Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C22⋊AΓL(1,𝔽8) |
| Fitting, socle | C25×C3 ⋊ ΓL(1,𝔽8) |
| derived, Hall | C22×AGL(1,𝔽8) ⋊ C32 |
| Sylow | C25 ⋊ C3×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C22⋊AΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C22×AGL(1,𝔽8) | C32 |
| Frattini | C1 | G |
| Fitting, socle | C25×C3 | ΓL(1,𝔽8) |
| LCS | G ▷ C22×AGL(1,𝔽8) | |
| UCS | C1 ◁ C3 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C22⋊AΓL(1,𝔽8), D3×C22⋊AΓL(1,𝔽8) |
| maximal normal subgroup of | C2×C3×C22⋊AΓL(1,𝔽8), D3×C22⋊AΓL(1,𝔽8) |
| maximal quotient of | C2×C3×C22⋊AΓL(1,𝔽8) |
Past the SmallGroups library coverage — no SmallGroups id.