Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#3227 ⋊ C2 |
| Sylow | C59 ⋊ #18621 |
1314 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3776 |
Polycyclic presentation:
2^8,59|a^2=g,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,d^b=dg,e^b=eg,f^b=fh,i^b=i^58,e^c=eh,f^c=fh,i^c=i^58974 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 146700);