Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#14582115)⋊C4 |
| Fitting | C2×C4×C337 ⋊ C8 |
| Sylow | C337 ⋊ #336 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2696 |
Polycyclic presentation:
2^6,337|a^2=d,b^2=e,d^2=f,b^a=bc,g^a=g^85,g^d=g^148,g^f=g^336376 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1640);