Finite Group DatabasebetaFinite Group Databasebeta| order | 18858 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D449⋊C7) |
| unambiguous semidirect product | D1347⋊C7 |
| unambiguous semidirect product | (C449⋊C7)⋊D3 |
| Fitting, socle, derived, Hall | C3×C449 ⋊ C2×C7 |
| Hall | C3×C449⋊C7 ⋊ C2 |
| Hall | C449⋊C7 ⋊ D3 |
| Hall | D1347 ⋊ C7 |
| Sylow | C449 ⋊ D3×C7 |
| Sylow | C3 ⋊ D449⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C449 | C2×C7 |
| LCS | G ▷ C3×C449 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1347 |
Polycyclic presentation:
2,3,7,449|b^a=b^2,d^a=d^448,d^c=d^324117 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D449⋊C7, C2×C3⋊(D449⋊C7) |
| maximal normal subgroup of | D3×D449⋊C7, C2×C3⋊(D449⋊C7) |
| maximal quotient of | C3⋊(Dic449⋊C7), C2×C3⋊(D449⋊C7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18858, 13);