Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #1397 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bg,h^b=h^12464 conjugacy classes — view the full character table.
| maximal subgroup of | #15750725, D13×#1397, C2×#13112969, … |
| maximal normal subgroup of | #15750725, D13×#1397, C2×#13112969, … |
| maximal quotient of | #15750246, #15750251, #15750605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 2643);