Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#11718825 |
| Sylow | C13 ⋊ C2×#440 |
544 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 237 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11718825, Dic13×#440, #15861438, … |
| maximal normal subgroup of | C4×#11718825, Dic13×#440, #15861438, … |
| maximal quotient of | C2×SD16⋊#1055, C2×#13113694, C2×#13113715, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13290);