Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C32 |
| direct product | C2×C3⋊#4208 |
| unambiguous semidirect product | (C2×C3)⋊#4208 |
| Fitting | C2×C3×#737 ⋊ C2 |
| Sylow | C3×#737 ⋊ C22 |
536 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | #14518716, #14518718, #14518719, … |
| maximal normal subgroup of | #14518716, #14518718, #14518719, … |
| maximal quotient of | #14518988, C4×C3⋊#4208, C4⋊(C3⋊#4208), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 861);