Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C27×C4 |
| unambiguous semidirect product | (C2×#6157)⋊#95 |
| Fitting | C2×#95×C53 ⋊ C4 |
| Sylow | C53 ⋊ #7554 |
3158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=h,b^a=bd,c^a=ce,i^b=i^30,i^g=i^52632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1084874);