Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#578 ⋊ C4 |
| Sylow | C53 ⋊ #22462 |
1320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=g,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,i^a=i^30,d^b=de,e^b=eh,f^c=fh,g^c=gh,i^c=i^52,e^d=eh,i^g=i^52344 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1109810);