Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q8×#6105 |
| Sylow | C13 ⋊ Q8×SD16 |
370 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
185 conjugacy classes — view the full character table.
| maximal subgroup of | #15852409, #15852416, #15852469, … |
| maximal normal subgroup of | #15852409, #15852416, #15852469, … |
| maximal quotient of | Q8×#88072, Q8×#88050, C4⋊C4×#6105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 17370);