Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#525 ⋊ C2 |
| Sylow | C13 ⋊ #3197 |
418 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,f^c=fg,h^c=h^12194 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3197, C2×#13125673, #16733555, … |
| maximal normal subgroup of | D13×#3197, C2×#13125673, #16733555, … |
| maximal quotient of | #15871980, #15871986, #15873204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15347);