Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #14714 |
2078 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=h,b^2=efh,c^2=f,d^2=g,b^a=be,c^a=cf,d^a=dg,i^a=i^23,i^b=i^30,i^h=i^52452 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1099209);