Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#11719171 |
| unambiguous semidirect product | D13⋊#379 |
| Fitting | C25×C13 ⋊ C4 |
| Sylow | C13 ⋊ C2×#379 |
3464 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 354 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13129735, D13⋊#1304, #16780142, … |
| maximal normal subgroup of | C2×#13129735, D13⋊#1304, #16780142, … |
| maximal quotient of | C2×#13130010, C4×#11719171, C2×#13130018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20951);