Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
| direct product | C2×#10589106 |
| Sylow | C32 ⋊ C2×#347 |
409 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 409 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | #72222740, #72227364, #72227370, … |
| maximal normal subgroup of | #72222740, #72227364, #72227370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 29938);