Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C3 |
| direct product | C22×C22⋊PSU(3,𝔽2) |
| Fitting | C24×C32 ⋊ Q8 |
| Sylow | C32 ⋊ C22×C22⋊Q8 |
2214 conjugacy classes of subgroups; only the 543 normal subgroups are shown.
This group has 2214 conjugacy classes of subgroups — too many to draw. Only its 543 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134362);