Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ #10703 |
1142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=g,d^2=h,f^2=h,b^a=bd,d^a=dh,f^a=fh,c^b=ch,i^b=i^30,i^f=i^52608 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1091862);