Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C37 |
| unambiguous semidirect product | C3⋊#22551388 |
| Fitting, socle, derived | C3×C372 ⋊ C2×C3 |
| Hall | C3×#16861552 ⋊ C2 |
| Sylow | C372 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C372 | C2×C3 |
| LCS | G ▷ C3×C372 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 333 |
A minimal faithful permutation representation — 2 generators on 77 points:
(2,3)(5,9,10,6,7,11)(8,17,18,12,13,26)(14,29,30,20,21,37)(15,28,24,22,19,16)(23,39,40,32,31,35)(25,27,38,34,33,36)(42,46,47,43,44,48)(45,54,55,49,50,64)(51,67,59,57,58,69)(52,66,62,60,56,53)(61,77,74,71,68,75)(63,65,70,72,73,76);(1,2,3)(4,5,8,14,21,31,36,37,34,24,10,9,15,23,33,13,19,26,35,40,18,28,17,27,32,22,7,11,16,25,30,38,39,29,20,12,6)(41,42,45,51,59,70,77,67,71,60,44,48,53,63,74,55,66,54,65,73,50,56,64,75,72,62,47,46,52,61,58,68,76,69,57,49,43)Polycyclic presentation:
2,3^2,37^2|c^a=c^2,d^a=d^36,e^a=e^36,d^b=d^26,e^b=e^10693 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 86);