Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C31×#100 ⋊ C2 |
| Sylow | C31 ⋊ #455 |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 496 |
Polycyclic presentation:
2^6,31|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^30,d^b=df,e^b=ef,g^b=g^30,d^c=df181 conjugacy classes — view the full character table.
| maximal subgroup of | #16847702, #16847703, #16847713, … |
| maximal normal subgroup of | #16847702, #16847703, #16847713, … |
| maximal quotient of | #16844665, #16844670, #16844693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 729);