Finite Group DatabasebetaFinite Group Databasebeta| order | 34914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C23×AGL(1,𝔽23) |
| unambiguous semidirect product | D23⋊(C3×C11×C23) |
| unambiguous semidirect product | (C3×D23)⋊(C11×C23) |
| unambiguous semidirect product | (C23⋊C11)⋊(C2×C3×C23) |
| Fitting, socle, Hall | C3×C232 ⋊ C2×C11 |
| derived | C23 ⋊ C2×C3×C11×C23 |
| Hall | C3×C23×C23⋊C11 ⋊ C2 |
| Hall | C23×C23⋊C11 ⋊ C2×C3 |
| Hall | C3×C23×D23 ⋊ C11 |
| Hall | C23×D23 ⋊ C3×C11 |
| Sylow | C232 ⋊ C2×C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | AGL(1,𝔽23) |
| commutator, cosocle, hypocenter | C23 | C2×C3×C11×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C232 | C2×C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C3×C23 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1518 |
1587 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34914, 18);