Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #417×C131 ⋊ C2 |
| Sylow | C131 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4192 |
Polycyclic presentation:
2^7,131|a^2=f,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^130,e^b=eg,h^b=h^130,h^c=h^1301474 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 13323);