Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C13 ⋊ #1798 |
312 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 92 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,f^2=g,b^a=bd,c^a=ce,h^a=h^8,c^b=cg,h^f=h^12104 conjugacy classes — view the full character table.
| maximal subgroup of | #16777459, #16777465, #16781335, … |
| maximal normal subgroup of | #16777459, #16777465, #16781335, … |
| maximal quotient of | #16781737, #16781739, #16781741, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20368);