Finite Group DatabasebetaFinite Group Databasebeta| order | 34730 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D3473 |
| unambiguous semidirect product | C23⋊(C5×D151) |
| Fitting, socle, Hall | C5×C23×C151 ⋊ C2 |
| derived, Hall | C23×C151 ⋊ C2×C5 |
| Hall | C5×C151 ⋊ D23 |
| Sylow | C151 ⋊ C5×D23 |
| Hall | C5×C23 ⋊ D151 |
| Sylow | C23 ⋊ C5×D151 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D3473 |
| commutator, cosocle, hypocenter | C23×C151 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C23×C151 | C2 |
| LCS | G ▷ C23×C151 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17365 |
8690 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34730, 5);