Finite Group DatabasebetaFinite Group Databasebeta| order | 2142 |
| isoclinism | isoclinic class of C17⋊AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C7×C17 ⋊ C2×C3 |
| derived, Hall | C7×C17 ⋊ C2×C32 |
| Hall | C3×C17×ΓL(1,𝔽8) ⋊ C2 |
| Hall | D119 ⋊ C32 |
| Hall | C3×ΓL(1,𝔽8) ⋊ D17 |
| Sylow | C17 ⋊ C3×AGL(1,𝔽7) |
| Sylow | C7 ⋊ C32×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C17⋊AGL(1,𝔽7) |
| commutator, cosocle, hypocenter | C7×C17 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C17 | C2×C3 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 357 |
141 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2142, 15);