Finite Group DatabasebetaFinite Group Databasebeta| order | 33327 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C23 |
| direct product | ΓL(1,𝔽8)×C232⋊C3 |
| unambiguous semidirect product | (C7⋊(C232⋊C3))⋊C3 |
| unambiguous semidirect product | (ΓL(1,𝔽8)×C232)⋊C3 |
| unambiguous semidirect product | (C7×C232⋊C3)⋊C3 |
| Fitting, socle, derived, Hall | C7×C232 ⋊ C32 |
| Sylow | C232 ⋊ C3×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C3×C232⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C232 | C32 |
| LCS | G ▷ C7×C232 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 483 |
895 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33327, 10);