Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C31×C4⋊C8 ⋊ C2 |
| Sylow | C31 ⋊ #331 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^6,31|a^2=d,c^2=f,d^2=ef,b^a=bc,c^a=ce,c^b=cf,d^b=def,g^b=g^30319 conjugacy classes — view the full character table.
| maximal subgroup of | D31×#331, C2×#14520792, #16844358, … |
| maximal normal subgroup of | D31×#331, C2×#14520792, #16844358, … |
| maximal quotient of | #16843531, #16843595, #16843747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 292);