Finite Group DatabasebetaFinite Group Databasebeta| order | 20874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C7⋊(D71⋊C7)) |
| unambiguous semidirect product | C7⋊(C3⋊(D71⋊C7)) |
| unambiguous semidirect product | (C71⋊C7)⋊D21 |
| unambiguous semidirect product | D1491⋊C7 |
| Fitting, socle, derived | C3×C7×C71 ⋊ C2×C7 |
| Hall | C3×C7×C71⋊C7 ⋊ C2 |
| Hall | C7×C71⋊C7 ⋊ D3 |
| Hall | C3×C71 ⋊ C7×D7 |
| Sylow | C71 ⋊ C7×D21 |
| Sylow | C3 ⋊ C7⋊(D71⋊C7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C71 | C2×C7 |
| LCS | G ▷ C3×C7×C71 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1491 |
Polycyclic presentation:
2,7,3,7,71|c^a=c^2,d^a=d^6,e^a=e^70,e^b=e^45189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20874, 27);