Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×C3⋊D3×Q32 |
| Fitting | C2×C32×Q32 ⋊ C2 |
| Sylow | C32 ⋊ C22×Q32 |
1080 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 225 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133482);