Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C8 |
| direct product | C3×#68094 |
| Fitting | C32×#322 ⋊ C2 |
| Sylow | C32 ⋊ #1721 |
517 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 517 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
198 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#1721, C3×#10784431, C3×#10784428, … |
| maximal normal subgroup of | C3×D3×#1721, C3×#10784431, C3×#10784428 |
| maximal quotient of | #72252791 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 16918);