Finite Group DatabasebetaFinite Group Databasebeta| order | 17157 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×C43⋊C7 |
| unambiguous semidirect product | C19⋊(C3×C43⋊C7) |
| unambiguous semidirect product | (C43×C19⋊C3)⋊C7 |
| Fitting, socle, derived, Hall | C19×C43 ⋊ C3×C7 |
| Hall | C19×C43⋊C7 ⋊ C3 |
| Hall | C43×C19⋊C3 ⋊ C7 |
| Sylow | C43 ⋊ C7×C19⋊C3 |
| Sylow | C19 ⋊ C3×C43⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C43 | C3×C7 |
| LCS | G ▷ C19×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 817 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C19⋊C3×C43⋊C7, C19⋊C3×D43⋊C7, D19⋊C3×C43⋊C7, … |
| maximal normal subgroup of | C2×C19⋊C3×C43⋊C7, C19⋊C3×D43⋊C7, D19⋊C3×C43⋊C7, … |
| maximal quotient of | C2×C19⋊C3×C43⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17157, 17);