Finite Group DatabasebetaFinite Group Databasebeta| order | 32410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D463⋊C7) |
| unambiguous semidirect product | (C463⋊C7)⋊D5 |
| unambiguous semidirect product | D2315⋊C7 |
| Fitting, socle, derived, Hall | C5×C463 ⋊ C2×C7 |
| Hall | C5×C463⋊C7 ⋊ C2 |
| Hall | D2315 ⋊ C7 |
| Hall | C463⋊C7 ⋊ D5 |
| Sylow | C463 ⋊ C7×D5 |
| Sylow | C5 ⋊ D463⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C463 | C2×C7 |
| LCS | G ▷ C5×C463 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2315 |
Polycyclic presentation:
2,5,7,463|b^a=b^4,d^a=d^462,d^c=d^412193 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32410, 12);