Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #499 |
258 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=d,c^2=d,e^2=f,c^a=ce,g^a=g^2,h^a=h^2,c^b=cdf,e^c=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | #11772152, C3⋊D3×#499, C2×#10592764, … |
| maximal normal subgroup of | #11772152, C3⋊D3×#499, C2×#10592764, … |
| maximal quotient of | #11786245, #11790087, #11790121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4646);