Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C13 ⋊ #2989 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=f,d^2=e,f^2=g,b^a=be,c^a=cg,d^a=de,h^a=h^8,c^b=ce,h^b=h^12,h^f=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #16793384, #16793387, #16793390, … |
| maximal normal subgroup of | #16793384, #16793387, #16793390, … |
| maximal quotient of | #16797592, #16797604, #16797605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21432);