Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C31×#99 ⋊ C2 |
| Sylow | C31 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 248 |
Polycyclic presentation:
2^6,31|a^2=d,b^a=bc,c^a=ce,e^a=ef,d^b=de,g^b=g^30,d^c=df178 conjugacy classes — view the full character table.
| maximal subgroup of | D31×AΣL(1,𝔽16), C2×#14520835, #16847350, … |
| maximal normal subgroup of | D31×AΣL(1,𝔽16), C2×#14520835, #16847350, … |
| maximal quotient of | #16843638, #16843658, #16843707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 335);