Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | #103×#261 |
| Fitting | C13×#103 ⋊ C4 |
| Sylow | C13 ⋊ C4×#103 |
332 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#103×#261, #261×#416, #261×#419, … |
| maximal normal subgroup of | C2×#103×#261, #261×#416, #261×#419, … |
| maximal quotient of | #261×Q8⋊C8, #16780472, #16780475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20279);