Finite Group DatabasebetaFinite Group Databasebeta| order | 1504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | SD16×D47 |
| Fitting | SD16×C47 ⋊ C2 |
| Sylow | C47 ⋊ C2×SD16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 376 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD16×D47, #135×D47, AGL(1,ℤ/8)×D47, … |
| maximal normal subgroup of | C2×SD16×D47, #135×D47, AGL(1,ℤ/8)×D47, … |
| maximal quotient of | #102×D47, #103×D47, #106×D47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1504, 158);