Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C22⋊#6862 |
| Sylow | C22 ⋊ #6862 |
73 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|a^3=e,b^3=d,b^a=bc,c^a=cd,f^a=fg,g^a=f,c^b=ce^268 conjugacy classes — view the full character table.
| derived subgroup of | #14516460 |
| maximal subgroup of | #14516422, #14516460, #14516509, … |
| maximal normal subgroup of | #14516422, #14516460, #14516509, … |
| maximal quotient of | Q8⋊#6862, C2×C22⋊#6862 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 128);