Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211×C3 |
| direct product | C22×#64091 |
| Fitting | C22×C32×C22⋊C4 ⋊ C2 |
| Sylow | C32 ⋊ C22×#120 |
13632 conjugacy classes of subgroups; only the 1401 normal subgroups are shown.
This group has 13632 conjugacy classes of subgroups — too many to draw. Only its 1401 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C3⋊D3×#120, #72214934, #72215014, … |
| maximal normal subgroup of | C22×C3⋊D3×#120, #72214934, #72215014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134259);