Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
| direct product | C2×#63694 |
488 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | #11920004, #11920193, #63694⋊C4, … |
| maximal normal subgroup of | #11920004, #11920193, #63694⋊C4, … |
| maximal quotient of | C2×((C22⋊C9)⋊C4)⋊C4, #11920379, C2×(C2×(C22⋊C9)⋊C2)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4986);