Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #21606 |
834 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6784 |
Polycyclic presentation:
2^8,53|a^2=g,b^2=e,d^2=eg,g^2=h,b^a=be,c^a=cf,i^a=i^23,c^b=ch,d^b=dh,d^c=dh,i^c=i^52,i^d=i^30,i^g=i^52362 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1106859);