Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#71458 |
| Fitting | C2×C32×D16 ⋊ C2 |
| Sylow | C32 ⋊ #2263 |
273 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10715810, #72222630, #72222634 |
| maximal normal subgroup of | C3×#10715810, #72222630, #72222634 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34599);