Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | Q8×(C22⋊C9)⋊C2 |
274 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
45 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×(C22⋊C9)⋊C2, #11920360, Q16×(C22⋊C9)⋊C2, … |
| maximal normal subgroup of | SD16×(C22⋊C9)⋊C2, #11920360, Q16×(C22⋊C9)⋊C2, … |
| maximal quotient of | #11920201, #11920202, #11920203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4975);