Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×D3×GU(2,𝔽3) |
| derived | C3×SL(2,𝔽3) ⋊ C22×C4 |
737 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 737 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#5429, D3×#85453, D3×#85544 |
| maximal normal subgroup of | C2×D3×#5429, D3×#85453, D3×#85544 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156285);