metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.61D14, Dic14.23D4, C4.49(D4×D7), C28⋊C8⋊28C2, C28.23(C2×D4), (C2×D4).44D14, (C2×C28).269D4, (C2×Q8).34D14, C7⋊5(Q8.D4), C4.4D4.4D7, (C4×Dic14)⋊21C2, C28.65(C4○D4), C4.1(D4⋊2D7), Q8⋊Dic7⋊19C2, C14.103(C4○D8), C2.10(C28⋊2D4), (C2×C28).372C23, (C4×C28).103C22, D4⋊Dic7.11C2, (D4×C14).60C22, (Q8×C14).52C22, C14.101(C4⋊D4), C4⋊Dic7.340C22, C2.22(D4.8D14), C2.17(D4.9D14), C14.118(C8.C22), (C2×Dic14).272C22, (C2×C7⋊Q16)⋊12C2, (C2×D4.D7).6C2, (C2×C14).503(C2×D4), (C2×C4).59(C7⋊D4), (C2×C7⋊C8).119C22, (C7×C4.4D4).2C2, (C2×C4).472(C22×D7), C22.178(C2×C7⋊D4), SmallGroup(448,588)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.61D14
G = < a,b,c,d | a4=b4=c14=1, d2=a2b, ab=ba, cac-1=dad-1=a-1b2, cbc-1=b-1, bd=db, dcd-1=b-1c-1 >
Subgroups: 460 in 112 conjugacy classes, 41 normal (39 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C8, C2×C4, C2×C4, D4, Q8, C23, C14, C14, C42, C42, C22⋊C4, C4⋊C4, C2×C8, SD16, Q16, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, C2×C14, C2×C14, D4⋊C4, Q8⋊C4, C4⋊C8, C4×Q8, C4.4D4, C2×SD16, C2×Q16, C7⋊C8, Dic14, Dic14, C2×Dic7, C2×C28, C2×C28, C7×D4, C7×Q8, C22×C14, Q8.D4, C2×C7⋊C8, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D4.D7, C7⋊Q16, C4×C28, C7×C22⋊C4, C2×Dic14, D4×C14, Q8×C14, C28⋊C8, D4⋊Dic7, Q8⋊Dic7, C4×Dic14, C2×D4.D7, C2×C7⋊Q16, C7×C4.4D4, C42.61D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C4○D4, D14, C4⋊D4, C4○D8, C8.C22, C7⋊D4, C22×D7, Q8.D4, D4×D7, D4⋊2D7, C2×C7⋊D4, C28⋊2D4, D4.8D14, D4.9D14, C42.61D14
►On 224 points
Generators in S224
(1 60 28 107)(2 68 22 101)(3 62 23 109)(4 70 24 103)(5 64 25 111)(6 58 26 105)(7 66 27 99)(8 108 15 61)(9 102 16 69)(10 110 17 63)(11 104 18 57)(12 112 19 65)(13 106 20 59)(14 100 21 67)(29 158 148 191)(30 222 149 209)(31 160 150 193)(32 224 151 197)(33 162 152 195)(34 212 153 199)(35 164 154 183)(36 214 141 201)(37 166 142 185)(38 216 143 203)(39 168 144 187)(40 218 145 205)(41 156 146 189)(42 220 147 207)(43 118 50 176)(44 170 51 126)(45 120 52 178)(46 172 53 114)(47 122 54 180)(48 174 55 116)(49 124 56 182)(71 206 133 219)(72 190 134 157)(73 208 135 221)(74 192 136 159)(75 210 137 223)(76 194 138 161)(77 198 139 211)(78 196 140 163)(79 200 127 213)(80 184 128 165)(81 202 129 215)(82 186 130 167)(83 204 131 217)(84 188 132 155)(85 181 92 123)(86 117 93 175)(87 169 94 125)(88 119 95 177)(89 171 96 113)(90 121 97 179)(91 173 98 115)
(1 120 14 113)(2 114 8 121)(3 122 9 115)(4 116 10 123)(5 124 11 117)(6 118 12 125)(7 126 13 119)(15 179 22 172)(16 173 23 180)(17 181 24 174)(18 175 25 182)(19 169 26 176)(20 177 27 170)(21 171 28 178)(29 141 73 128)(30 129 74 142)(31 143 75 130)(32 131 76 144)(33 145 77 132)(34 133 78 146)(35 147 79 134)(36 135 80 148)(37 149 81 136)(38 137 82 150)(39 151 83 138)(40 139 84 152)(41 153 71 140)(42 127 72 154)(43 65 94 105)(44 106 95 66)(45 67 96 107)(46 108 97 68)(47 69 98 109)(48 110 85 70)(49 57 86 111)(50 112 87 58)(51 59 88 99)(52 100 89 60)(53 61 90 101)(54 102 91 62)(55 63 92 103)(56 104 93 64)(155 162 205 198)(156 199 206 163)(157 164 207 200)(158 201 208 165)(159 166 209 202)(160 203 210 167)(161 168 197 204)(183 220 213 190)(184 191 214 221)(185 222 215 192)(186 193 216 223)(187 224 217 194)(188 195 218 211)(189 212 219 196)
