Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#478 ⋊ C4 |
| Sylow | C53 ⋊ #21619 |
868 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=g,b^2=e,d^2=eg,f^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^23,d^b=dh,f^c=fh,i^d=i^30,i^g=i^52311 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1106874);