Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C337 ⋊ #346 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5392 |
Polycyclic presentation:
2^6,337|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bf,g^a=g^85,g^b=g^189,g^c=g^148,g^d=g^336,g^e=g^336376 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1644);