Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #123×#261 |
| Fitting | C13×#123 ⋊ C4 |
| Sylow | C13 ⋊ C4×#123 |
688 conjugacy classes of subgroups.
| transitive degree | μt(G) = 208 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | #261×#352, #261×#458, C2×#123×#261, … |
| maximal normal subgroup of | #261×#352, #261×#458, C2×#123×#261, … |
| maximal quotient of | #261×#386, #261×#388, #261×#385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20975);