Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#336 ⋊ C4 |
| Sylow | C53 ⋊ #7025 |
622 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=f,e^2=h,b^a=bc,c^a=cf,e^a=efg,i^a=i^30,c^b=cg,i^d=i^52596 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1083500);