Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #1801 |
272 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 80 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=f,b^2=d,c^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^8,f^c=fg,h^f=h^12128 conjugacy classes — view the full character table.
| maximal subgroup of | #16777418, #16777419, #16777666, … |
| maximal normal subgroup of | #16777418, #16777419, #16777666, … |
| maximal quotient of | #16781725, #16781726, #16781733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20376);