Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #8232 |
516 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 15104 |
Polycyclic presentation:
2^8,59|a^2=e,b^2=f,c^2=eg,d^2=g,f^2=gh,b^a=bd,d^a=dg,f^a=fgh,c^b=cg,d^b=dh,i^b=i^581676 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 60525);