Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#88118 |
| Fitting | C22×Q8×C13 ⋊ C4 |
| Sylow | C13 ⋊ C22×#104 |
856 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 856 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) = 416 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | #16785501, #16785503, #16785897, … |
| maximal normal subgroup of | #16785501, #16785503, #16785897, … |
| maximal quotient of | C22×#11718243, C22×Q8⋊#1057, C2×#13130130, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21135);