Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C3×C4 |
No aliases for this group.
| Fitting | C32×#97 ⋊ C2 |
| Sylow | C32 ⋊ #433 |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|b^2=e,c^2=d,d^2=f,b^a=bf,c^a=ce,g^a=g^2,h^a=h^2,c^b=cf108 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#433, C2×#10592408, D3×#4709, … |
| maximal normal subgroup of | C3⋊D3×#433, C2×#10592408, D3×#4709, … |
| maximal quotient of | #11783511, #11783606, #11784222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4290);