Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | Q8×Q16×C59 ⋊ C2 |
| Sylow | C59 ⋊ #19844 |
590 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7552 |
Polycyclic presentation:
2^8,59|a^2=gh,b^2=h,c^2=h,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,d^b=de,e^b=eg,i^b=i^58,f^c=fh,e^d=eg1055 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 160246);