Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C13 ⋊ #1845 |
280 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^7,13|a^2=f,b^2=dg,c^2=e,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^c=h^12212 conjugacy classes — view the full character table.
| maximal subgroup of | #15778958, #15778959, #15778963, … |
| maximal normal subgroup of | #15778958, #15778959, #15778963, … |
| maximal quotient of | #15756658, #15756673, #15756687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 4668);