Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C25 |
| direct product | C3×#85297 |
| Fitting | C22×C3×C22⋊C4 ⋊ D3 |
1338 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 1338 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
114 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11923460, C3×#11714540, D3×#85297, … |
| maximal normal subgroup of | C3×#11714540, D3×#85297, #72252962 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 156593);