Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×#82612 |
| Fitting | C2×C32×#120 ⋊ C2 |
| Sylow | C32 ⋊ #2846 |
7175 conjugacy classes of subgroups; only the 490 normal subgroups are shown.
This group has 7175 conjugacy classes of subgroups — too many to draw. Only its 490 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | #72252255 |
| maximal normal subgroup of | #72252255 |
| maximal quotient of | C3×#10943957, C3×#10943884 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 90167);