Finite Group DatabasebetaFinite Group Databasebeta| order | 2142 |
| isoclinism | isoclinic class of C3⋊D357 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D357 |
| unambiguous semidirect product | C7⋊(C3⋊D51) |
| unambiguous semidirect product | C17⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C7×C17 ⋊ C2 |
| Hall | C32×C17 ⋊ D7 |
| Hall | C7×C17 ⋊ C3⋊D3 |
| Hall | C32×C7 ⋊ D17 |
| Sylow | C17 ⋊ C3⋊D21 |
| Sylow | C32 ⋊ D119 |
| Sylow | C7 ⋊ C3⋊D51 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C17 | C2 |
| LCS | G ▷ C32×C7×C17 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1071 |
Polycyclic presentation:
2,3^2,7,17|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^16537 conjugacy classes — view the full character table.
| maximal subgroup of | D17×C3⋊D21, D7×C3⋊D51, C3⋊D3×D119, … |
| maximal normal subgroup of | D17×C3⋊D21, D7×C3⋊D51, C3⋊D3×D119, … |
| maximal quotient of | C3⋊Dic357, C2×C3⋊D357, C3⋊D2499, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2142, 32);