Finite Group DatabasebetaFinite Group Databasebeta| order | 15712 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | SD16×D491 |
| Fitting | SD16×C491 ⋊ C2 |
| Sylow | C491 ⋊ C2×SD16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3928 |
1729 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×SD16×D491, #135×D491, AGL(1,ℤ/8)×D491, … |
| maximal normal subgroup of | C2×SD16×D491, #135×D491, AGL(1,ℤ/8)×D491, … |
| maximal quotient of | #102×D491, #103×D491, #106×D491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15712, 158);