Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #1416 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=g,c^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^12,c^b=ce,e^b=ef,f^b=fg170 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1416, C2×#13113017, #15783352, … |
| maximal normal subgroup of | D13×#1416, C2×#13113017, #15783352, … |
| maximal quotient of | #15750372, #15750477, #15750555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2691);