Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C2×D13⋊M32 |
| unambiguous semidirect product | D13⋊(C2×M32) |
| Sylow | C13 ⋊ C22×M32 |
400 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | #16789043, #16789047, #16789053, … |
| maximal normal subgroup of | #16789043, #16789047, #16789053, … |
| maximal quotient of | C2×#13131037, C4×D13⋊M32, C2×#13131042, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 21472);