Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#88117 |
| unambiguous semidirect product | D13⋊(C2×#103) |
| Fitting | C22×Q8×C13 ⋊ C4 |
| Sylow | C13 ⋊ C22×#103 |
816 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 258 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 | #16785497, #16785498, #16785904, … |
| maximal normal subgroup of | #16785497, #16785498, #16785904, … |
| maximal quotient of | C22×Q8⋊#1057, C2×D13⋊(Q8⋊C8), C22×#11718244, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21125);