Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for Symm(4)

Name:

Symm(4)

Group order:

24 = 2³ ⋅ 3

Number of classes:

5

InfoText value:

symmetric group on 4 points

Main table:

S₄

Group constructions in GAP:

AGL( 2, 2 ), AtlasStabilizer( "A5.2", "S5G1-p5B0" ), AtlasStabilizer( "A6", "A6G1-p15aB0" ), AtlasStabilizer( "A6", "A6G1-p15bB0" ), AtlasStabilizer( "L2(11).2", "L211d2G1-p55aB0" ), AtlasStabilizer( "L3(2)", "L27G1-p7aB0" ), AtlasStabilizer( "L3(2)", "L27G1-p7bB0" ), AtlasStabilizer( "L3(3)", "L33G1-p234B0" ), AtlasSubgroup( "A5.2", 2 ), AtlasSubgroup( "A6", 4 ), AtlasSubgroup( "A6", 5 ), AtlasSubgroup( "L2(11).2", 3 ), AtlasSubgroup( "L2(113)", 4 ), AtlasSubgroup( "L2(113)", 5 ), AtlasSubgroup( "L3(2)", 1 ), AtlasSubgroup( "L3(2)", 2 ), PrimitiveGroup( 4, 2 ), SmallGroup( 24, 12 ), SymmetricGroup( 4 ), TransitiveGroup( 4, 5 ), TransitiveGroup( 6, 7 ), TransitiveGroup( 6, 8 ), TransitiveGroup( 8, 14 ), TransitiveGroup( 12, 8 ), TransitiveGroup( 12, 9 ), TransitiveGroup( 24, 10 )

Stored class fusions from this table:

L₂(31), L₃(2)

Stored class fusions to this table:

2.S₄, 2⁴:(3 × 3):2, 3 × 2.S₄, (A₄ × 3):2, (A₄ × 3.L₃(4)).2, (A₄ × 3.L₃(4).2₃).2, (A₄ × A₅):2, (A₄ × D₁₀).2, (A₄ × G₂(4)):2, (A₄ × L₃(4):2₃):2, (A₄ × O₈⁺(2).3).2, (A₄ × U₄(2)):2, (A₆ × A₄):2, (A₇ × A₄):2, (A₈ × A₄):2, (A₉ × A₄):2, F₃₊N5, A₄

File created automatically by GAP on 20-May-2025.