Finite Group DatabasebetaFinite Group Databasebeta| order | 32074 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×D29⋊C7 |
| unambiguous semidirect product | D29⋊(C7×C79) |
| unambiguous semidirect product | (C29⋊C7)⋊(C2×C79) |
| unambiguous semidirect product | (D29×C79)⋊C7 |
| Fitting, socle, Hall | C29×C79 ⋊ C2×C7 |
| derived, Sylow | C29 ⋊ C2×C7×C79 |
| Hall | C79×C29⋊C7 ⋊ C2 |
| Hall | D29×C79 ⋊ C7 |
| Hall | C29⋊C7 ⋊ C2×C79 |
| Hall | D29 ⋊ C7×C79 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C79 | D29⋊C7 |
| commutator, cosocle, hypocenter | C29 | C2×C7×C79 |
| Frattini | C1 | G |
| Fitting, socle | C29×C79 | C2×C7 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C79 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2291 |
1264 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32074, 11);