Finite Group Databasebeta

Rational groups

Groups whose character values are all rational integers.

ordergroupconjugacy classesclass signature
1C1 #11
2C2 #221:2
4C22 #543x1:2
6D3 #732:3,3:2
8D4 #1251:2,2x2:2,2:4
8Q8 #1351:2,3x2:4
8C23 #1487x1:2
12C2×D3 #2361:2,2:3,2:6,2x3:2
16C2×D4 #39103x1:2,4x2:2,2x2:4
16C2×Q8 #40103x1:2,6x2:4
16C24 #421615x1:2
18C3⋊D3 #4764x2:3,9:2
24S4 #7153:2,6:2,6:4,8:3
24C22×D3 #73123x1:2,2:3,3x2:6,4x3:2
32#120143x1:2,6x2:2,4:2,3x4:4
32#127143x1:2,6x2:4,4x4:2
32C4⋊Q8 #128143x1:2,6x2:4,4x4:4
32AGL(1,ℤ/8) #136111:2,2:2,2x2:4,3x4:2,4:4,2x4:8
32#137111:2,2:2,2x2:4,4:2,3x4:4,2x4:8
32C22×D4 #139207x1:2,8x2:2,4x2:4
32C22×Q8 #140207x1:2,12x2:4
32H(5,𝔽2) #142171:2,9x2:2,6x2:4
322−1+4 #143171:2,5x2:2,10x2:4
32C25 #1443231x1:2
36D32 #15892x2:3,2x3:2,4:3,2x6:6,9:2
36C2×C3⋊D3 #161121:2,4x2:3,4x2:6,2x9:2
48D3×D4 #236151:2,2x2:2,2:3,2:4,2:6,2x3:2,2x4:6,4:12,2x6:2,6:4
48D3×Q8 #238151:2,2:3,3x2:4,2:6,2x3:2,3x4:12,3x6:4
48C2×S4 #246101:2,2x3:2,2x6:2,2x6:4,8:3,8:6
48C23×D3 #249247x1:2,2:3,7x2:6,8x3:2
54C3⋊(C3⋊D3) #2781513x2:3,27:2
64#453161:2,2:2,2x2:4,4x4:2,4x4:4,8:2,2x8:8
64#456161:2,2:2,2x2:4,2x4:2,6x4:4,8:4,2x8:8
64B(4,𝔽2) #457161:2,3x2:2,5x4:2,3x4:4,3x8:4
64#496163x1:2,2x2:4,2x4:4,4x4:8,3x8:2,8:4
64#497163x1:2,2x2:4,2x4:4,4x4:8,8:2,3x8:4
64#501163x1:2,2x2:4,2x4:4,4x4:8,4x8:4
64C2×#120 #521287x1:2,12x2:2,2x4:2,6x4:4
64C2×#127 #530287x1:2,12x2:4,8x4:2
64C2×C4⋊Q8 #531287x1:2,12x2:4,8x4:4
64#534223x1:2,6x2:2,4x4:2,8x4:4
64#535223x1:2,2x2:2,4x2:4,6x4:2,6x4:4
64#536223x1:2,2x2:2,4x2:4,2x4:2,10x4:4
64#537223x1:2,2x2:2,4x2:4,4x4:2,8x4:4
64#543223x1:2,6x2:2,12x4:4
64#544223x1:2,2x2:2,4x2:4,12x4:4
64D42 #545253x1:2,8x2:2,4x2:4,4x4:2,5x4:4
64D4×Q8 #549253x1:2,4x2:2,8x2:4,9x4:4
64Q82 #558253x1:2,12x2:4,9x4:4
64#560193x1:2,6x4:2,9x4:4
64H(3,𝔽4) #561193x1:2,6x4:2,9x4:4
64#562193x1:2,4x4:2,11x4:4
64#563193x1:2,2x4:2,13x4:4
64#564193x1:2,15x4:4
64C2×AGL(1,ℤ/8) #573223x1:2,2x2:2,4x2:4,6x4:2,2x4:4,4x4:8
64C2×#137 #574223x1:2,2x2:2,4x2:4,2x4:2,6x4:4,4x4:8
