Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#88107 |
| Fitting | C23×C4×C13 ⋊ C4 |
| Sylow | C13 ⋊ C22×#99 |
1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 1112 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 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #16785414, #16785416, #16785438, … |
| maximal normal subgroup of | #16785414, #16785416, #16785438, … |
| maximal quotient of | C22×#11718287, C22×#11718285, C2×#13130073, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21104);