Finite Group DatabasebetaFinite Group Databasebeta| order | 32361 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C23×C67 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×C23×C67 |
| unambiguous semidirect product | C7⋊(C3×C23×C67) |
| unambiguous semidirect product | (C7×C23)⋊(C3×C67) |
| Fitting, socle, Hall | C7×C23×C67 ⋊ C3 |
| derived, Sylow | C7 ⋊ C3×C23×C67 |
| Hall | C7×C67 ⋊ C3×C23 |
| Hall | C7×C23 ⋊ C3×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C67 | ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C7 | C3×C23×C67 |
| Frattini | C1 | G |
| Fitting, socle | C7×C23×C67 | C3 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C23×C67 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10787 |
7705 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32361, 3);