Finite Group DatabasebetaFinite Group Databasebeta| order | 34914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×C3⋊AGL(1,𝔽23) |
| unambiguous semidirect product | C3⋊(C23×AGL(1,𝔽23)) |
| unambiguous semidirect product | D69⋊(C11×C23) |
| unambiguous semidirect product | (C23⋊C11)⋊(D3×C23) |
| Fitting, socle, Hall | C3×C232 ⋊ C2×C11 |
| derived | C3×C23 ⋊ C2×C11×C23 |
| Hall | C3×C23×C23⋊C11 ⋊ C2 |
| Hall | C23×C23⋊C11 ⋊ D3 |
| Hall | C23×D69 ⋊ C11 |
| Sylow | C232 ⋊ D3×C11 |
| Sylow | C3 ⋊ C23×AGL(1,𝔽23) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊AGL(1,𝔽23) |
| commutator, cosocle, hypocenter | C3×C23 | C2×C11×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C232 | C2×C11 |
| LCS | G ▷ C3×C23 | |
| UCS | C1 ◁ C23 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1518 |
828 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34914, 39);