Finite Group DatabasebetaFinite Group Databasebeta| order | 23622 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C127 ⋊ C2×C3 |
| Hall | #26044672 ⋊ C2 |
| Hall | D3937 ⋊ C3 |
| Sylow | C127 ⋊ D31⋊C3 |
| Sylow | C31 ⋊ D127⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C127 | C2×C3 |
| LCS | G ▷ C31×C127 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 158 |
| transitive degree | μt(G) = 3937 |
A minimal faithful permutation representation — 2 generators on 158 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,64)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,69,70,49,50,93)(34,67,68,52,48,61)(37,42,66,54,55,62)(40,82,80,58,59,57)(51,98,74,72,73,100)(53,96,97,75,71,90)(56,65,95,77,78,91)(60,108,109,83,84,86)(63,113,106,87,88,81)(76,121,105,102,99,119)(79,94,101,103,104,120)(85,125,124,110,111,117)(89,127,126,114,115,112)(92,122,123,116,118,107)(129,133,134,130,131,135)(132,141,142,136,137,149)(138,151,152,144,145,157)(139,150,146,147,143,140)(148,158,155,154,153,156);(1,2,5,11,19,32,51,74,101,122,127,125,121,98,102,75,52,33,20,4,8,13,23,37,56,79,105,70,95,113,108,96,69,94,110,83,58,36,10,16,24,38,57,81,107,124,97,47,66,82,67,46,65,92,114,87,55,18,29,39,41,61,86,112,126,109,68,28,43,44,27,42,63,89,116,78,31,48,59,62,64,90,117,123,106,80,45,15,26,14,25,40,60,85,104,50,71,84,88,91,93,119,103,77,54,35,22,7,6,12,21,34,53,76,73,99,111,115,118,120,100,72,49,30,17,9,3)(128,129,132,138,146,134,133,139,148,155,142,150,141,145,153,152,157,158,151,137,143,149,156,154,147,131,135,140,144,136,130)Polycyclic presentation:
2,3,31,127|c^a=c^30,d^a=d^126,c^b=c^25,d^b=d^19662 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23622, 24);