Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×M16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #7904 |
838 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=g,d^2=g,e^2=h,f^2=gh,b^a=bd,c^a=ch,d^a=dg,f^a=fg,i^a=i^30,c^b=cgh,i^e=i^52596 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1085786);