Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#2115 ⋊ C2 |
| Sylow | C59 ⋊ #12685 |
890 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 155 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3776 |
Polycyclic presentation:
2^8,59|a^2=f,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^58,d^b=dh,e^b=eh,f^b=fh,i^b=i^58,d^c=dh1340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 85022);