Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C13×Q16 ⋊ C4 |
| Sylow | C13 ⋊ #1340 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=g,c^2=fg,e^2=g,f^2=g,b^a=bc,c^a=ce,f^a=fg,h^a=h^8,c^b=cf,d^b=defg,e^b=eg,f^b=fg,d^c=dg,h^d=h^1262 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13129808, D13⋊#1340, #16787618, … |
| maximal normal subgroup of | C2×#13129808, D13⋊#1340, #16787618, … |
| maximal quotient of | #16776967, #16776969, #16776975, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19482);