Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#69698 |
| Sylow | C32 ⋊ #1596 |
793 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 793 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10767815, #72252350, #72252352 |
| maximal normal subgroup of | C3×#10767815, #72252350, #72252352 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 12024);