Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C22⋊C4×C3⋊S4 |
| Fitting | C22×C3×C22⋊C4 ⋊ D3 |
1578 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1578 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | #120×C3⋊S4, C22⋊C4×A4⋊S4 |
| maximal normal subgroup of | #120×C3⋊S4 |
| maximal quotient of | C22⋊C4×A4⋊S4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156856);