Finite Group DatabasebetaFinite Group Databasebeta| order | 2142 |
| isoclinism | isoclinic class of C3⋊D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C3 |
| direct product | C17×C3⋊D21 |
| unambiguous semidirect product | C3⋊(C17×D21) |
| unambiguous semidirect product | C7⋊(C17×C3⋊D3) |
| Fitting, socle, Hall | C32×C7×C17 ⋊ C2 |
| derived, Hall | C32×C7 ⋊ C2×C17 |
| Hall | C32×C17 ⋊ D7 |
| Hall | C7×C17 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D7×C17 |
| Sylow | C7 ⋊ C17×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C3⋊D21 |
| commutator, cosocle, hypocenter | C32×C7 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C17 | C2 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C17 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 1071 |
A minimal faithful permutation representation — 3 generators on 30 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20)(21,22)(23,24)(26,27)(29,30);(18,19,21,23,24,22,20)(28,29,30);(25,26,27)561 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×C3⋊D21, D7×C17×C3⋊D3, D119⋊(C3⋊D3), … |
| maximal normal subgroup of | D17×C3⋊D21, D7×C17×C3⋊D3, D119⋊(C3⋊D3), … |
| maximal quotient of | C17×C3⋊Dic21, C2×C17×C3⋊D21, C17×C3⋊D147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2142, 31);