Finite Group DatabasebetaFinite Group Databasebeta| order | 17157 |
| isoclinism | isoclinic class of C43⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C19 · Schur multiplier (H2) = C1 |
| direct product | C3×C19×C43⋊C7 |
| unambiguous semidirect product | (C3×C43)⋊(C7×C19) |
| unambiguous semidirect product | (C3×C19×C43)⋊C7 |
| Fitting, socle, Hall | C3×C19×C43 ⋊ C7 |
| derived, Sylow | C43 ⋊ C3×C7×C19 |
| Hall | C19×C43 ⋊ C3×C7 |
| Hall | C3×C43 ⋊ C7×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C19 | C43⋊C7 |
| commutator, cosocle, hypocenter | C43 | C3×C7×C19 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C43 | C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C3×C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2451 |
741 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×C19×C43⋊C7, C3×C19×D43⋊C7, C3×D19×C43⋊C7, … |
| maximal normal subgroup of | C2×C3×C19×C43⋊C7, C3×C19×D43⋊C7, C3×D19×C43⋊C7, … |
| maximal quotient of | C2×C3×C19×C43⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17157, 2);