Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#11719078 |
| Sylow | C13 ⋊ C2×#446 |
400 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 186 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | #16780448, #16797452, C4×#11719078, … |
| maximal normal subgroup of | #16780448, #16797452, C4×#11719078, … |
| maximal quotient of | C2×#13130635, C2×#13130636, C2×#13130631, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21297);