Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C32 ⋊ #364 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=c,c^2=e,d^2=f,e^2=f,b^a=bd,g^a=g^2,h^a=h^2,d^b=df108 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#364, C2×#10589377, D3×#4511, … |
| maximal normal subgroup of | C3⋊D3×#364, C2×#10589377, D3×#4511, … |
| maximal quotient of | #11772161, #11772204, #11772290, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1259);