Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | (C3×A4)⋊C27 |
| Fitting | C22×C3×C27 ⋊ C3 |
| Sylow | C22 ⋊ C32⋊C27 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
3^5,2^2|b^3=c,c^3=e,b^a=bd,f^a=fg,g^a=f180 conjugacy classes — view the full character table.
| derived subgroup of | #14516477 |
| maximal subgroup of | (C3⋊S4)⋊C27, #14516477, #14516520, … |
| maximal normal subgroup of | (C3⋊S4)⋊C27, #14516477, #14516520, … |
| maximal quotient of | (C3×SL(2,𝔽3))⋊C27, C2×(C3×A4)⋊C27 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 151);