Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#71089 |
| Fitting | C32×#469 ⋊ C2 |
| Sylow | C32 ⋊ #2190 |
517 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 517 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10950415, #72219792, #72219793 |
| maximal normal subgroup of | C3×#10950415, #72219792, #72219793 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 32276);