Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C32 ⋊ #365 |
53 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=cde,c^2=e,d^2=e,e^2=f,b^a=bce,d^a=df,g^a=g^2h^2,h^a=g^2h,c^b=ce,d^b=de,e^b=ef,g^b=gh^2,h^b=g^2h^2,g^c=g^2,h^c=h^224 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10590084, #11797111, #11797141, … |
| maximal normal subgroup of | C2×#10590084, #11797111, #11797141, … |
| maximal quotient of | #11772187, #11772432, C2×#10590084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 1966);