Finite Group DatabasebetaFinite Group Databasebeta| order | 32305 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C7×C13×C71⋊C5 |
| unambiguous semidirect product | (C7×C71)⋊(C5×C13) |
| unambiguous semidirect product | (C7×C13×C71)⋊C5 |
| Fitting, socle, Hall | C7×C13×C71 ⋊ C5 |
| derived, Sylow | C71 ⋊ C5×C7×C13 |
| Hall | C13×C71 ⋊ C5×C7 |
| Hall | C7×C71 ⋊ C5×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C13 | C71⋊C5 |
| commutator, cosocle, hypocenter | C71 | C5×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C71 | C5 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C7×C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6461 |
1729 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32305, 3);