Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C2×C4×D4×C53 ⋊ C4 |
| Sylow | C53 ⋊ #34058 |
2858 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=h,b^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,i^a=i^30,c^b=cf,i^h=i^52608 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1114169);