Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C2 |
| direct product | D32×C27 |
| unambiguous semidirect product | (C3×D3)⋊(C2×C27) |
| Fitting, Sylow | C32×C27 ⋊ C22 |
| derived | C32 ⋊ C22×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | D32 |
| commutator, hypocenter | C32 | C22×C27 |
| Frattini | C9 | C3×D32 |
| Fitting | C32×C27 | C22 |
| socle | C33 | C22×C9 |
| prime radical | C3×D32 | C9 |
| cosocle | C32×C9 | C22×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C27 | |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
243 conjugacy classes — view the full character table.
| maximal subgroup of | C27×GO+(4,𝔽2), D32⋊D27, D32×D27, … |
| maximal normal subgroup of | C27×GO+(4,𝔽2), D32⋊D27, D32×D27, … |
| maximal quotient of | D3×Dic3×C27, C27×#624, C27×#625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 434);