Finite Group DatabasebetaFinite Group Databasebeta| order | 1664 |
| isoclinism | isoclinic class of #6095 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×D104 |
| Fitting | C82×C13 ⋊ C2 |
| Sylow | C13 ⋊ C8×D8 |
196 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
440 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #15749567, #15749569, #15749573, … |
| maximal normal subgroup of | #15749567, #15749569, #15749573, … |
| maximal quotient of | C8×#88061, C8×#88058, #15756833, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1664, 3306);