Finite Group Databasebeta

Ambivalent but not rational groups

Groups whose character table is real-valued but not integer-valued.

ordergroupconjugacy classesclass signature
96#914181:2,2:3,2:4,2:6,4:2,4:4,4:8,4:12,2x4:24,6:2,6:4,8:6,8:12,2x12:2,12:8
96#915181:2,2:3,2:4,2:6,4:2,4:4,4:8,4:12,2x4:24,6:2,6:4,8:6,8:12,2x12:4,12:8
96D3×Q16 #917211:2,2:3,2:4,2:6,2x2:8,2x3:2,2x4:4,4:12,2x4:24,6:4,2x6:8,2x8:12,2x12:4
96A4⋊Q8 #978141:2,2:4,2x3:2,6:4,8:3,8:6,2x8:12,4x12:4
96C4⋊S4 #980141:2,2:4,2x3:2,6:4,8:3,8:6,2x8:12,2x12:2,2x12:4
96C2×#226 #981163x1:2,2x6:4,4x6:8,8:3,3x8:6,2x12:4
96#984131:2,2:4,6:2,6:4,8:3,8:6,2x8:12,2x12:4,2x12:8
96#986131:2,2:4,6:2,6:4,8:3,8:6,2x8:12,2x12:2,2x12:8
96C22×Dic6 #998367x1:2,2:3,4x2:4,7x2:6,8x2:12,8x6:4
96C22×D12 #1000367x1:2,2:3,4x2:4,7x2:6,8x2:12,8x6:2
96#1009271:2,3x2:2,2:3,4x2:4,2:6,2x2:12,3x4:6,3x4:12,6x6:2,2x6:4
96#1010271:2,3x2:2,2:3,4x2:4,2:6,2x2:12,3x4:6,3x4:12,2x6:2,6x6:4
98D49 #1026263x2:7,21x2:49,49:2
98C7⋊D7 #10292624x2:7,49:2
100C2×D25 #1036281:2,2x2:5,2x2:10,10x2:25,10x2:50,2x25:2
100D52 #1045164x2:5,4x4:5,2x5:2,4x10:10,25:2
100C2×C5⋊D5 #1047281:2,12x2:5,12x2:10,2x25:2
102D51 #1052272:3,8x2:17,16x2:51,51:2
104Dic26 #1058291:2,2:4,6x2:13,6x2:26,12x2:52,2x26:4
104D52 #1060291:2,2:4,6x2:13,6x2:26,12x2:52,2x26:2
104C22×D13 #1067323x1:2,6x2:13,18x2:26,4x13:2
106D53 #10712826x2:53,53:2
108C2×D27 #1077301:2,2:3,2:6,3x2:9,3x2:18,9x2:27,9x2:54,2x27:2
108D3×D9 #1089182x2:3,3x2:9,3:2,4:3,3x4:9,6:6,3x6:18,9:2,18:6,27:2
108C2×C3⋊D9 #1100301:2,4x2:3,4x2:6,9x2:9,9x2:18,2x27:2
110D55 #1124292x2:5,5x2:11,20x2:55,55:2
112D56 #1133311:2,2:4,3x2:7,2x2:8,3x2:14,6x2:28,12x2:56,2x28:2
112Dic28 #1134311:2,2:4,3x2:7,2x2:8,3x2:14,6x2:28,12x2:56,2x28:4
112C2×Dic14 #1154343x1:2,2x2:4,3x2:7,9x2:14,12x2:28,4x14:4
112C2×D28 #1156343x1:2,2x2:4,3x2:7,9x2:14,12x2:28,4x14:2
112D4×D7 #1158251:2,2x2:2,2:4,3x2:7,3x2:14,6x4:14,3x4:28,2x7:2,2x14:2,14:4
