Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C4×Q8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #3461 |
1012 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8384 |
Polycyclic presentation:
2^7,131|b^2=f,c^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,h^a=h^130,c^b=cf2644 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 17943);