Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C8 |
| direct product | C3×#71276 |
| Fitting | C32×#493 ⋊ C2 |
| Sylow | C32 ⋊ #1712 |
641 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 641 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#1712, C3×#10784427, C3×#10784430, … |
| maximal normal subgroup of | C3×D3×#1712, C3×#10784427, C3×#10784430, … |
| maximal quotient of | #72245269 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 16597);