Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C8 |
| direct product | C3×#71279 |
| Fitting | C32×#493 ⋊ C2 |
| Sylow | C32 ⋊ #1721 |
565 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 565 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#1721, C3×#10784427, C3×#10784426, … |
| maximal normal subgroup of | C3×D3×#1721, C3×#10784427, C3×#10784426 |
| maximal quotient of | #72252793 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 16915);