Finite Group DatabasebetaFinite Group Databasebeta| order | 4544 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #125×C71 ⋊ C2 |
| Sylow | C71 ⋊ #488 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2272 |
Polycyclic presentation:
2^6,71|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^70,g^b=g^70,g^c=g^70512 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4544, 906);