Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C59×#1783 ⋊ C2 |
| Sylow | C59 ⋊ #23906 |
2502 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 211 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|f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^58,c^b=cg,f^b=fh,e^c=eh,f^c=fh,i^c=i^58,f^d=fh974 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 201204);