64C23×D4 #5804015x1:2,16x2:2,8x2:4
64C23×Q8 #5814015x1:2,24x2:4
64C2×H(5,𝔽2) #583343x1:2,18x2:2,12x2:4
64C2×2−1+4 #584343x1:2,10x2:2,20x2:4
64C26 #5866463x1:2
72GO+(4,𝔽2) #64392x4:3,2x6:2,9:2,2x12:6,18:4
72PSU(3,𝔽2) #64468:3,9:2,3x18:4
72C3⋊S4 #64692:3,3:2,6:6,3x8:3,18:2,18:4
72C2×D32 #649181:2,2x2:3,2x2:6,4x3:2,4:3,4:6,4x6:6,2x9:2
72C22×C3⋊D3 #652243x1:2,4x2:3,12x2:6,4x9:2
96C2×D3×D4 #1002303x1:2,4x2:2,2:3,2x2:4,3x2:6,4x3:2,4x4:6,2x4:12,4x6:2,2x6:4
96C2×D3×Q8 #1005303x1:2,2:3,6x2:4,3x2:6,4x3:2,6x4:12,6x6:4
96C22×S4 #1019203x1:2,4x3:2,4x6:2,4x6:4,8:3,3x8:6
96#1020103x3:2,6:2,12:2,3x12:4,32:3
96C24×D3 #10234815x1:2,2:3,15x2:6,16x3:2
108((C3⋊D3)⋊C3)⋊C2 #1090112:3,2x6:3,3x9:2,12:3,3x18:6
108D3×C3⋊D3 #1112185x2:3,3:2,4x4:3,4x6:6,9:2,18:6,27:2
108C2×C3⋊(C3⋊D3) #1117301:2,13x2:3,13x2:6,2x27:2
120S5 #1224710:2,15:2,20:3,20:6,24:5,30:4
128#1655203x1:2,3x4:4,3x8:2,3x8:4,6x8:8,16:2
128#1660203x1:2,3x4:4,8:2,5x8:4,6x8:8,16:4
128#2196201:2,2:2,6x4:2,3x4:4,2x8:2,3x8:4,2x16:4,16:8
128#2199171:2,2:2,2x4:2,4:4,3x8:2,5x8:4,2x16:4,16:8
128#2200171:2,2:2,2x4:2,4:4,3x8:2,5x8:4,2x16:4,16:8
128#2201171:2,2:2,2x4:2,4:4,8:2,7x8:4,2x16:4,16:8
128#2202171:2,2:2,3x4:4,4x8:2,4x8:4,3x16:8
128#2203171:2,2:2,3x4:4,2x8:2,6x8:4,3x16:8
128#2205201:2,2:2,9x4:4,8:2,4x8:4,3x16:8
128#2403387x1:2,8x2:2,10x4:2,8x4:4,4x8:4
128#2433387x1:2,4x2:2,4x2:4,8x4:2,10x4:4,2x8:2,2x8:4
128#2434387x1:2,4x2:2,4x2:4,18x4:4,4x8:4
128#2551387x1:2,8x2:4,18x4:4,4x8:4
128#2613327x1:2,4x2:2,8x4:2,4x4:4,8:2,7x8:4
128#2614327x1:2,4x2:2,12x4:4,8:2,7x8:4
128#2615327x1:2,4x2:4,6x4:2,6x4:4,2x8:2,6x8:4
128#2616327x1:2,4x2:4,6x4:2,6x4:4,8x8:4
128#2656327x1:2,4x2:2,12x4:4,4x8:2,4x8:4
128#2657327x1:2,4x2:4,12x4:4,6x8:2,2x8:4
128#2658327x1:2,4x2:4,12x4:4,2x8:2,6x8:4
128#2659327x1:2,4x2:2,12x4:4,8x8:4
128#2660327x1:2,4x2:4,12x4:4,8x8:4
128#2669327x1:2,8x4:2,10x4:4,2x8:2,4x8:4
128#2675327x1:2,6x4:2,12x4:4,2x8:2,4x8:4
128#2677327x1:2,2x4:2,16x4:4,6x8:4

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