Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#11719427 |
| Sylow | C13 ⋊ C2×Q82 |
1112 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 581 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
218 conjugacy classes — view the full character table.
| maximal subgroup of | #15754684, #15755035, #15755039, … |
| maximal normal subgroup of | #15754684, #15755035, #15755039, … |
| maximal quotient of | C2×#13117748, C2×#13117750, C2×#13117922, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 18085);