Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D3×#817 |
| Sylow | C32 ⋊ C2×#106 |
278 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4566, D3×#4518, D3×#4513, … |
| maximal normal subgroup of | D3×#4566, D3×#4518, D3×#4513, … |
| maximal quotient of | D3×#4457, #11776875, #11776986, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 2555);