Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C3 |
| direct product | C22×#64128 |
| Fitting | C22×C32×Q16 ⋊ C2 |
| Sylow | C32 ⋊ C22×#135 |
4512 conjugacy classes of subgroups; only the 881 normal subgroups are shown.
This group has 4512 conjugacy classes of subgroups — too many to draw. Only its 881 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152616);