Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×#5417 |
| Fitting | C22×C3×Q8 ⋊ D3 |
166 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
57 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5417, #11922179, #11922193, … |
| maximal normal subgroup of | D3×#5417, #11922179, #11922193, … |
| maximal quotient of | C3×#73051, C3×#73053, C3×#73094, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5485);