Finite Group DatabasebetaFinite Group Databasebeta| order | 992 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C31 ⋊ C2 |
| Sylow | C31 ⋊ SD32 |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^5,31|b^2=cd,c^2=d,d^2=e,b^a=bc,c^a=cde,d^a=de,f^a=f^30251 conjugacy classes — view the full character table.
| maximal subgroup of | SD32×D31, C2×#11758388, #14521480, … |
| maximal normal subgroup of | SD32×D31, C2×#11758388, #14521480, … |
| maximal quotient of | #14520851, #14520854, #14520877, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(992, 6);