Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | D4×PSU(3,𝔽2) |
| Fitting | C32×D4 ⋊ Q8 |
| Sylow | C32 ⋊ D4×Q8 |
307 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 36 |
30 conjugacy classes — view the full character table.
| maximal subgroup of | #11779242, #11780315, D4×AΓL(1,𝔽9), … |
| maximal normal subgroup of | #11779242, #11780315, D4×AΓL(1,𝔽9), … |
| maximal quotient of | C22⋊C4×PSU(3,𝔽2), D4×#3777, C4⋊C4×PSU(3,𝔽2), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8426);