Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#11718796 |
| Fitting | C22×C13×M16 ⋊ C2 |
| Sylow | C13 ⋊ C2×#469 |
596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#13112820, C2×#13112822, C2×#13112826, … |
| maximal normal subgroup of | C2×#13112820, C2×#13112822, C2×#13112826, … |
| maximal quotient of | C2×#13114315, C2×#13114349, C2×#13114397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 14106);