Finite Group DatabasebetaFinite Group Databasebeta| order | 34914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11×C23 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×C23×C23⋊C11 |
| unambiguous semidirect product | (C2×C23)⋊(C3×C11×C23) |
| unambiguous semidirect product | (C2×C3×C23)⋊(C11×C23) |
| Fitting, socle, Hall | C2×C3×C232 ⋊ C11 |
| derived | C23 ⋊ C2×C3×C11×C23 |
| Hall | C3×C232 ⋊ C2×C11 |
| Hall | C2×C232 ⋊ C3×C11 |
| Sylow | C232 ⋊ C2×C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C23 | C23⋊C11 |
| commutator, cosocle, hypocenter | C23 | C2×C3×C11×C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C232 | C11 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2×C3×C23 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1518 |
1794 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34914, 64);