Finite Group DatabasebetaFinite Group Databasebeta| order | 34914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C23⋊C11)⋊D23) |
| unambiguous semidirect product | (C23⋊C11)⋊D69 |
| Fitting, socle, derived, Hall | C3×C232 ⋊ C2×C11 |
| Hall | C3×C23×C23⋊C11 ⋊ C2 |
| Hall | C23×C23⋊C11 ⋊ D3 |
| Hall | C3⋊(C23⋊D23) ⋊ C11 |
| Sylow | C232 ⋊ D3×C11 |
| Sylow | C3 ⋊ (C23⋊C11)⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C232 | C2×C11 |
| LCS | G ▷ C3×C232 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 759 |
A minimal faithful permutation representation — 2 generators on 49 points:
(2,3)(5,8,9,16,17,24,19,20,10,21,22,6,7,11,12,23,18,13,25,14,15,26)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49);(1,2,3)(4,5,7,10,9,13,15,23,12,18,20,26,22,25,24,16,17,21,19,11,14,8,6)(27,28,30,32,34,36,38,40,42,44,46,48,49,47,45,43,41,39,37,35,33,31,29)Polycyclic presentation:
2,11,3,23^2|c^a=c^2,d^a=d^22,e^a=e^22,d^b=d^2465 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34914, 40);