Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C59 ⋊ #11844 |
432 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1888 |
Polycyclic presentation:
2^8,59|a^2=e,c^2=h,d^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fh,i^a=i^58,c^b=cfh,d^b=dg,e^b=efg,d^c=dh,e^d=eh1139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 80451);