Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #1372 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=ceg,c^2=eg,d^2=f,e^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^8,h^d=h^12140 conjugacy classes — view the full character table.
| maximal subgroup of | #16777810, #16777811, #16777812, … |
| maximal normal subgroup of | #16777810, #16777811, #16777812, … |
| maximal quotient of | #16777010, #16777137, #16777980, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19543);