Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C3⋊D3×#365 |
| Fitting | C32×#365 ⋊ C2 |
| Sylow | C32 ⋊ C2×#365 |
456 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 127 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 | C3⋊D3×AGL(1,ℤ/16), C2×C3⋊D3×#365, D32×#365, … |
| maximal normal subgroup of | C3⋊D3×AGL(1,ℤ/16), C2×C3⋊D3×#365, D32×#365, … |
| maximal quotient of | C3⋊D3×#1368, C2×C3⋊D3×#365 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 31097);