Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×D3×#214 |
| Sylow | C32 ⋊ C22×SD16 |
630 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 160 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#214, D3×#4758, D3×#4757, … |
| maximal normal subgroup of | C4×D3×#214, D3×#4758, D3×#4757, … |
| maximal quotient of | C2×D3×#832, C2×D3×#810, C2×D3×#808, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 6985);