Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C59×#1422 ⋊ C2 |
| Sylow | C59 ⋊ #13648 |
184 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3776 |
Polycyclic presentation:
2^8,59|a^2=e,c^2=e,d^2=h,e^2=f,f^2=g,g^2=h,b^a=bd,c^a=ch,d^a=dh,d^b=dh,i^b=i^58,i^c=i^581712 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 90136);