Finite Group DatabasebetaFinite Group Databasebeta| order | 15616 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C61 ⋊ C4 |
| Sylow | C61 ⋊ #21811 |
1302 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3904 |
Polycyclic presentation:
2^8,61|a^2=g,b^2=eh,c^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^11,c^b=ceh,f^c=fh,i^g=i^60472 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15616, 1107389);