Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C53×#577 ⋊ C4 |
| Sylow | C53 ⋊ #60184 |
2604 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=g,c^2=g,f^2=h,g^2=h,b^a=bf,c^a=ch,f^a=fh,i^a=i^30,f^b=fh,i^c=i^30,e^d=eh,i^g=i^52368 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1115050);