Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C32 ⋊ #359 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=c,c^2=e,d^2=f,e^2=f,b^a=bcd,g^a=g^2h^2,h^a=g^2,c^b=ce,e^b=ef,g^b=gh^2,h^b=h^2,g^c=g^2h,h^c=gh,g^d=g^2,h^d=h^2,g^e=g^2,h^e=h^227 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10593167, #11796780, #11796809, … |
| maximal normal subgroup of | C2×#10593167, #11796780, #11796809, … |
| maximal quotient of | #11771580, #11771598, #11771897, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5049);