Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C13×#449 ⋊ C2 |
| Sylow | C13 ⋊ #3319 |
414 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=eg,b^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^12,c^b=cg,d^b=de,h^b=h^12,f^c=fg143 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3319, C2×#13126996, #16739679, … |
| maximal normal subgroup of | D13×#3319, C2×#13126996, #16739679, … |
| maximal quotient of | #15878478, #15879220, #15879996, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 16670);