Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #1367 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=c,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^8,h^d=h^12152 conjugacy classes — view the full character table.
| maximal subgroup of | #16776951, #16776952, #16776953, … |
| maximal normal subgroup of | #16776951, #16776952, #16776953, … |
| maximal quotient of | #16777005, #16777006, #16777127, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19532);