Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D13×#500 |
| Fitting | C13×#500 ⋊ C2 |
| Sylow | C13 ⋊ C2×#500 |
424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | D13×#1364, D13×#1365, #15774208, … |
| maximal normal subgroup of | D13×#1364, D13×#1365, #15774208, … |
| maximal quotient of | D13×#1845, D13×#1942, D13×#1990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 15015);