Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#70928 |
| Sylow | C32 ⋊ #2180 |
336 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 336 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) = 96 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#10948643, C3×#10948634, #72222787, … |
| maximal normal subgroup of | C3×#10948643, C3×#10948634, #72222787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 31919);