Finite Group DatabasebetaFinite Group Databasebeta| order | 9408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | #100×ΓL(1,𝔽8)⋊D7 |
| Fitting | C72×#100 ⋊ C2×C3 |
| Hall | #100×C7⋊D7 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ C2×#100 |
| Sylow | C72 ⋊ C2×C3×#100 |
930 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
242 conjugacy classes — view the full character table.
| maximal subgroup of | #453×ΓL(1,𝔽8)⋊D7, #100×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| maximal normal subgroup of | #453×ΓL(1,𝔽8)⋊D7, #100×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.