Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11718280 |
| unambiguous semidirect product | D13⋊#358 |
| Fitting | C2×C13×Q16 ⋊ C4 |
| Sylow | C13 ⋊ C2×#358 |
232 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
86 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11718280, #261×#358, #16789497, … |
| maximal normal subgroup of | C4×#11718280, #261×#358, #16789497, … |
| maximal quotient of | C2×#13129792, D13⋊#1332, C2×#13129793, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20816);