Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C59×#2029 ⋊ C2 |
| Sylow | C59 ⋊ #32873 |
854 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 854 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 944 |
Polycyclic presentation:
2^8,59|b^2=g,c^2=g,b^a=be,c^a=cf,g^a=gh,i^a=i^58,c^b=cg,d^b=def,e^b=eh,f^b=fh,d^c=de,f^c=fh782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 318183);