Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C2×C34 |
No aliases for this group.
| Fitting | C22×C32⋊C9 ⋊ C3 |
| Sylow | C22 ⋊ C9×H(3,𝔽3) |
225 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
3^5,2^2|c^3=d,b^a=be,f^a=fg,g^a=f,c^b=ce132 conjugacy classes — view the full character table.
| derived subgroup of | #14518096 |
| maximal subgroup of | #14518003, #14518096, ((C3⋊D3)⋊A4)⋊C9, … |
| maximal normal subgroup of | #14518003, #14518096, ((C3⋊D3)⋊A4)⋊C9, … |
| maximal quotient of | #14517184, C2×#11757775 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 500);