Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×C22⋊C16 ⋊ C4 |
| Sylow | C53 ⋊ #12612 |
474 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,e^2=g,g^2=h,b^a=bd,c^a=ch,i^a=i^23,i^b=i^23,i^c=i^30,i^e=i^52,i^f=i^52632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1096010);