Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | #385×C131 ⋊ C2 |
| Sylow | C131 ⋊ #2379 |
520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8384 |
Polycyclic presentation:
2^7,131|a^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cef,d^b=de,h^b=h^130,h^c=h^130,h^d=h^1301858 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 7683);