Finite Group DatabasebetaFinite Group Databasebeta| order | 17504 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | SD16×D547 |
| Fitting | SD16×C547 ⋊ C2 |
| Sylow | C547 ⋊ C2×SD16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4376 |
1925 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×SD16×D547, #135×D547, AGL(1,ℤ/8)×D547, … |
| maximal normal subgroup of | C2×SD16×D547, #135×D547, AGL(1,ℤ/8)×D547, … |
| maximal quotient of | #102×D547, #103×D547, #106×D547, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17504, 158);