Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×AΓL(1,𝔽8) |
| Fitting, socle, Sylow | C25 ⋊ C3×ΓL(1,𝔽8) |
| derived, Hall | C22×AGL(1,𝔽8) ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22×AGL(1,𝔽8) | C32 |
| Fitting, socle | C25 | C3×ΓL(1,𝔽8) |
| LCS | G ▷ C22×AGL(1,𝔽8) | |
| UCS | C1 | |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32 |
32 conjugacy classes — view the full character table.
| maximal subgroup of | C2×A4×AΓL(1,𝔽8), A4×AGL(3,𝔽2), S4×AΓL(1,𝔽8) |
| maximal normal subgroup of | C2×A4×AΓL(1,𝔽8), S4×AΓL(1,𝔽8) |
| maximal quotient of | C2×A4×AΓL(1,𝔽8) |
Past the SmallGroups library coverage — no SmallGroups id.