Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D3×Q8×A4 |
| Fitting | C22×C3×Q8 ⋊ C2×C3 |
422 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#5416, D3×#5417, #11922193, … |
| maximal normal subgroup of | D3×#5416, D3×#5417, #11922193, … |
| maximal quotient of | A4×#887, A4×#896, A4×#888, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8498);