Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#88116 |
| Fitting | C4×D4×C13 ⋊ C4 |
| Sylow | C13 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 98 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 | C8×#88116, #16780527, #16780531, … |
| maximal normal subgroup of | C8×#88116, #16780527, #16780531, … |
| maximal quotient of | C4×D4⋊#1057, C4×#11718244, #16780461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20270);