Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#63797 |
| Fitting | C22×C32×C8 ⋊ C22 |
| Sylow | C32 ⋊ C23×D8 |
4121 conjugacy classes of subgroups; only the 692 normal subgroups are shown.
This group has 4121 conjugacy classes of subgroups — too many to draw. Only its 692 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal quotient of | #72222810 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152552);