$	$C_1$	$C_{11}$	$2 \cdot 5$	$2 \cdot 5$	$11$	$11$	$1$	$2$	$10$	$1$	$2$	$10$	Cyclic
13.1	$C_{13}$	$13$	$13$	$1$	$1$	$1$	$1$	$13$	$2$	$2$	$2$	$C_{13}$	$C_1$	$C_1$	$C_{13}$	$2^{2} \cdot 3$	$2^{2} \cdot 3$	$13$	$13$	$1$	$2$	$12$	$1$	$2$	$12$	Cyclic
17.1	$C_{17}$	$17$	$17$	$1$	$1$	$1$	$1$	$17$	$2$	$2$	$2$	$C_{17}$	$C_1$	$C_1$	$C_{17}$	$2^{4}$	$2^{4}$	$17$	$17$	$1$	$2$	$16$	$1$	$2$	$16$	Cyclic
19.1	$C_{19}$	$19$	$19$	$1$	$1$	$1$	$1$	$19$	$2$	$2$	$2$	$C_{19}$	$C_1$	$C_1$	$C_{19}$	$2 \cdot 3^{2}$	$2 \cdot 3^{2}$	$19$	$19$	$1$	$2$	$18$	$1$	$2$	$18$	Cyclic
23.1	$C_{23}$	$23$	$23$	$1$	$1$	$1$	$1$	$23$	$2$	$2$	$2$	$C_{23}$	$C_1$	$C_1$	$C_{23}$	$2 \cdot 11$	$2 \cdot 11$	$23$	$23$	$1$	$2$	$22$	$1$	$2$	$22$	Cyclic
29.1	$C_{29}$	$29$	$29$	$1$	$1$	$1$	$1$	$29$	$2$	$2$	$2$	$C_{29}$	$C_1$	$C_1$	$C_{29}$	$2^{2} \cdot 7$	$2^{2} \cdot 7$	$29$	$29$	$1$	$2$	$28$	$1$	$2$	$28$	Cyclic
31.1	$C_{31}$	$31$	$31$	$1$	$1$	$1$	$1$	$31$	$2$	$2$	$2$	$C_{31}$	$C_1$	$C_1$	$C_{31}$	$2 \cdot 3 \cdot 5$	$2 \cdot 3 \cdot 5$	$31$	$31$	$1$	$2$	$30$	$1$	$2$	$30$	Cyclic
37.1	$C_{37}$	$37$	$37$	$1$	$1$	$1$	$1$	$37$	$2$	$2$	$2$	$C_{37}$	$C_1$	$C_1$	$C_{37}$	$2^{2} \cdot 3^{2}$	$2^{2} \cdot 3^{2}$	$37$	$37$	$1$	$2$	$36$	$1$	$2$	$36$	Cyclic
41.1	$C_{41}$	$41$	$41$	$1$	$1$	$1$	$1$	$41$	$2$	$2$	$2$	$C_{41}$	$C_1$	$C_1$	$C_{41}$	$2^{3} \cdot 5$	$2^{3} \cdot 5$	$41$	$41$	$1$	$2$	$40$	$1$	$2$	$40$	Cyclic
43.1	$C_{43}$	$43$	$43$	$1$	$1$	$1$	$1$	$43$	$2$	$2$	$2$	$C_{43}$	$C_1$	$C_1$	$C_{43}$	$2 \cdot 3 \cdot 7$	$2 \cdot 3 \cdot 7$	$43$	$43$	$1$	$2$	$42$	$1$	$2$	$42$	Cyclic
47.1	$C_{47}$	$47$	$47$	$1$	$1$	$1$	$1$	$47$	$2$	$2$	$2$	$C_{47}$	$C_1$	$C_1$	$C_{47}$	$2 \cdot 23$	$2 \cdot 23$	$47$	$47$	$1$	$2$	$46$	$1$	$2$	$46$	Cyclic
53.1	$C_{53}$	$53$	$53$	$1$	$1$	$1$	$1$	$53$	$2$	$2$	$2$	$C_{53}$	$C_1$	$C_1$	$C_{53}$	$2^{2} \cdot 13$	$2^{2} \cdot 13$	$53$	$53$	$1$	$2$	$52$	$1$	$2$	$52$	Cyclic
59.1	$C_{59}$	$59$	$59$	$1$	$1$	$1$	$1$	$59$	$2$	$2$	$2$	$C_{59}$	$C_1$	$C_1$	$C_{59}$	$2 \cdot 29$	$2 \cdot 29$	$59$	$59$	$1$	$2$	$58$	$1$	$2$	$58$	Cyclic
