Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×(C2×S4)⋊C4 |
| Fitting | C24×C3×C4 ⋊ D3 |
1476 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 1476 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C4×GL(2,ℤ/4) |
| maximal normal subgroup of | C2×C3×C4×GL(2,ℤ/4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156778);