Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ D4×M16 |
544 conjugacy classes of subgroups.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^a=h^5,h^b=h^12,d^c=dg,h^c=h^8,h^d=h^12,h^f=h^12110 conjugacy classes — view the full character table.
| maximal subgroup of | #16782640, #16782642, #16782648, … |
| maximal normal subgroup of | #16782640, #16782642, #16782648, … |
| maximal quotient of | #16796320, #16796326, #16796334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21251);