Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×(C2×#261)⋊Q8 |
| unambiguous semidirect product | D13⋊#391 |
| Fitting | C22×Q8×C13 ⋊ C4 |
| Sylow | C13 ⋊ C2×#391 |
928 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 928 conjugacy classes of subgroups — too many to draw. Only its 274 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 | #16785376, #16785377, #16785905, … |
| maximal normal subgroup of | #16785376, #16785377, #16785905, … |
| maximal quotient of | C2×#13130013, C2×#13130015, C4×(C2×#261)⋊Q8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20968);