Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D13⋊#430 |
| Sylow | C13 ⋊ C2×#430 |
460 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=e,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^8,c^b=cg,h^d=h^12,h^f=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #16785818, #16785822, #16785831, … |
| maximal normal subgroup of | #16785818, #16785822, #16785831, … |
| maximal quotient of | D13⋊#1565, #16794914, #16794916, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21170);