(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)(197 198 199 200 201 202 203 204 205 206 207 208 209 210)(211 212 213 214 215 216 217 218 219 220 221 222 223 224)
(1 199 178 219 14 163 171 189)(2 205 172 211 8 155 179 195)(3 197 180 217 9 161 173 187)(4 203 174 223 10 167 181 193)(5 209 182 215 11 159 175 185)(6 201 176 221 12 165 169 191)(7 207 170 213 13 157 177 183)(15 188 121 162 22 218 114 198)(16 194 115 168 23 224 122 204)(17 186 123 160 24 216 116 210)(18 192 117 166 25 222 124 202)(19 184 125 158 26 214 118 208)(20 190 119 164 27 220 126 200)(21 196 113 156 28 212 120 206)(29 65 36 87 73 105 80 50)(30 93 81 111 74 56 37 57)(31 63 38 85 75 103 82 48)(32 91 83 109 76 54 39 69)(33 61 40 97 77 101 84 46)(34 89 71 107 78 52 41 67)(35 59 42 95 79 99 72 44)(43 148 112 141 94 135 58 128)(45 146 100 153 96 133 60 140)(47 144 102 151 98 131 62 138)(49 142 104 149 86 129 64 136)(51 154 106 147 88 127 66 134)(53 152 108 145 90 139 68 132)(55 150 110 143 92 137 70 130)
G:=sub<Sym(224)| (1,60,28,107)(2,68,22,101)(3,62,23,109)(4,70,24,103)(5,64,25,111)(6,58,26,105)(7,66,27,99)(8,108,15,61)(9,102,16,69)(10,110,17,63)(11,104,18,57)(12,112,19,65)(13,106,20,59)(14,100,21,67)(29,158,148,191)(30,222,149,209)(31,160,150,193)(32,224,151,197)(33,162,152,195)(34,212,153,199)(35,164,154,183)(36,214,141,201)(37,166,142,185)(38,216,143,203)(39,168,144,187)(40,218,145,205)(41,156,146,189)(42,220,147,207)(43,118,50,176)(44,170,51,126)(45,120,52,178)(46,172,53,114)(47,122,54,180)(48,174,55,116)(49,124,56,182)(71,206,133,219)(72,190,134,157)(73,208,135,221)(74,192,136,159)(75,210,137,223)(76,194,138,161)(77,198,139,211)(78,196,140,163)(79,200,127,213)(80,184,128,165)(81,202,129,215)(82,186,130,167)(83,204,131,217)(84,188,132,155)(85,181,92,123)(86,117,93,175)(87,169,94,125)(88,119,95,177)(89,171,96,113)(90,121,97,179)(91,173,98,115), (1,120,14,113)(2,114,8,121)(3,122,9,115)(4,116,10,123)(5,124,11,117)(6,118,12,125)(7,126,13,119)(15,179,22,172)(16,173,23,180)(17,181,24,174)(18,175,25,182)(19,169,26,176)(20,177,27,170)(21,171,28,178)(29,141,73,128)(30,129,74,142)(31,143,75,130)(32,131,76,144)(33,145,77,132)(34,133,78,146)(35,147,79,134)(36,135,80,148)(37,149,81,136)(38,137,82,150)(39,151,83,138)(40,139,84,152)(41,153,71,140)(42,127,72,154)(43,65,94,105)(44,106,95,66)(45,67,96,107)(46,108,97,68)(47,69,98,109)(48,110,85,70)(49,57,86,111)(50,112,87,58)(51,59,88,99)(52,100,89,60)(53,61,90,101)(54,102,91,62)(55,63,92,103)(56,104,93,64)(155,162,205,198)(156,199,206,163)(157,164,207,200)(158,201,208,165)(159,166,209,202)(160,203,210,167)(161,168,197,204)(183,220,213,190)(184,191,214,221)(185,222,215,192)(186,193,216,223)(187,224,217,194)(188,195,218,211)(189,212,219,196), (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)(197,198,199,200,201,202,203,204,205,206,207,208,209,210)(211