60.5	$A_5$	$2^{2} \cdot 3 \cdot 5$	$2 \cdot 3 \cdot 5$	$-1$	$0$	$1$	$2$	$5$	$59$	$9$	$2$	$C_1$	$A_5$	$A_5$	$C_1$	$2^{3} \cdot 3 \cdot 5$	$2$	$5$	$5$	$3$	$3$	$4$	$3$	$3$	$4$	Simple
61.1	$C_{61}$	$61$	$61$	$1$	$1$	$1$	$1$	$61$	$2$	$2$	$2$	$C_{61}$	$C_1$	$C_1$	$C_{61}$	$2^{2} \cdot 3 \cdot 5$	$2^{2} \cdot 3 \cdot 5$	$61$	$61$	$1$	$2$	$60$	$1$	$2$	$60$	Cyclic
67.1	$C_{67}$	$67$	$67$	$1$	$1$	$1$	$1$	$67$	$2$	$2$	$2$	$C_{67}$	$C_1$	$C_1$	$C_{67}$	$2 \cdot 3 \cdot 11$	$2 \cdot 3 \cdot 11$	$67$	$67$	$1$	$2$	$66$	$1$	$2$	$66$	Cyclic
71.1	$C_{71}$	$71$	$71$	$1$	$1$	$1$	$1$	$71$	$2$	$2$	$2$	$C_{71}$	$C_1$	$C_1$	$C_{71}$	$2 \cdot 5 \cdot 7$	$2 \cdot 5 \cdot 7$	$71$	$71$	$1$	$2$	$70$	$1$	$2$	$70$	Cyclic
73.1	$C_{73}$	$73$	$73$	$1$	$1$	$1$	$1$	$73$	$2$	$2$	$2$	$C_{73}$	$C_1$	$C_1$	$C_{73}$	$2^{3} \cdot 3^{2}$	$2^{3} \cdot 3^{2}$	$73$	$73$	$1$	$2$	$72$	$1$	$2$	$72$	Cyclic
79.1	$C_{79}$	$79$	$79$	$1$	$1$	$1$	$1$	$79$	$2$	$2$	$2$	$C_{79}$	$C_1$	$C_1$	$C_{79}$	$2 \cdot 3 \cdot 13$	$2 \cdot 3 \cdot 13$	$79$	$79$	$1$	$2$	$78$	$1$	$2$	$78$	Cyclic
83.1	$C_{83}$	$83$	$83$	$1$	$1$	$1$	$1$	$83$	$2$	$2$	$2$	$C_{83}$	$C_1$	$C_1$	$C_{83}$	$2 \cdot 41$	$2 \cdot 41$	$83$	$83$	$1$	$2$	$82$	$1$	$2$	$82$	Cyclic
89.1	$C_{89}$	$89$	$89$	$1$	$1$	$1$	$1$	$89$	$2$	$2$	$2$	$C_{89}$	$C_1$	$C_1$	$C_{89}$	$2^{3} \cdot 11$	$2^{3} \cdot 11$	$89$	$89$	$1$	$2$	$88$	$1$	$2$	$88$	Cyclic
97.1	$C_{97}$	$97$	$97$	$1$	$1$	$1$	$1$	$97$	$2$	$2$	$2$	$C_{97}$	$C_1$	$C_1$	$C_{97}$	$2^{5} \cdot 3$	$2^{5} \cdot 3$	$97$	$97$	$1$	$2$	$96$	$1$	$2$	$96$	Cyclic
101.1	$C_{101}$	$101$	$101$	$1$	$1$	$1$	$1$	$101$	$2$	$2$	$2$	$C_{101}$	$C_1$	$C_1$	$C_{101}$	$2^{2} \cdot 5^{2}$	$2^{2} \cdot 5^{2}$	$101$	$101$	$1$	$2$	$100$	$1$	$2$	$100$	Cyclic
103.1	$C_{103}$	$103$	$103$	$1$	$1$	$1$	$1$	$103$	$2$	$2$	$2$	$C_{103}$	$C_1$	$C_1$	$C_{103}$	$2 \cdot 3 \cdot 17$	$2 \cdot 3 \cdot 17$	$103$	$103$	$1$	$2$	$102$	$1$	$2$	$102$	Cyclic
107.1	$C_{107}$	$107$	$107$	$1$	$1$	$1$	$1$	$107$	$2$	$2$	$2$	$C_{107}$	$C_1$	$C_1$	$C_{107}$	$2 \cdot 53$	$2 \cdot 53$	$107$	$107$	$1$	$2$	$106$	$1$	$2$	$106$	Cyclic
