Finite Group DatabasebetaFinite Group Databasebeta| order | 32410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×D463⋊C7 |
| unambiguous semidirect product | D463⋊(C5×C7) |
| unambiguous semidirect product | (C463⋊C7)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D463)⋊C7 |
| Fitting, socle, Hall | C5×C463 ⋊ C2×C7 |
| derived, Sylow | C463 ⋊ C2×C5×C7 |
| Hall | C5×C463⋊C7 ⋊ C2 |
| Hall | C5×D463 ⋊ C7 |
| Hall | C463⋊C7 ⋊ C2×C5 |
| Hall | D463 ⋊ C5×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D463⋊C7 |
| commutator, cosocle, hypocenter | C463 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C5×C463 | C2×C7 |
| LCS | G ▷ C463 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2315 |
235 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32410, 10);