Finite Group DatabasebetaFinite Group Databasebeta| order | 15104 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q8×C16×C59 ⋊ C2 |
| Sylow | C59 ⋊ #12050 |
224 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 91 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=e,b^2=f,c^2=e,d^2=f,e^2=g,g^2=h,b^a=bd,c^a=ch,d^a=df,i^a=i^58,d^b=df2396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15104, 81348);