Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #88101 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22×#88104 |
| Sylow | C13 ⋊ C22×#108 |
480 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | #16785705, #16785708, #16785721, … |
| maximal normal subgroup of | #16785705, #16785708, #16785721, … |
| maximal quotient of | C22×#11718255, C22×#11718254, C2×#13130386, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21168);