Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | D3×#806 |
| Fitting | C32×C22⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ C2×#99 |
446 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
63 conjugacy classes — view the full character table.
| maximal subgroup of | D32×#99, C2×D3×#806, D3×#4740, … |
| maximal normal subgroup of | D32×#99, C2×D3×#806, D3×#4740, … |
| maximal quotient of | D3×#4468, D3×#4469, #11773790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2285);