Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | #578×C131 ⋊ C2 |
| Sylow | C131 ⋊ #3586 |
1412 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4192 |
Polycyclic presentation:
2^7,131|b^2=g,f^2=g,b^a=bf,e^a=eg,f^a=fg,f^b=fg,d^c=dg,h^c=h^130,h^d=h^130,h^e=h^1301471 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 19295);