Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D3×Dic24 |
| Sylow | C32 ⋊ C2×Q32 |
176 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 176 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) = 192 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4520, D3×#4449, D3×#4522, … |
| maximal normal subgroup of | D3×#4520, D3×#4449, D3×#4522, … |
| maximal quotient of | D3×#4503, D3×#4504, #11797717, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2119);