Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C3×C4×D3×Q8 |
| Fitting | C32×C4×Q8 ⋊ C2 |
| Sylow | C32 ⋊ C2×C4×Q8 |
631 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×Q8⋊C8, D3×#4535, C3×#68231, … |
| maximal normal subgroup of | C3×D3×Q8⋊C8, D3×#4535, C3×#68231, … |
| maximal quotient of | C3×C4×D3×C4⋊C4, C3×C4×#887, C3×C4×Q8×Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7550);