Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | A4×#932 |
| unambiguous semidirect product | (C22×#932)⋊C3 |
| Fitting | C23×C3×D4 ⋊ C2×C3 |
854 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 87 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 | A4×#85489, #72258598, S4×#932, … |
| maximal normal subgroup of | #72258598, S4×#932, D3×A4×AGL(1,ℤ/8) |
| maximal quotient of | A4×#85489 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157368);