Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C22×#63694 |
2986 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 2986 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#11724027, C22×#63694⋊C3, C22×#11722396, … |
| maximal normal subgroup of | C22×#63694⋊C3, A4×#63694, #72269060 |
| maximal quotient of | #72245816, C22×#11722396 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 155428);