Finite Group DatabasebetaFinite Group Databasebeta| order | 4544 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | H(5,𝔽2)×C71 ⋊ C2 |
| Sylow | C71 ⋊ #453 |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 568 |
Polycyclic presentation:
2^6,71|d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^70,d^b=df,e^b=ef,d^c=df611 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4544, 717);