109.1	$C_{109}$	$109$	$109$	$1$	$1$	$1$	$1$	$109$	$2$	$2$	$2$	$C_{109}$	$C_1$	$C_1$	$C_{109}$	$2^{2} \cdot 3^{3}$	$2^{2} \cdot 3^{3}$	$109$	$109$	$1$	$2$	$108$	$1$	$2$	$108$	Cyclic
113.1	$C_{113}$	$113$	$113$	$1$	$1$	$1$	$1$	$113$	$2$	$2$	$2$	$C_{113}$	$C_1$	$C_1$	$C_{113}$	$2^{4} \cdot 7$	$2^{4} \cdot 7$	$113$	$113$	$1$	$2$	$112$	$1$	$2$	$112$	Cyclic
127.1	$C_{127}$	$127$	$127$	$1$	$1$	$1$	$1$	$127$	$2$	$2$	$2$	$C_{127}$	$C_1$	$C_1$	$C_{127}$	$2 \cdot 3^{2} \cdot 7$	$2 \cdot 3^{2} \cdot 7$	$127$	$127$	$1$	$2$	$126$	$1$	$2$	$126$	Cyclic
131.1	$C_{131}$	$131$	$131$	$1$	$1$	$1$	$1$	$131$	$2$	$2$	$2$	$C_{131}$	$C_1$	$C_1$	$C_{131}$	$2 \cdot 5 \cdot 13$	$2 \cdot 5 \cdot 13$	$131$	$131$	$1$	$2$	$130$	$1$	$2$	$130$	Cyclic
137.1	$C_{137}$	$137$	$137$	$1$	$1$	$1$	$1$	$137$	$2$	$2$	$2$	$C_{137}$	$C_1$	$C_1$	$C_{137}$	$2^{3} \cdot 17$	$2^{3} \cdot 17$	$137$	$137$	$1$	$2$	$136$	$1$	$2$	$136$	Cyclic
139.1	$C_{139}$	$139$	$139$	$1$	$1$	$1$	$1$	$139$	$2$	$2$	$2$	$C_{139}$	$C_1$	$C_1$	$C_{139}$	$2 \cdot 3 \cdot 23$	$2 \cdot 3 \cdot 23$	$139$	$139$	$1$	$2$	$138$	$1$	$2$	$138$	Cyclic
149.1	$C_{149}$	$149$	$149$	$1$	$1$	$1$	$1$	$149$	$2$	$2$	$2$	$C_{149}$	$C_1$	$C_1$	$C_{149}$	$2^{2} \cdot 37$	$2^{2} \cdot 37$	$149$	$149$	$1$	$2$	$148$	$1$	$2$	$148$	Cyclic
151.1	$C_{151}$	$151$	$151$	$1$	$1$	$1$	$1$	$151$	$2$	$2$	$2$	$C_{151}$	$C_1$	$C_1$	$C_{151}$	$2 \cdot 3 \cdot 5^{2}$	$2 \cdot 3 \cdot 5^{2}$	$151$	$151$	$1$	$2$	$150$	$1$	$2$	$150$	Cyclic
157.1	$C_{157}$	$157$	$157$	$1$	$1$	$1$	$1$	$157$	$2$	$2$	$2$	$C_{157}$	$C_1$	$C_1$	$C_{157}$	$2^{2} \cdot 3 \cdot 13$	$2^{2} \cdot 3 \cdot 13$	$157$	$157$	$1$	$2$	$156$	$1$	$2$	$156$	Cyclic
163.1	$C_{163}$	$163$	$163$	$1$	$1$	$1$	$1$	$163$	$2$	$2$	$2$	$C_{163}$	$C_1$	$C_1$	$C_{163}$	$2 \cdot 3^{4}$	$2 \cdot 3^{4}$	$163$	$163$	$1$	$2$	$162$	$1$	$2$	$162$	Cyclic
167.1	$C_{167}$	$167$	$167$	$1$	$1$	$1$	$1$	$167$	$2$	$2$	$2$	$C_{167}$	$C_1$	$C_1$	$C_{167}$	$2 \cdot 83$	$2 \cdot 83$	$167$	$167$	$1$	$2$	$166$	$1$	$2$	$166$	Cyclic
