Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C2×C8 |
| direct product | M32×AGL(1,𝔽9) |
| Fitting | C32×M32 ⋊ C8 |
| Sylow | C32 ⋊ C8×M32 |
399 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | #72252853, #72269065 |
| maximal normal subgroup of | #72252853 |
| maximal quotient of | #72269065 |
Past the SmallGroups library coverage — no SmallGroups id.