Finite Group DatabasebetaFinite Group Databasebeta| order | 462 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D33 |
| unambiguous semidirect product | C3⋊(C7×D11) |
| unambiguous semidirect product | C11⋊(D3×C7) |
| Fitting, socle, Hall | C3×C7×C11 ⋊ C2 |
| derived, Hall | C3×C11 ⋊ C2×C7 |
| Hall | C7×C11 ⋊ D3 |
| Hall | C3×C7 ⋊ D11 |
| Sylow | C11 ⋊ D3×C7 |
| Sylow | C3 ⋊ C7×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D33 |
| commutator, cosocle, hypocenter | C3×C11 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C11 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 231 |
A minimal faithful permutation representation — 2 generators on 21 points:
(2,3)(4,5,6,7,8,9,10)(12,13)(14,15)(16,17)(18,19)(20,21);(1,2,3)(11,12,14,16,18,20,21,19,17,15,13)126 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C7×D11, D7×D33, D21⋊D11, … |
| maximal normal subgroup of | D3×C7×D11, D7×D33, D21⋊D11, … |
| maximal quotient of | C7×Dic33, C2×C7×D33, C7×D99, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(462, 9);