Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#137×C53 ⋊ C4 |
| Sylow | C53 ⋊ #11033 |
1264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fh,i^a=i^30,c^b=cf,f^b=fh,g^b=gh,i^b=i^52,d^c=dh,f^c=fh,g^c=gh,i^g=i^52332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1092769);