Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#10592892 |
| Fitting | C2×C32×#135 ⋊ C2 |
| Sylow | C32 ⋊ C2×#509 |
1200 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 1200 conjugacy classes of subgroups — too many to draw. Only its 297 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊D3×#509, C2×#11797944, C2×#11797953, … |
| maximal normal subgroup of | C2×C3⋊D3×#509, C2×#11797944, C2×#11797953, … |
| maximal quotient of | C2×#11797804 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133550);