Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Fitting | C53×#390 ⋊ C4 |
| Sylow | C53 ⋊ #13832 |
1998 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=g,b^2=h,c^2=eg,b^a=be,c^a=cf,d^a=def,i^a=i^23,c^b=cef,d^b=de,i^b=i^23,i^c=i^30,i^g=i^52,i^h=i^52440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1098326);