Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | SD16×D31 |
| Fitting | SD16×C31 ⋊ C2 |
| Sylow | C31 ⋊ C2×SD16 |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 248 |
119 conjugacy classes — view the full character table.
| maximal subgroup of | C2×SD16×D31, #135×D31, AGL(1,ℤ/8)×D31, … |
| maximal normal subgroup of | C2×SD16×D31, #135×D31, AGL(1,ℤ/8)×D31, … |
| maximal quotient of | #102×D31, #103×D31, #106×D31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 108);