Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | Q8×C4⋊C4×C61 ⋊ C2 |
| Sylow | C61 ⋊ #22671 |
1018 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=h,c^2=f,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^60,d^b=de,e^b=eh,e^d=eh,i^d=i^601558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 187858);