Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D32×SD32 |
| Fitting | C32×SD32 ⋊ C22 |
| Sylow | C32 ⋊ C22×SD32 |
845 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 845 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#509 |
| maximal normal subgroup of | D32×#509 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133469);