Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×Dic9 |
| Sylow | C9 ⋊ C4×Q16 |
165 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 165 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | #11797648, SD32×Dic9, #11797693, … |
| maximal normal subgroup of | #11797648, SD32×Dic9, #11797693, … |
| maximal quotient of | Q16×C9⋊C8, #11777521, #11777840, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 743);