Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| direct product | A4×#812 |
| unambiguous semidirect product | (C22×#812)⋊C3 |
242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | A4×#73104 |
| maximal quotient of | A4×#73104 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155327);