Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C59×#2080 ⋊ C2 |
| Sylow | C59 ⋊ #32702 |
480 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1888 |
Polycyclic presentation:
2^8,59|a^2=efg,c^2=e,d^2=ef,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=def,e^a=eh,f^a=fh,c^b=cg,d^b=de,e^b=eh,g^b=gh,i^d=i^58794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 316450);