Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C59×#1810 ⋊ C2 |
| Sylow | C59 ⋊ #13395 |
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 89 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|c^2=dg,e^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fh,g^a=gh,i^a=i^58,c^b=cf,d^c=dh,e^c=egh,g^c=gh1316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 88828);