Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C13×#447 ⋊ C2 |
| Sylow | C13 ⋊ #3012 |
764 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|d^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,e^b=eg,d^c=dg,h^d=h^12146 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#3012, C2×#13124135, #16729381, … |
| maximal normal subgroup of | D13×#3012, C2×#13124135, #16729381, … |
| maximal quotient of | #15836118, #15836154, #15836206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13809);