Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#10593251 |
| Fitting | C2×C32×C8 ⋊ C8 |
| Sylow | C32 ⋊ C2×#322 |
286 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | #72244965, #97×AGL(1,𝔽9), #72252964 |
| maximal normal subgroup of | #72244965, #97×AGL(1,𝔽9), #72252964 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7532);