Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11718245 |
| Sylow | C13 ⋊ C2×#332 |
256 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
98 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#11718245, #16780710, #16780718, … |
| maximal normal subgroup of | C4×#11718245, #16780710, #16780718, … |
| maximal quotient of | C2×#13129654, C2×#13129655, #16778273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20005);