112Q8×D7 #1160251:2,3x2:4,3x2:7,3x2:14,9x4:28,2x7:2,3x14:4
112C23×D7 #1169407x1:2,3x2:7,21x2:14,8x7:2
114D57 #1176302:3,9x2:19,18x2:57,57:2
116C2×D29 #1182321:2,14x2:29,14x2:58,2x29:2
118D59 #11883129x2:59,59:2
120SL(2,𝔽5) #119591:2,2x12:5,2x12:10,20:3,20:6,30:4
120#1204211:2,2:3,2x2:5,2:6,2x2:10,2x4:15,2x4:30,6:4,4x6:20,10:4,2x10:12,30:4
120Dic30 #1216331:2,2:3,2:4,2x2:5,2:6,2x2:10,2x2:12,4x2:15,4x2:20,4x2:30,8x2:60,2x30:4
120D60 #1218331:2,2:3,2:4,2x2:5,2:6,2x2:10,2x2:12,4x2:15,4x2:20,4x2:30,8x2:60,2x30:2
120C2×A5 #1225101:2,2x12:5,2x12:10,2x15:2,20:3,20:6
120C5⋊S4 #1228132x2:5,3:2,2x6:10,8:3,4x8:15,30:2,30:4
120C2×D3×D5 #1232241:2,2:3,2x2:5,2:6,2x2:10,2x3:2,2x4:15,2x4:30,2x5:2,4x6:10,2x10:6,2x15:2
120C22×D15 #1236363x1:2,2:3,2x2:5,3x2:6,6x2:10,4x2:15,12x2:30,4x15:2
122D61 #12403230x2:61,61:2
124C2×D31 #1245341:2,15x2:31,15x2:62,2x31:2
126D63 #1256332:3,3x2:7,3x2:9,6x2:21,18x2:63,63:2
126C3⋊D21 #1266334x2:3,3x2:7,24x2:21,63:2
128D64 #1429351:2,2:4,2x2:8,4x2:16,8x2:32,16x2:64,2x32:2
128Q128 #1431351:2,2:4,2x2:8,4x2:16,8x2:32,16x2:64,2x32:4
128#1595233x1:2,2x2:2,2x4:2,2x4:4,4x8:2,5x8:4,4x8:8
128#1605233x1:2,2x2:2,4x4:4,9x8:4,4x8:8
128#1619263x1:2,4x2:4,4x4:2,4:4,4x4:8,2x8:2,2x8:4,4x8:8,16:2
128#1633263x1:2,4x2:4,5x4:4,4x4:8,4x8:4,4x8:8,16:4
128#1649263x1:2,4x2:4,2x4:2,3x4:4,4x4:8,4x8:4,4x8:8,16:4
128#1712383x1:2,6x2:4,24x2:8,4x16:2
128#1713383x1:2,6x2:4,24x2:8,4x16:4
128#1721263x1:2,6x2:4,12x4:8,3x16:2,16:4
128#1722263x1:2,6x2:4,12x4:8,16:2,3x16:4
128#1723263x1:2,6x2:4,12x4:8,4x16:4
128#2184293x1:2,2x2:2,2x2:4,4x2:8,4:4,2x4:8,8x4:16,4x8:2,16:2,16:4
128#2188293x1:2,2x2:2,2x2:4,4x2:8,4:4,2x4:8,8x4:16,4x8:4,2x16:4
128#2190201:2,2:2,2x2:4,4:2,4:4,2x4:8,2x8:2,2x8:4,8:8,4x8:16,16:2,16:4
128#2191201:2,2:2,2x2:4,4:2,4:4,2x4:8,2x8:2,2x8:4,8:8,4x8:16,2x16:4
128#2192231:2,2:2,2x2:4,2x2:8,4:2,4:4,4:8,4x4:16,3x8:2,8:4,8:8,2x8:16,16:2,16:8
128#2195231:2,2:2,2x2:4,2x2:8,4:2,4:4,4:8,4x4:16,8:2,3x8:4,8:8,2x8:16,16:4,16:8
