Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24×C3 |
| direct product | C4×#64269 |
| Fitting | C24×C3×C4 ⋊ D3 |
1182 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#64269⋊C3, C4×C3⋊(A4⋊S4) |
| maximal normal subgroup of | C4×#64269⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157044);