Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#63544 |
| Sylow | C32 ⋊ C2×M32 |
218 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11772302, #11772319, #11772339, … |
| maximal normal subgroup of | #11772302, #11772319, #11772339, … |
| maximal quotient of | C2×#10589104, C4×#63544, C2×#10589108, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2509);