direct product, abelian, monomial
Aliases: C142, SmallGroup(196,12)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C142 |
| C1 — C142 |
| C1 — C142 |
Generators and relations for C142
G = < a,b | a14=b14=1, ab=ba >
Smallest permutation representation of C142
►Regular action on 196 points
Generators in S196
(1 2 3 4 5 6 7 8 9 10 11 12 13 14)(15 16 17 18 19 20 21 22 23 24 25 26 27 28)(29 30 31 32 33 34 35 36 37 38 39 40 41 42)(43 44 45 46 47 48 49 50 51 52 53 54 55 56)(57 58 59 60 61 62 63 64 65 66 67 68 69 70)(71 72 73 74 75 76 77 78 79 80 81 82 83 84)(85 86 87 88 89 90 91 92 93 94 95 96 97 98)(99 100 101 102 103 104 105 106 107 108 109 110 111 112)(113 114 115 116 117 118 119 120 121 122 123 124 125 126)(127 128 129 130 131 132 133 134 135 136 137 138 139 140)(141 142 143 144 145 146 147 148 149 150 151 152 153 154)(155 156 157 158 159 160 161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176 177 178 179 180 181 182)(183 184 185 186 187 188 189 190 191 192 193 194 195 196)
(1 182 165 183 86 123 107 75 146 16 60 44 29 138)(2 169 166 184 87 124 108 76 147 17 61 45 30 139)(3 170 167 185 88 125 109 77 148 18 62 46 31 140)(4 171 168 186 89 126 110 78 149 19 63 47 32 127)(5 172 155 187 90 113 111 79 150 20 64 48 33 128)(6 173 156 188 91 114 112 80 151 21 65 49 34 129)(7 174 157 189 92 115 99 81 152 22 66 50 35 130)(8 175 158 190 93 116 100 82 153 23 67 51 36 131)(9 176 159 191 94 117 101 83 154 24 68 52 37 132)(10 177 160 192 95 118 102 84 141 25 69 53 38 133)(11 178 161 193 96 119 103 71 142 26 70 54 39 134)(12 179 162 194 97 120 104 72 143 27 57 55 40 135)(13 180 163 195 98 121 105 73 144 28 58 56 41 136)(14 181 164 196 85 122 106 74 145 15 59 43 42 137)
G:=sub<Sym(196)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42)(43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70)(71,72,73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96,97,98)(99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126)(127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154)(155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182)(183,184,185,186,187,188,189,190,191,192,193,194,195,196), (1,182,165,183,86,123,107,75,146,16,60,44,29,138)(2,169,166,184,87,124,108,76,147,17,61,45,30,139)(3,170,167,185,88,125,109,77,148,18,62,46,31,140)(4,171,168,186,89,126,110,78,149,19,63,47,32,127)(5,172,155,187,90,113,111,79,150,20,64,48,33,128)(6,173,156,188,91,114,112,80,151,21,65,49,34,129)(7,174,157,189,92,115,99,81,152,22,66,50,35,130)(8,175,158,190,93,116,100,82,153,23,67,51,36,131)(9,176,159,191,94,117,101,83,154,24,68,52,37,132)(10,177,160,192,95,118,102,84,141,25,69,53,38,133)(11,178,161,193,96,119,103,71,142,26,70,54,39,134)(12,179,162,194,97,120,104,72,143,27,57,55,40,135)(13,180,163,195,98,121,105,73,144,28,58,56,41,136)(14,181,164,196,85,122,106,74,145,15,59,43,42,137)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41,42)(43,44,45,46,47,48,49,50,51,52,53,54,55,56)(57,58,59,60,61,62,63,64,65,66,67,68,69,70)(71,72,73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96,97,98)(99,100,101,102,103,104,105,106,107,108,109,110,111,112)(113,114,115,116,117,118,119,120,121,122,123,124,125,126)(127,128,129,130,131,132