Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C59×#2032 ⋊ C2 |
| Sylow | C59 ⋊ #32874 |
688 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1888 |
Polycyclic presentation:
2^8,59|b^2=g,c^2=g,d^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,d^b=def,e^b=eh,f^b=fh,d^c=de,f^c=fh,i^d=i^58695 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 318184);