Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for S₄

Name:

s4

Group order:

24 = 2³ ⋅ 3

Number of classes:

5

InfoText value:

origin: CAS library, names:= s4 order: 2^3.3 = 24 number of classes: 5 source: generated by dixon-algorithm aachen [1982] comments: symmetric group, catalogue nr.24.15 test: orth, min, sym(3) constructions: AGL(2,2), tests: 1.o.r., pow[2,3]

Duplicates:

A6M5, Symm(4)

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:

2 × S₄, S₅, A₆, A₇, L₂(11).2, L₂(13).2, L₂(17), L₂(23), L₂(113), L₃(2), L₃(3), M₁₁

Stored class fusions to this table:

2.S₄, 3 × 2.S₄, 3 × S₄, (2⁴:A₄ × A₄).2, (13:6 × A₄).2, (A₄ × 11:5).2, (A₄ × L₃(4)):2₁, A₄

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