Finite Group DatabasebetaFinite Group Databasebeta| order | 28224 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | AΓL(1,𝔽8)2 |
| Fitting, socle, Sylow | C26 ⋊ ΓL(1,𝔽8)2 |
| derived, Hall | AGL(1,𝔽8)2 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | AGL(1,𝔽8)2 | C32 |
| Fitting, socle | C26 | ΓL(1,𝔽8)2 |
| LCS | G ▷ AGL(1,𝔽8)2 | |
| UCS | C1 | |
287 conjugacy classes of subgroups; only the 18 normal subgroups are shown.
This group has 287 conjugacy classes of subgroups — too many to draw. Only its 18 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
64 conjugacy classes — view the full character table.
| holomorph of | AΓL(1,𝔽8) |
Past the SmallGroups library coverage — no SmallGroups id.