Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C2×C33 |
| direct product | A4×#733 |
| Fitting | C22×#733 ⋊ C3 |
| Sylow | C22 ⋊ C3×#733 |
145 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
68 conjugacy classes — view the full character table.
| derived subgroup of | A4⋊(#733⋊C2) |
| maximal subgroup of | S4×#733, A4⋊(#733⋊C2), A4×#733⋊C2, … |
| maximal normal subgroup of | S4×#733, A4⋊(#733⋊C2), A4×#733⋊C2, … |
| maximal quotient of | SL(2,𝔽3)×#733, C2×A4×#733 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 537);