Finite Group DatabasebetaFinite Group Databasebeta| order | 34916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×#31775459 |
| Fitting, socle | C2×C29×C43 ⋊ C2×C7 |
| derived, Hall | C29×C43 ⋊ C22×C7 |
| Hall | #22576608 ⋊ C22 |
| Hall | C2×D1247 ⋊ C7 |
| Sylow | C43 ⋊ C2×D29⋊C7 |
| Sylow | C29 ⋊ C2×D43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #31775459 |
| commutator, cosocle, hypocenter | C29×C43 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C29×C43 | C2×C7 |
| LCS | G ▷ C29×C43 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2494 |
206 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34916, 72);