Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×#10592568 |
| Fitting | C2×C32×#106 ⋊ C2 |
| Sylow | C32 ⋊ C2×#442 |
1824 conjugacy classes of subgroups; only the 393 normal subgroups are shown.
This group has 1824 conjugacy classes of subgroups — too many to draw. Only its 393 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3⋊D3×#442, #72222685, C2×#11797950, … |
| maximal normal subgroup of | C2×C3⋊D3×#442, #72222685, C2×#11797950, … |
| maximal quotient of | C2×#11797950, D3×#10592568, C2×#11777337 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 94157);