Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×GO+(4,𝔽2) |
| Fitting | C32×C8 ⋊ D4 |
| Sylow | C32 ⋊ C8×D4 |
210 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | GO+(4,𝔽2)⋊C16, C8×AΓL(1,𝔽9), #11777459, … |
| maximal normal subgroup of | GO+(4,𝔽2)⋊C16, C8×AΓL(1,𝔽9), #11777459, … |
| maximal quotient of | C8×#3774, #11777163, C8×#3775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5163);