Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C22×C4⋊Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ #60860 |
2006 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|b^2=f,c^2=f,g^2=h,b^a=bf,c^a=cg,d^a=df,e^a=eh,g^a=gh,i^a=i^52,c^b=cf,g^c=gh1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1041834);