Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C13×#533 ⋊ C2 |
| Sylow | C13 ⋊ #3461 |
1012 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|b^2=f,c^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^b=h^12,h^d=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #15829501, #15829507, #15829602, … |
| maximal normal subgroup of | #15829501, #15829507, #15829602, … |
| maximal quotient of | #16021608, #16021620, #16021624, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17941);