Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#480 ⋊ C2 |
| Sylow | C13 ⋊ #3294 |
494 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,h^b=h^12,f^c=fg,h^c=h^12149 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3294, C2×#13126647, #16739409, … |
| maximal normal subgroup of | D13×#3294, C2×#13126647, #16739409, … |
| maximal quotient of | #15878323, #15879126, #15880053, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 16321);