Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D13⋊#333 |
| Sylow | C13 ⋊ C2×#333 |
256 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^7,13|a^2=e,b^2=g,d^2=g,e^2=fg,b^a=bd,d^a=df,h^a=h^8,d^b=dg,e^b=efg,h^c=h^12,h^e=h^1280 conjugacy classes — view the full character table.
| maximal subgroup of | #16778071, #261×#333, #16780717, … |
| maximal normal subgroup of | #16778071, #261×#333, #16780717, … |
| maximal quotient of | D13⋊#1272, #16778277, #16778278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20010);