Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #6104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#88048 |
| Sylow | C13 ⋊ C22×#106 |
600 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
296 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15768812, #15768814, #15768820, … |
| maximal normal subgroup of | #15768812, #15768814, #15768820, … |
| maximal quotient of | C22×#11718072, C2×#13113591, C2×#13113606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 13081);