Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×D3×#217 |
| Sylow | C32 ⋊ C22×C22⋊C4 |
1414 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 1414 conjugacy classes of subgroups — too many to draw. Only its 352 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4527, D3×#4526, #11785689, … |
| maximal normal subgroup of | D3×#4527, D3×#4526, #11785689, … |
| maximal quotient of | C2×D3×C3⋊#95, C4×D3×#217, C2×#10591237, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7373);