Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | SD16×C3⋊Dic3 |
| Sylow | C32 ⋊ C4×SD16 |
366 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#622, SD16⋊#622, #11777432, … |
| maximal normal subgroup of | SD16×#622, SD16⋊#622, #11777432, … |
| maximal quotient of | SD16×C3⋊(C3⋊C8), #11777424, #11777473, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4742);