Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4×C8×C13 ⋊ C4 |
| Sylow | C13 ⋊ #1414 |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=f,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^5,c^b=cfg,d^b=defg,e^b=eg,h^b=h^12,d^c=dfg,e^d=eg,h^d=h^12113 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊#1414, C2×#13129984, #16791324, … |
| maximal normal subgroup of | D13⋊#1414, C2×#13129984, #16791324, … |
| maximal quotient of | #16777757, #16777770, #16777877, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19658);