Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C53×C64 ⋊ C4 |
| Sylow | C53 ⋊ #7511 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,g^2=h,b^a=bg,d^a=dh,c^b=ch,i^b=i^30,i^d=i^52920 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1084790);