Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C13×#135 ⋊ C2 |
| Sylow | C13 ⋊ #3584 |
1424 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|e^2=g,f^2=g,b^a=bf,f^a=fg,f^b=fg,d^c=dg,h^d=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #15778623, #15778625, #15778628, … |
| maximal normal subgroup of | #15778623, #15778625, #15778628, … |
| maximal quotient of | #16726480, #16726594, #16727033, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19279);