Finite Group DatabasebetaFinite Group Databasebeta| order | 34914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×#26042794 |
| Fitting, socle, Hall | C3×C232 ⋊ C2×C11 |
| derived, Sylow | C232 ⋊ C2×C3×C11 |
| Hall | C3×#19154121 ⋊ C2 |
| Hall | #19154121 ⋊ C2×C3 |
| Hall | C3×C23×D23 ⋊ C11 |
| Hall | C23×D23 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #26042794 |
| commutator, cosocle, hypocenter | C232 | C2×C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C3×C232 | C2×C11 |
| LCS | G ▷ C232 | |
| UCS | C1 ◁ C3 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1518 |
147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34914, 23);