Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C13×#497 ⋊ C2 |
| Sylow | C13 ⋊ #3154 |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|b^2=e,c^2=f,e^2=g,b^a=be,c^a=cf,e^a=eg,h^b=h^12,d^c=dg,h^c=h^12,h^d=h^12128 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3154, C2×#13125311, #16732427, … |
| maximal normal subgroup of | D13×#3154, C2×#13125311, #16732427, … |
| maximal quotient of | #15850757, #15850772, #15850805, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14985);