Finite Group DatabasebetaFinite Group Databasebeta| order | 32046 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C7 |
| direct product | C2×C109⋊#3862 |
| unambiguous semidirect product | (C2×C109)⋊#3862 |
| Fitting, socle, Hall | C2×C72×C109 ⋊ C3 |
| derived, Hall | C72×C109 ⋊ C2×C3 |
| Hall | C2×C109 ⋊ #3862 |
| Sylow | C109 ⋊ C2×#3862 |
| Hall | C2×C72 ⋊ C109⋊C3 |
| Sylow | C72 ⋊ C2×C109⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C109⋊#3862 |
| commutator, cosocle, hypocenter | C72×C109 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C109 | C3 |
| LCS | G ▷ C72×C109 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4578 |
3566 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32046, 89);