Finite Group DatabasebetaFinite Group Databasebeta| order | 32046 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×ΓL(1,𝔽8)⋊D109 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C7×D109) |
| Fitting, socle, Hall | C72×C109 ⋊ C2×C3 |
| derived | C7×C109 ⋊ C2×C3×C7 |
| Hall | C7×ΓL(1,𝔽8)×C109 ⋊ C2 |
| Hall | C7×D763 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ D109 |
| Sylow | C109 ⋊ C7×AGL(1,𝔽7) |
| Sylow | C72 ⋊ C3×D109 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | ΓL(1,𝔽8)⋊D109 |
| commutator, cosocle, hypocenter | C7×C109 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C109 | C2×C3 |
| LCS | G ▷ C7×C109 | |
| UCS | C1 ◁ C7 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4578 |
1939 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32046, 37);