Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | #99×AGL(1,𝔽9) |
| Fitting | C32×#99 ⋊ C8 |
| Sylow | C32 ⋊ C8×#99 |
719 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 719 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | #99×AΓL(1,𝔽9), B(4,𝔽2)×AGL(1,𝔽9), #72253263 |
| maximal normal subgroup of | #99×AΓL(1,𝔽9), B(4,𝔽2)×AGL(1,𝔽9), #72253263 |
Past the SmallGroups library coverage — no SmallGroups id.