Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D3×#827 |
| Sylow | C32 ⋊ C2×SD32 |
193 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 193 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
54 conjugacy classes — view the full character table.
| maximal subgroup of | D32×SD32, C2×D3×#827, D3×#4912, … |
| maximal normal subgroup of | D32×SD32, C2×D3×#827, D3×#4912, … |
| maximal quotient of | D3×#4562, D3×#4492, D3×#4490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2909);