Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C3 |
| direct product | C22×#64095 |
| Fitting | C22×C32×C22⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ C22×#123 |
5904 conjugacy classes of subgroups; only the 1321 normal subgroups are shown.
This group has 5904 conjugacy classes of subgroups — too many to draw. Only its 1321 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134376);