Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #1837 |
188 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=e,c^2=d,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^8,h^b=h^12,h^f=h^12140 conjugacy classes — view the full character table.
| maximal subgroup of | #16777360, #16777362, #16777371, … |
| maximal normal subgroup of | #16777360, #16777362, #16777371, … |
| maximal quotient of | #16782356, #16782358, #16782360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20435);