Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | #120×Dic13 |
| Sylow | C13 ⋊ C4×#120 |
1224 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 289 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
224 conjugacy classes — view the full character table.
| maximal subgroup of | Dic13×AΣL(1,𝔽16), #15778880, Dic13×B(4,𝔽2), … |
| maximal normal subgroup of | Dic13×AΣL(1,𝔽16), #15778880, Dic13×B(4,𝔽2), … |
| maximal quotient of | Dic13×#386, Dic13×#385, Dic13×#379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7013);