Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×D4×#261 |
| unambiguous semidirect product | D13⋊(C2×C4×D4) |
| Fitting | C22×D4×C13 ⋊ C4 |
| Sylow | C13 ⋊ C22×C4×D4 |
2528 conjugacy classes of subgroups; only the 850 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 850 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #16785412, #16785417, #16785495, … |
| maximal normal subgroup of | #16785412, #16785417, #16785495, … |
| maximal quotient of | C22×C22⋊C4×#261, C22×C4⋊C4×#261, C2×C4×D4×#261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21484);