Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#63930 |
| Sylow | C32 ⋊ C22×SD16 |
714 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | #11787459, #11787461, #11791991, … |
| maximal normal subgroup of | #11787459, #11787461, #11791991, … |
| maximal quotient of | C2×#10591416, C2×#10590601, C2×#10590575, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6989);