Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D13⋊#360 |
| Fitting | C13×#135 ⋊ C4 |
| Sylow | C13 ⋊ C2×#360 |
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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=e,d^2=f,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^8,d^b=dfg,e^b=eg,f^b=fg,h^c=h^12,h^e=h^1274 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#360, #16789542, #16789869, … |
| maximal normal subgroup of | #261×#360, #16789542, #16789869, … |
| maximal quotient of | D13⋊#1333, D13⋊#1334, #16787328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20828);