Finite Group DatabasebetaFinite Group Databasebeta| order | 36567 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C17 · Schur multiplier (H2) = C3 |
| direct product | C32×C239⋊C17 |
| unambiguous semidirect product | C239⋊(C32×C17) |
| unambiguous semidirect product | (C3×C239)⋊(C3×C17) |
| unambiguous semidirect product | (C32×C239)⋊C17 |
| Fitting, socle, Hall | C32×C239 ⋊ C17 |
| derived, Sylow | C239 ⋊ C32×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C239⋊C17 |
| commutator, cosocle, hypocenter | C239 | C32×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C239 | C17 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C32 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2151 |
279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36567, 4);