Finite Group DatabasebetaFinite Group Databasebeta| order | 2142 |
| isoclinism | isoclinic class of ΓL(1,𝔽8)×D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D17×C7⋊C9 |
| unambiguous semidirect product | C17⋊(C2×C7⋊C9) |
| unambiguous semidirect product | (C7×D17)⋊C9 |
| derived, Hall | C7×C17 ⋊ C2×C9 |
| Hall | C17×C7⋊C9 ⋊ C2 |
| Hall | C7×D17 ⋊ C9 |
| Sylow | C17 ⋊ C2×C7⋊C9 |
| Sylow | C7 ⋊ C9×D17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×D17 |
| commutator, hypocenter | C7×C17 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C17 | C2×C3 |
| prime radical | C3×C7×D17 | C3 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1071 |
A minimal faithful permutation representation — 2 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,20,21)(22,24,23)(25,26,28,27,29,31,30,32,33);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(18,19,20,22,21,23,24)150 conjugacy classes — view the full character table.
| maximal subgroup of | C7⋊C9×#595, (C7⋊C9)⋊#595, D17×D7⋊C9, … |
| maximal normal subgroup of | C7⋊C9×#595, (C7⋊C9)⋊#595, D17×D7⋊C9, … |
| maximal quotient of | C7⋊C9×Dic17, C2×D17×C7⋊C9, D17×C49⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2142, 2);