,133,134,135,136,137,138,139,140)(141,142,143,144,145,146,147,148,149,150,151,152,153,154)(155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182)(183,184,185,186,187,188,189,190,191,192,193,194,195,196), (1,182,165,183,86,123,107,75,146,16,60,44,29,138)(2,169,166,184,87,124,108,76,147,17,61,45,30,139)(3,170,167,185,88,125,109,77,148,18,62,46,31,140)(4,171,168,186,89,126,110,78,149,19,63,47,32,127)(5,172,155,187,90,113,111,79,150,20,64,48,33,128)(6,173,156,188,91,114,112,80,151,21,65,49,34,129)(7,174,157,189,92,115,99,81,152,22,66,50,35,130)(8,175,158,190,93,116,100,82,153,23,67,51,36,131)(9,176,159,191,94,117,101,83,154,24,68,52,37,132)(10,177,160,192,95,118,102,84,141,25,69,53,38,133)(11,178,161,193,96,119,103,71,142,26,70,54,39,134)(12,179,162,194,97,120,104,72,143,27,57,55,40,135)(13,180,163,195,98,121,105,73,144,28,58,56,41,136)(14,181,164,196,85,122,106,74,145,15,59,43,42,137) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14),(15,16,17,18,19,20,21,22,23,24,25,26,27,28),(29,30,31,32,33,34,35,36,37,38,39,40,41,42),(43,44,45,46,47,48,49,50,51,52,53,54,55,56),(57,58,59,60,61,62,63,64,65,66,67,68,69,70),(71,72,73,74,75,76,77,78,79,80,81,82,83,84),(85,86,87,88,89,90,91,92,93,94,95,96,97,98),(99,100,101,102,103,104,105,106,107,108,109,110,111,112),(113,114,115,116,117,118,119,120,121,122,123,124,125,126),(127,128,129,130,131,132,133,134,135,136,137,138,139,140),(141,142,143,144,145,146,147,148,149,150,151,152,153,154),(155,156,157,158,159,160,161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176,177,178,179,180,181,182),(183,184,185,186,187,188,189,190,191,192,193,194,195,196)], [(1,182,165,183,86,123,107,75,146,16,60,44,29,138),(2,169,166,184,87,124,108,76,147,17,61,45,30,139),(3,170,167,185,88,125,109,77,148,18,62,46,31,140),(4,171,168,186,89,126,110,78,149,19,63,47,32,127),(5,172,155,187,90,113,111,79,150,20,64,48,33,128),(6,173,156,188,91,114,112,80,151,21,65,49,34,129),(7,174,157,189,92,115,99,81,152,22,66,50,35,130),(8,175,158,190,93,116,100,82,153,23,67,51,36,131),(9,176,159,191,94,117,101,83,154,24,68,52,37,132),(10,177,160,192,95,118,102,84,141,25,69,53,38,133),(11,178,161,193,96,119,103,71,142,26,70,54,39,134),(12,179,162,194,97,120,104,72,143,27,57,55,40,135),(13,180,163,195,98,121,105,73,144,28,58,56,41,136),(14,181,164,196,85,122,106,74,145,15,59,43,42,137)]])
C142 is a maximal subgroup of
C72⋊7D4
196 conjugacy classes
| class | 1 | 2A | 2B | 2C | 7A | ··· | 7AV | 14A | ··· | 14EN |
| order | 1 | 2 | 2 | 2 | 7 | ··· | 7 | 14 | ··· | 14 |
| size | 1 | 1 | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
196 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C7 | C14 |
| kernel | C142 | C7×C14 | C2×C14 | C14 |
| # reps | 1 | 3 | 48 | 144 |
Matrix representation of C142 ►in GL2(𝔽29) generated by
| 25 | 0 |
| 0 | 5 |
| 9 | 0 |
| 0 | 1 |
G:=sub<GL(2,GF(29))| [25,0,0,5],[9,0,0,1] >;
C142 in GAP, Magma, Sage, TeX
C_{14}^2 % in TeX
G:=Group("C14^2"); // GroupNames label
G:=SmallGroup(196,12);
// by ID
G=gap.SmallGroup(196,12);
# by ID
G:=PCGroup([4,-2,-2,-7,-7]);
// Polycyclic
G:=Group<a,b|a^14=b^14=1,a*b=b*a>;
// generators/relations
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