Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#494 ⋊ C4 |
| Sylow | C53 ⋊ #7530 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=d,b^2=h,c^2=fg,e^2=gh,f^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^30,c^b=cfgh,d^b=def,e^b=egh,f^b=fh,d^c=dfg,e^d=egh,f^d=fh,i^d=i^52311 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1084838);