Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#1844 ⋊ C2 |
| Sylow | C59 ⋊ #26081 |
690 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3776 |
Polycyclic presentation:
2^8,59|a^2=f,b^2=eh,c^2=f,d^2=e,e^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^58,c^b=cg,g^b=gh,i^b=i^58,g^c=gh,i^c=i^581322 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 228469);