128#2246383x1:2,6x2:4,8x2:8,16x2:16,4x16:2
128#2247383x1:2,6x2:4,8x2:8,16x2:16,4x16:4
128#2250263x1:2,2x2:4,4x2:8,2x4:4,2x4:8,8x4:16,3x16:2,16:4
128#2251263x1:2,2x2:4,4x2:8,2x4:4,2x4:8,8x4:16,16:2,3x16:4
128#2252383x1:2,6x2:4,8x2:8,16x2:16,4x16:4
128#2255263x1:2,2x2:4,4x2:8,2x4:4,2x4:8,8x4:16,4x16:4
128C2×D32 #2259383x1:2,2x2:4,4x2:8,8x2:16,16x2:32,4x16:2
128C2×Q64 #2261383x1:2,2x2:4,4x2:8,8x2:16,16x2:32,4x16:4
128#2263261:2,2:2,2x2:4,2x2:8,4x2:16,4:8,2x4:16,8x4:32,3x16:2,16:4
128#2264261:2,2:2,2x2:4,2x2:8,4x2:16,4:8,2x4:16,8x4:32,16:2,3x16:4
128C2×#447 #2996387x1:2,4x2:2,4x2:4,8x4:2,2x4:4,8x4:8,2x8:2,2x8:4
128C2×#451 #2999387x1:2,4x2:2,4x2:4,10x4:4,8x4:8,4x8:4
128#3008323x1:2,2x2:2,4x2:4,8x4:2,4x4:4,4x4:8,2x8:2,2x8:4,2x8:8
128#3011323x1:2,2x2:2,4x2:4,4x4:2,8x4:4,4x4:8,4x8:4,2x8:8
128C2×#493 #3144447x1:2,12x2:4,16x2:8,8x8:2
128C2×#494 #3145447x1:2,12x2:4,16x2:8,8x8:4
128#3155323x1:2,2x2:2,4x2:4,4x2:8,4x4:4,6x4:8,6x8:2,2x8:4
128#3156323x1:2,2x2:2,4x2:4,4x2:8,4x4:4,6x4:8,2x8:2,6x8:4
128C2×#500 #3159447x1:2,12x2:4,16x2:8,8x8:4
128#3164323x1:2,2x2:2,4x2:4,4x2:8,4x4:4,6x4:8,8x8:4
128#3199263x1:2,2x2:4,3x4:2,3x4:4,4x4:8,4x8:2,4x8:4,2x8:8
128#3202263x1:2,2x2:4,3x4:2,3x4:4,4x4:8,8x8:4,2x8:8
128#3203263x1:2,2x2:4,3x4:2,3x4:4,4x4:8,2x8:2,6x8:4,2x8:8
128#3205323x1:2,2x2:2,8x2:4,2x4:4,8x4:8,6x8:2,2x8:4
128#3209323x1:2,2x2:2,8x2:4,2x4:4,8x4:8,8x8:4
128#3220263x1:2,2x2:4,4:2,5x4:4,4x4:8,5x8:2,3x8:4,2x8:8
128#3223263x1:2,2x2:4,4:2,5x4:4,4x4:8,8:2,7x8:4,2x8:8
128#3226323x1:2,2x2:2,8x2:4,2x4:4,8x4:8,2x8:2,6x8:4
128#3230323x1:2,2x2:2,8x2:4,2x4:4,8x4:8,8x8:4
128#3243263x1:2,2x2:4,4:2,5x4:4,4x4:8,8:2,7x8:4,2x8:8
128#3259263x1:2,2x2:4,4:2,5x4:4,4x4:8,4x8:2,4x8:4,2x8:8
128#3261263x1:2,2x2:4,4:2,5x4:4,4x4:8,8x8:4,2x8:8
128#3262263x1:2,2x2:4,4:2,5x4:4,4x4:8,2x8:2,6x8:4,2x8:8
128#3264293x1:2,2x2:2,2x2:4,5x4:2,4x4:4,4x4:8,3x8:2,3x8:4,2x8:8

About ambivalent but not rational groups →