Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C3×#84110 |
| Fitting | C2×C32×H(5,𝔽2) ⋊ C2 |
| Sylow | C32 ⋊ #3026 |
2049 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 2049 conjugacy classes of subgroups — too many to draw. Only its 322 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | #72252325, C3×#10826736, #72252342, … |
| maximal normal subgroup of | #72252325, C3×#10826736, #72252342, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99348);