Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
| direct product | D3×(C2×S4)⋊C4 |
| Fitting | C23×C3×C4 ⋊ C2×D3 |
1456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 1456 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×GL(2,ℤ/4)⋊C4, D3×#85495, D3×#85297, … |
| maximal normal subgroup of | D3×GL(2,ℤ/4)⋊C4, D3×#85495, D3×#85297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156058);