Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#471 ⋊ C2 |
| Sylow | C13 ⋊ #3290 |
454 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,c^b=cg,d^b=de,e^b=eg,h^b=h^12,f^c=fg,e^d=eg,h^d=h^12125 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3290, C2×#13126619, #16739155, … |
| maximal normal subgroup of | D13×#3290, C2×#13126619, #16739155, … |
| maximal quotient of | #15854183, #15854212, #15854223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 16293);