Finite Group DatabasebetaFinite Group Databasebeta| order | 4544 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C71 ⋊ #478 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2272 |
Polycyclic presentation:
2^6,71|a^2=d,b^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^70,g^b=g^70,e^c=ef509 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4544, 851);