Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C59 ⋊ #7244 |
192 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 192 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) = 7552 |
Polycyclic presentation:
2^8,59|a^2=d,b^2=e,c^2=fgh,d^2=g,e^2=fg,f^2=h,b^a=bc,c^a=cf,e^a=efg,f^a=fh,i^a=i^58,c^b=ch,d^b=dg1664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 56674);