Finite Group DatabasebetaFinite Group Databasebeta| order | 34430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D1565 |
| unambiguous semidirect product | C5⋊(C11×D313) |
| unambiguous semidirect product | C313⋊(D5×C11) |
| Fitting, socle, Hall | C5×C11×C313 ⋊ C2 |
| derived, Hall | C5×C313 ⋊ C2×C11 |
| Hall | C11×C313 ⋊ D5 |
| Sylow | C313 ⋊ D5×C11 |
| Hall | C5×C11 ⋊ D313 |
| Sylow | C5 ⋊ C11×D313 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D1565 |
| commutator, cosocle, hypocenter | C5×C313 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C313 | C2 |
| LCS | G ▷ C5×C313 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17215 |
8624 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34430, 7);