Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C3 |
| direct product | C3⋊D3×#335 |
| Fitting | C32×#335 ⋊ C2 |
| Sylow | C32 ⋊ C2×#335 |
600 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#1372, C8×D8×C3⋊D3, C3⋊D3×#1331 |
| maximal normal subgroup of | C3⋊D3×#1372, C8×D8×C3⋊D3, C3⋊D3×#1331 |
| maximal quotient of | C3⋊D3×#1372 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 10784);