Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #60619 |
2206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|b^2=g,c^2=f,f^2=h,g^2=h,b^a=bf,c^a=cg,f^a=fh,g^a=gh,e^b=eh,i^b=i^52,d^c=dh,i^c=i^521202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1038884);