Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C59 ⋊ #8756 |
546 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 107 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=f,c^2=d,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^58,f^b=fg,e^c=eg,f^c=fh1310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 63101);