Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C8×Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #8201 |
502 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=eg,d^2=g,e^2=h,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,i^b=i^30,i^f=i^52608 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1087234);