Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C32 ⋊ #368 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=c,c^2=f,d^2=ef,e^2=f,b^a=bd,g^a=g^2,h^a=h^2,d^b=de,e^b=ef78 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#368, C2×#10589359, D3×#4493, … |
| maximal normal subgroup of | C3⋊D3×#368, C2×#10589359, D3×#4493, … |
| maximal quotient of | #11772218, #11772231, #11772380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1241);