Character Table info for S3
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Name:
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S3
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Group order:
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6 = 2 ⋅ 3
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Number of classes:
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3
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InfoText value:
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constructions: AGL(1,3)
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Group constructions in GAP:
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AGL( 1, 3 ),
AtlasStabilizer( "A5", "A5G1-p10B0" ),
AtlasSubgroup( "A5", 3 ),
DihedralGroup( 6 ),
PSL( 2, 2 ),
PSU( 2, 2 ),
PSp( 2, 2 ),
PrimitiveGroup( 3, 2 ),
SmallGroup( 6, 1 ),
SymmetricGroup( 3 ),
TransitiveGroup( 3, 2 ),
TransitiveGroup( 6, 2 )
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Stored class fusions from this table:
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(S5 × S5 × S5):S3,
A5,
L3(2),
S3 × 2
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Stored class fusions to this table:
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1/2(8 × S3),
2.S3,
3.(2 × 21+8):(U4(2):2 × 2),
32:2,
33:S3,
35:2S6,
(2.A4 × 3).2,
(2.A5 × 3).2,
(2.A6 × 3).21,
(2.A7 × 3).2,
(2.A8 × 3).2,
(2.A9 × 3).2,
(22 × 3).2,
(24:S5 × 3).2,
(3 × 2.D10).2,
(3 × 21+6−.U4(2)).2,
(3 × 22+8:(A5 × S3)).2,
(3 × 24+6:3A6).2,
(3 × 33:S3):2,
(3 × 3(1+2)+:2A4).2,
(3 × 13:6).2,
(3 × A6).21,
(3 × D10).2,
(3 × G2(3)):2,
(3 × G2(4)).2,
(3 × L2(16):2).2,
(3 × L2(25)).22,
(3 × L3(4).22).2,
(3 × M10):2,
(3 × O8+(3):3):2,
(3 × O8−(2)):2,
(3 × U5(2)).2,
(A4 × 3):2,
(A5 × 3):2,
(A7 × 3):2,
(A8 × 3):2,
(A9 × 3):2,
(A10 × 3):2,
(S3 × 2.Fi22).2,
(S3 × 2.U4(3).22).2,
(S5 × S5 × S5):S3,
C3,
D24,
D114,
D120,
NRS(M24, [29]a),
NRS(M24, [29]b),
S3 × 5:4,
[29].S3a,
[29].S3b,
bd6,
(3 × A6):22