Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C13 ⋊ #1784 |
564 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 94 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=f,b^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^8,f^b=fg,h^f=h^12128 conjugacy classes — view the full character table.
| maximal subgroup of | #16777630, #16777647, #16777650, … |
| maximal normal subgroup of | #16777630, #16777647, #16777650, … |
| maximal quotient of | #16781024, #16781026, #16781038, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20344);