Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #88066 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×#88068 |
| Fitting | C4×C13×Q16 ⋊ C2 |
| Sylow | C13 ⋊ C4×SD32 |
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
212 conjugacy classes — view the full character table.
| maximal subgroup of | #15774643, C8×#88068, #15774656, … |
| maximal normal subgroup of | #15774643, C8×#88068, #15774656, … |
| maximal quotient of | C8×#88068, #15774819, #15774828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 6362);