Finite Group DatabasebetaFinite Group Databasebeta| order | 28224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | ΓL(1,𝔽8)2×#453 |
| Fitting, Hall | C72×#453 ⋊ C32 |
| Sylow | C72 ⋊ C32×#453 |
2352 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #453×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| maximal normal subgroup of | #453×ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
Past the SmallGroups library coverage — no SmallGroups id.