Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C32×C8 ⋊ C8 |
| Sylow | C32 ⋊ #334 |
65 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^6,3^2|a^2=c,b^2=d,c^2=e,d^2=f,b^a=bd,d^a=df,g^a=g^2h^2,h^a=g^2,g^c=g^2h,h^c=gh,g^e=g^2,h^e=h^236 conjugacy classes — view the full character table.
| maximal subgroup of | #11771613, #11771631, #11772055, … |
| maximal normal subgroup of | #11771613, #11771631, #11772055, … |
| maximal quotient of | #11770756, #11772170, #11772171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5134);