Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C3 |
| direct product | Q16×C3⋊(C3⋊C8) |
| Sylow | C32 ⋊ C8×Q16 |
492 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1152 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 11235);