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^12428 conjugacy classes — view the full character table.
| maximal subgroup of | #15750375, #15750376, #15750378, … |
| maximal normal subgroup of | #15750375, #15750376, #15750378, … |
| maximal quotient of | #15749661, #15749789, #15750602, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2584);