Finite Group DatabasebetaFinite Group Databasebeta| order | 32067 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C509 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×C509 |
| unambiguous semidirect product | C7⋊(C9×C509) |
| unambiguous semidirect product | (C7×C509)⋊C9 |
| derived, Sylow | C7 ⋊ C9×C509 |
| Hall | C7×C509 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C509 | ΓL(1,𝔽8) |
| commutator, hypocenter | C7 | C9×C509 |
| Frattini | C3 | ΓL(1,𝔽8)×C509 |
| Fitting, socle, prime radical | C3×C7×C509 | C3 |
| cosocle | C3×C7 | C3×C509 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C3×C509 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32067 |
7635 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32067, 2);