Finite Group DatabasebetaFinite Group Databasebeta| order | 9408 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24×C7 |
| direct product | #99×#64425 |
| Fitting | C72×#99 ⋊ C2×C3 |
| Hall | #99×C7⋊D7 ⋊ C3 |
| Hall | #3862 ⋊ C2×#99 |
| Sylow | C72 ⋊ C2×C3×#99 |
1050 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | B(4,𝔽2)×#64425, #99×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| maximal normal subgroup of | B(4,𝔽2)×#64425, #99×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.