Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #13424 |
612 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 73 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|a^2=h,c^2=d,e^2=h,b^a=bd,c^a=ce,e^a=eh,f^a=fgh,i^a=i^58,c^b=cf,e^b=eg,e^c=eh,g^c=gh,f^e=fh959 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 89015);