Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C59×#2841 ⋊ C2 |
| Sylow | C59 ⋊ #12125 |
440 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 63 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|b^2=f,c^2=h,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=gh,i^a=i^58,c^b=ch,d^b=df,e^b=egh,d^c=dg,e^d=eh779 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 81795);