Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C337 ⋊ #478 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10784 |
Polycyclic presentation:
2^6,337|a^2=d,b^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^336,g^b=g^336,e^c=ef2371 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 851);