Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C337 ⋊ C2 |
| Sylow | C337 ⋊ #578 |
248 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10784 |
Polycyclic presentation:
2^6,337|a^2=f,b^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^336,e^b=ef,g^b=g^336,d^c=df3382 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1366);