Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of C9⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C2×C34 |
| direct product | C9×C22⋊H(3,𝔽3) |
| Fitting | C22×C32×C9 ⋊ C3 |
| Sylow | C22 ⋊ C9×H(3,𝔽3) |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
180 conjugacy classes — view the full character table.
| derived subgroup of | C9⋊#6258 |
| maximal subgroup of | C9×(C3⋊S4)⋊C3, C9×#6258, #14518054, … |
| maximal normal subgroup of | C9×(C3⋊S4)⋊C3, C9×#6258, #14518054, … |
| maximal quotient of | C9×Q8⋊H(3,𝔽3), C2×C9×C22⋊H(3,𝔽3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 553);