Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | H(3,𝔽3)⋊(C22⋊C9) |
| Sylow | C22 ⋊ H(3,𝔽3)⋊C9 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|a^3=c,b^a=bd,f^a=fg,g^a=f,d^b=de84 conjugacy classes — view the full character table.
| derived subgroup of | #14516491 |
| maximal subgroup of | #14516449, #14516491, #272⋊(C22⋊C9), … |
| maximal normal subgroup of | #14516449, #14516491, #272⋊(C22⋊C9), … |
| maximal quotient of | #14515887, C2×H(3,𝔽3)⋊(C22⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 178);