Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C31×C4⋊Q8 ⋊ C2 |
| Sylow | C31 ⋊ #486 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^6,31|b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^30,g^b=g^30,g^c=g^30232 conjugacy classes — view the full character table.
| maximal subgroup of | #16844800, #16844801, #16844807, … |
| maximal normal subgroup of | #16844800, #16844801, #16844807, … |
| maximal quotient of | #16845838, #16846393, #16846516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 897);