Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | SD16×#157 |
| Fitting | C32×SD16 ⋊ C4 |
| Sylow | C32 ⋊ C4×SD16 |
190 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
42 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×AGL(1,𝔽9), SD16⋊AGL(1,𝔽9), C2×SD16×#157, … |
| maximal normal subgroup of | SD16×AGL(1,𝔽9), SD16⋊AGL(1,𝔽9), C2×SD16×#157, … |
| maximal quotient of | #11777185, SD16×#622, #11777187, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5663);