Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C4×M16×C53 ⋊ C2 |
| Sylow | C53 ⋊ #60693 |
1998 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|c^2=g,d^2=f,e^2=h,g^2=h,b^a=bf,c^a=cg,g^a=gh,i^a=i^52,c^b=ch,d^c=dh2144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1039550);