Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#11718086 |
| Sylow | C13 ⋊ C2×#365 |
152 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 416 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | #15778302, C4×#11718086, #15778338, … |
| maximal normal subgroup of | #15778302, C4×#11718086, #15778338, … |
| maximal quotient of | C2×#13112901, #15774478, #15774552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6280);