Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D13⋊#350 |
| Sylow | C13 ⋊ C2×#350 |
224 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
Polycyclic presentation:
2^7,13|a^2=e,d^2=g,e^2=f,f^2=g,b^a=bd,h^a=h^8,d^b=dg,e^b=eg,h^c=h^12,h^e=h^12116 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#350, #16789318, #16789368, … |
| maximal normal subgroup of | #261×#350, #16789318, #16789368, … |
| maximal quotient of | D13⋊#1315, #16786714, D13⋊#1323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20750);