168.42	$\GL(3,2)$	$2^{3} \cdot 3 \cdot 7$	$2^{2} \cdot 3 \cdot 7$	$-1$	$0$	$1$	$2$	$6$	$179$	$15$	$2$	$C_1$	$\GL(3,2)$	$\GL(3,2)$	$C_1$	$2^{4} \cdot 3 \cdot 7$	$2$	$7$	$7$	$3$	$6$	$6$	$3$	$6$	$6$	Simple
173.1	$C_{173}$	$173$	$173$	$1$	$1$	$1$	$1$	$173$	$2$	$2$	$2$	$C_{173}$	$C_1$	$C_1$	$C_{173}$	$2^{2} \cdot 43$	$2^{2} \cdot 43$	$173$	$173$	$1$	$2$	$172$	$1$	$2$	$172$	Cyclic
179.1	$C_{179}$	$179$	$179$	$1$	$1$	$1$	$1$	$179$	$2$	$2$	$2$	$C_{179}$	$C_1$	$C_1$	$C_{179}$	$2 \cdot 89$	$2 \cdot 89$	$179$	$179$	$1$	$2$	$178$	$1$	$2$	$178$	Cyclic
181.1	$C_{181}$	$181$	$181$	$1$	$1$	$1$	$1$	$181$	$2$	$2$	$2$	$C_{181}$	$C_1$	$C_1$	$C_{181}$	$2^{2} \cdot 3^{2} \cdot 5$	$2^{2} \cdot 3^{2} \cdot 5$	$181$	$181$	$1$	$2$	$180$	$1$	$2$	$180$	Cyclic
191.1	$C_{191}$	$191$	$191$	$1$	$1$	$1$	$1$	$191$	$2$	$2$	$2$	$C_{191}$	$C_1$	$C_1$	$C_{191}$	$2 \cdot 5 \cdot 19$	$2 \cdot 5 \cdot 19$	$191$	$191$	$1$	$2$	$190$	$1$	$2$	$190$	Cyclic
193.1	$C_{193}$	$193$	$193$	$1$	$1$	$1$	$1$	$193$	$2$	$2$	$2$	$C_{193}$	$C_1$	$C_1$	$C_{193}$	$2^{6} \cdot 3$	$2^{6} \cdot 3$	$193$	$193$	$1$	$2$	$192$	$1$	$2$	$192$	Cyclic
197.1	$C_{197}$	$197$	$197$	$1$	$1$	$1$	$1$	$197$	$2$	$2$	$2$	$C_{197}$	$C_1$	$C_1$	$C_{197}$	$2^{2} \cdot 7^{2}$	$2^{2} \cdot 7^{2}$	$197$	$197$	$1$	$2$	$196$	$1$	$2$	$196$	Cyclic
199.1	$C_{199}$	$199$	$199$	$1$	$1$	$1$	$1$	$199$	$2$	$2$	$2$	$C_{199}$	$C_1$	$C_1$	$C_{199}$	$2 \cdot 3^{2} \cdot 11$	$2 \cdot 3^{2} \cdot 11$	$199$	$199$	$1$	$2$	$198$	$1$	$2$	$198$	Cyclic
211.1	$C_{211}$	$211$	$211$	$1$	$1$	$1$	$1$	$211$	$2$	$2$	$2$	$C_{211}$	$C_1$	$C_1$	$C_{211}$	$2 \cdot 3 \cdot 5 \cdot 7$	$2 \cdot 3 \cdot 5 \cdot 7$	$211$	$211$	$1$	$2$	$210$	$1$	$2$	$210$	Cyclic
223.1	$C_{223}$	$223$	$223$	$1$	$1$	$1$	$1$	$223$	$2$	$2$	$2$	$C_{223}$	$C_1$	$C_1$	$C_{223}$	$2 \cdot 3 \cdot 37$	$2 \cdot 3 \cdot 37$	$223$	$223$	$1$	$2$	$222$	$1$	$2$	$222$	Cyclic

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

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