Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | D16×C3⋊Dic3 |
| Sylow | C32 ⋊ C4×D16 |
522 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 167 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C3⋊D3×D16, #72269625, #72269638 |
| maximal normal subgroup of | C4×C3⋊D3×D16, #72269625, #72269638 |
| maximal quotient of | #72269638 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 31638);