Finite Group DatabasebetaFinite Group Databasebeta| order | 32732 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D7×D167 |
| unambiguous semidirect product | (D7×C167)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D167)⋊(C2×C7) |
| unambiguous semidirect product | D1169⋊(C2×C7) |
| Fitting, socle, Hall | C72×C167 ⋊ C22 |
| derived | C7×C167 ⋊ C22×C7 |
| Sylow | C167 ⋊ C2×C7×D7 |
| Sylow | C72 ⋊ C2×D167 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D7×D167 |
| commutator, cosocle, hypocenter | C7×C167 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C167 | C22 |
| LCS | G ▷ C7×C167 | |
| UCS | C1 ◁ C7 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2338 |
2975 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32732, 19);