Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C13 ⋊ #1401 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 77 |
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^8,c^b=cg,d^b=dg,h^d=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13129953, D13⋊#1401, #16791179, … |
| maximal normal subgroup of | C2×#13129953, D13⋊#1401, #16791179, … |
| maximal quotient of | #16777704, #16777764, D4⋊#88036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 19627);