Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C53 ⋊ #60327 |
1812 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=g,e^2=g,g^2=h,b^a=bf,d^a=df,i^a=i^23,c^b=cfh,d^b=dh,e^b=eh,e^c=eh,i^c=i^52,i^d=i^52,i^e=i^30,i^g=i^52323 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1116111);