Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C32 ⋊ #365 |
99 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=d,b^2=c,c^2=e,e^2=f,b^a=bc,c^a=ce,e^a=ef,h^a=h^2,d^b=df,g^b=g^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4487, D3×#4513, C2×#10589136, … |
| maximal normal subgroup of | D3×#4487, D3×#4513, C2×#10589136, … |
| maximal quotient of | #11772183, #11772428, C2×#10589136, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1018);