Finite Group DatabasebetaFinite Group Databasebeta| order | 32868 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D2739 |
| unambiguous semidirect product | (C2×C3)⋊D2739 |
| unambiguous semidirect product | (C2×C11)⋊(C3⋊D249) |
| unambiguous semidirect product | (C2×C83)⋊(C3⋊D33) |
| Fitting, socle | C2×C32×C11×C83 ⋊ C2 |
| derived, Hall | C32×C11×C83 ⋊ C22 |
| Hall | C11×C83 ⋊ C2×C3⋊D3 |
| Hall | C32×C83 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D83 |
| Sylow | C83 ⋊ C2×C3⋊D33 |
| Sylow | C11 ⋊ C2×C3⋊D249 |
| Sylow | C32 ⋊ C2×D913 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D2739 |
| commutator, cosocle, hypocenter | C32×C11×C83 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C11×C83 | C2 |
| LCS | G ▷ C32×C11×C83 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16434 |
8220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32868, 76);