Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23 |
| direct product | C3×#4527 |
| Sylow | C32 ⋊ #342 |
350 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#342, C2×C3×#4527, D3×#4527, … |
| maximal normal subgroup of | C3×D3×#342, C2×C3×#4527, D3×#4527, … |
| maximal quotient of | C3×#67674, C3×#67678, C3×#67617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1153);