Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #32704 |
556 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 944 |
Polycyclic presentation:
2^8,59|a^2=efg,c^2=fg,d^2=ef,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=def,e^a=eh,f^a=fh,i^a=i^58,c^b=cg,d^b=de,e^b=eh,g^b=gh1316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 316473);