Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C2×C4×D4×C53 ⋊ C4 |
| Sylow | C53 ⋊ #13813 |
2882 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=g,b^2=h,c^2=g,d^2=g,b^a=be,c^a=cf,d^b=de,i^b=i^30,i^h=i^52620 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1098290);