Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C4⋊C8×C61 ⋊ C2 |
| Sylow | C61 ⋊ #23678 |
1016 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7808 |
Polycyclic presentation:
2^8,61|a^2=f,b^2=h,d^2=e,g^2=h,b^a=be,c^a=cf,c^b=cg,g^b=gh,i^b=i^60,g^c=gh,i^c=i^602464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 198730);