Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #1365 |
86 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=d,b^2=eg,c^2=fg,d^2=efg,f^2=g,b^a=bc,c^a=ce,h^a=h^8,c^b=cf,d^b=def,f^b=fg,h^d=h^1271 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13129855, D13⋊#1365, #16788498, … |
| maximal normal subgroup of | C2×#13129855, D13⋊#1365, #16788498, … |
| maximal quotient of | #16777050, #16777051, #16777528, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19529);