Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| direct product | A4×GU(2,𝔽3) |
| unambiguous semidirect product | (C22×GU(2,𝔽3))⋊C3 |
| derived | C22×SL(2,𝔽3) ⋊ C3×C4 |
213 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | A4×GL(2,𝔽5), S4×GU(2,𝔽3) |
| maximal normal subgroup of | S4×GU(2,𝔽3) |
| maximal quotient of | SL(2,𝔽3)×GU(2,𝔽3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155464);