Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #9785 |
594 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3776 |
Polycyclic presentation:
2^8,59|a^2=f,b^2=dfg,c^2=e,d^2=gh,e^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=egh,i^a=i^58,c^b=cg,d^b=dh,f^b=fh,i^b=i^581316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 69100);