Finite Group DatabasebetaFinite Group Databasebeta| order | 9408 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽8)×AΓL(1,𝔽8) |
| Fitting, socle, Sylow | C26 ⋊ C7×ΓL(1,𝔽8) |
| derived | C23×AGL(1,𝔽8) ⋊ C3×C7 |
| Hall | AGL(1,𝔽8)2 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C23×AGL(1,𝔽8) | C3×C7 |
| Fitting, socle | C26 | C7×ΓL(1,𝔽8) |
| LCS | G ▷ C23×AGL(1,𝔽8) | |
| UCS | C1 | |
116 conjugacy classes of subgroups; only the 12 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 12 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.
| maximal subgroup of | AΓL(1,𝔽8)2 |
| maximal normal subgroup of | AΓL(1,𝔽8)2 |
Past the SmallGroups library coverage — no SmallGroups id.