Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C2×#11718261 |
| Sylow | C13 ⋊ C2×#364 |
168 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 168 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) = 416 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | #16777151, #16777152, #16777154, … |
| maximal normal subgroup of | #16777151, #16777152, #16777154, … |
| maximal quotient of | C2×#13129858, #16788650, C2×#13129865, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 20848);