Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C337 ⋊ C4 |
| Sylow | C337 ⋊ #347 |
46 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=be,d^a=df,c^b=cf,g^b=g^189,g^d=g^3361366 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1440);