Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C22×Q16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #22460 |
1286 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=g,c^2=h,e^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^30,d^b=de,e^b=eh,i^b=i^52,g^c=gh,e^d=eh,i^d=i^52,i^g=i^52416 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1109805);