Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C2×C8×GO+(4,𝔽2) |
| Fitting | C2×C32×C8 ⋊ D4 |
| Sylow | C32 ⋊ C2×C8×D4 |
954 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 207 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 | C2×C8×AΓL(1,𝔽9), #97×GO+(4,𝔽2), #72252964, … |
| maximal normal subgroup of | C2×C8×AΓL(1,𝔽9), #97×GO+(4,𝔽2), #72252964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 93198);