Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C16×GO+(4,𝔽2) |
| Fitting | C32×C16 ⋊ D4 |
| Sylow | C32 ⋊ D4×C16 |
272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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 | C16×AΓL(1,𝔽9), C3×C16×GO+(4,𝔽2), C32×GO+(4,𝔽2), … |
| maximal normal subgroup of | C16×AΓL(1,𝔽9), C3×C16×GO+(4,𝔽2), C32×GO+(4,𝔽2), … |
| maximal quotient of | C3×C16×GO+(4,𝔽2), C32×GO+(4,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 31470);