Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#63941 |
| Fitting | C22×C32×Q8 ⋊ C22 |
| Sylow | C32 ⋊ C22×AGL(1,ℤ/8) |
3885 conjugacy classes of subgroups; only the 652 normal subgroups are shown.
This group has 3885 conjugacy classes of subgroups — too many to draw. Only its 652 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152686);