Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#85544 |
| Fitting | C3×#585 ⋊ D3 |
630 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11715001, C3×#11923520, C3×#11714723, … |
| maximal normal subgroup of | C3×#11715001, C3×#11714723, D3×#85544, … |
| maximal quotient of | #72245649 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156839);