Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #1413 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=f,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^12,c^b=cf,d^b=def,e^b=eg,d^c=dfg,e^d=eg110 conjugacy classes — view the full character table.
| maximal subgroup of | #15750765, #15750766, #15750768, … |
| maximal normal subgroup of | #15750765, #15750766, #15750768, … |
| maximal quotient of | #15750310, #15750328, #15750459, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2683);