Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C42×GO+(4,𝔽2) |
| Fitting | C32×C42 ⋊ D4 |
| Sylow | C32 ⋊ C42×D4 |
1422 conjugacy classes of subgroups; only the 303 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 303 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C42×AΓL(1,𝔽9), #127×GO+(4,𝔽2), #72220536, … |
| maximal normal subgroup of | C42×AΓL(1,𝔽9), #127×GO+(4,𝔽2), #72220536, … |
| maximal quotient of | #97×GO+(4,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34841);