Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C31×M32 ⋊ C2 |
| Sylow | C31 ⋊ #349 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^6,31|a^2=d,d^2=e,e^2=f,b^a=bc,c^a=cf,d^b=df,g^b=g^30322 conjugacy classes — view the full character table.
| maximal subgroup of | D31×#349, C2×#14520830, #16847330, … |
| maximal normal subgroup of | D31×#349, C2×#14520830, #16847330, … |
| maximal quotient of | #16843634, #16843650, #16843668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 330);