Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×#88124 |
| Sylow | C13 ⋊ C4×#125 |
484 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1664 |
440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15750890, #15750964, #15750967, … |
| maximal normal subgroup of | #15750890, #15750964, #15750967, … |
| maximal quotient of | C4×#11718594, C4×#11718589, C4×#11718597, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 7070);