Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C53 ⋊ C4 |
| Sylow | C53 ⋊ #8100 |
994 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=g,b^a=bd,d^a=dg,f^a=fh,i^a=i^30,d^b=dh,e^b=eg,i^e=i^52572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1086789);