Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #92172 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#92172 |
| Fitting | C2×C32⋊C27 ⋊ C2 |
| derived | C3×C27 ⋊ C22×C3 |
| Sylow | C32⋊C27 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92172 |
| commutator, cosocle, hypocenter | C3×C27 | C22×C3 |
| Frattini | C3×C9 | C2×C3×D3 |
| Fitting | C2×C32⋊C27 | C2 |
| socle | C2×C32 | C3×D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C2 | |
127 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | #92172⋊C4, #14515766, #14515769, … |
| maximal normal subgroup of | #92172⋊C4, #14515766, #14515769, … |
| maximal quotient of | #14515937, C4×#92172, C4⋊#92172, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 201);