Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C337 ⋊ C4 |
| Sylow | C337 ⋊ #519 |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5392 |
Polycyclic presentation:
2^6,337|a^2=f,b^2=e,c^2=e,b^a=be,d^a=de,g^a=g^148,c^b=ce,g^f=g^336874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1617);