Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | C3×#5713 |
| Sylow | C32 ⋊ #559 |
526 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#71284, C3×#68402, #11778928, … |
| maximal normal subgroup of | C3×#71284, C3×#68402, #11778928, … |
| maximal quotient of | C3×#74325, C3×#76303, C3×#83173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7692);