Finite Group DatabasebetaFinite Group Databasebeta| order | 34914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C2×C3×C529⋊C11 |
| unambiguous semidirect product | (C2×C529)⋊(C3×C11) |
| unambiguous semidirect product | (C2×C3×C529)⋊C11 |
| Fitting, Hall | C2×C3×C529 ⋊ C11 |
| derived, Sylow | C529 ⋊ C2×C3×C11 |
| Hall | C3×C529 ⋊ C2×C11 |
| Hall | C2×C529 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C529⋊C11 |
| commutator, cosocle, hypocenter | C529 | C2×C3×C11 |
| Frattini | C23 | C2×C3×C23⋊C11 |
| Fitting | C2×C3×C529 | C11 |
| socle | C2×C3×C23 | C23⋊C11 |
| LCS | G ▷ C529 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3174 |
354 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34914, 5);