Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C23 |
| direct product | C4×C22⋊(Q8⋊C9) |
| derived | C22×Q8 ⋊ C4×C9 |
| Sylow | C22×C4×Q8 ⋊ C9 |
627 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 627 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153824);