Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C13×C4⋊Q8 ⋊ C4 |
| Sylow | C13 ⋊ #1407 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=g,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^8,c^b=cf,d^b=defg,e^b=eg,d^c=dfg,e^d=eg,h^d=h^1256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13129965, D13⋊#1407, #16791236, … |
| maximal normal subgroup of | C2×#13129965, D13⋊#1407, #16791236, … |
| maximal quotient of | #16777742, #16777785, #16777852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19639);