Finite Group DatabasebetaFinite Group Databasebeta| order | 33282 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×(C43⋊C3)⋊D43 |
| unambiguous semidirect product | (C43⋊C3)⋊(C3×D43) |
| Fitting, socle | C3×C432 ⋊ C2×C3 |
| derived, Sylow | C432 ⋊ C2×C32 |
| Hall | C3×C43×C43⋊C3 ⋊ C2 |
| Hall | C43⋊D43 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C43⋊C3)⋊D43 |
| commutator, cosocle, hypocenter | C432 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C432 | C2×C3 |
| LCS | G ▷ C432 | |
| UCS | C1 ◁ C3 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 387 |
1110 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33282, 41);