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,199,178,219,14,163,171,189)(2,205,172,211,8,155,179,195)(3,197,180,217,9,161,173,187)(4,203,174,223,10,167,181,193)(5,209,182,215,11,159,175,185)(6,201,176,221,12,165,169,191)(7,207,170,213,13,157,177,183)(15,188,121,162,22,218,114,198)(16,194,115,168,23,224,122,204)(17,186,123,160,24,216,116,210)(18,192,117,166,25,222,124,202)(19,184,125,158,26,214,118,208)(20,190,119,164,27,220,126,200)(21,196,113,156,28,212,120,206)(29,65,36,87,73,105,80,50)(30,93,81,111,74,56,37,57)(31,63,38,85,75,103,82,48)(32,91,83,109,76,54,39,69)(33,61,40,97,77,101,84,46)(34,89,71,107,78,52,41,67)(35,59,42,95,79,99,72,44)(43,148,112,141,94,135,58,128)(45,146,100,153,96,133,60,140)(47,144,102,151,98,131,62,138)(49,142,104,149,86,129,64,136)(51,154,106,147,88,127,66,134)(53,152,108,145,90,139,68,132)(55,150,110,143,92,137,70,130)>;
G:=Group( (1,60,28,107)(2,68,22,101)(3,62,23,109)(4,70,24,103)(5,64,25,111)(6,58,26,105)(7,66,27,99)(8,108,15,61)(9,102,16,69)(10,110,17,63)(11,104,18,57)(12,112,19,65)(13,106,20,59)(14,100,21,67)(29,158,148,191)(30,222,149,209)(31,160,150,193)(32,224,151,197)(33,162,152,195)(34,212,153,199)(35,164,154,183)(36,214,141,201)(37,166,142,185)(38,216,143,203)(39,168,144,187)(40,218,145,205)(41,156,146,189)(42,220,147,207)(43,118,50,176)(44,170,51,126)(45,120,52,178)(46,172,53,114)(47,122,54,180)(48,174,55,116)(49,124,56,182)(71,206,133,219)(72,190,134,157)(73,208,135,221)(74,192,136,159)(75,210,137,223)(76,194,138,161)(77,198,139,211)(78,196,140,163)(79,200,127,213)(80,184,128,165)(81,202,129,215)(82,186,130,167)(83,204,131,217)(84,188,132,155)(85,181,92,123)(86,117,93,175)(87,169,94,125)(88,119,95,177)(89,171,96,113)(90,121,97,179)(91,173,98,115), (1,120,14,113)(2,114,8,121)(3,122,9,115)(4,116,10,123)(5,124,11,117)(6,118,12,125)(7,126,13,119)(15,179,22,172)(16,173,23,180)(17,181,24,174)(18,175,25,182)(19,169,26,176)(20,177,27,170)(21,171,28,178)(29,141,73,128)(30,129,74,142)(31,143,75,130)(32,131,76,144)(33,145,77,132)(34,133,78,146)(35,147,79,134)(36,135,80,148)(37,149,81,136)(38,137,82,150)(39,151,83,138)(40,139,84,152)(41,153,71,140)(42,127,72,154)(43,65,94,105)(44,106,95,66)(45,67,96,107)(46,108,97,68)(47,69,98,109)(48,110,85,70)(49,57,86,111)(50,112,87,58)(51,59,88,99)(52,100,89,60)(53,61,90,101)(54,102,91,62)(55,63,92,103)(56,104,93,64)(155,162,205,198)(156,199,206,163)(157,164,207,200)(158,201,208,165)(159,166,209,202)(160,203,210,167)(161,168,197,204)(183,220,213,190)(184,191,214,221)(185,222,215,192)(186,193,216,223)(187,224,217,194)(188,195,218,211)(189,212,219,196), (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)(197,198,199,200,201,202,203,204,205,206,207,208,209,210)(211,212,213,214,215,216,217,218,219,220,221,222,223,224), (1,199,178,219,14,163,171,189)(2,205,172,211,8,155,179,195)(3,197,180,217,9,161,173,187)(4,203,174,223,10,167,181,193)(5,209,182,215,11,159,175,185)(6,201,176,221,12,165,169,191)(7,207,170,213,13,157,177,183)(15,188,121,162,22,218,114,198)(16,194,115,168,23,224,122,204)(17,186,123,160,24,216,116,210)(18,192,117,166,25,222,124,202)(19,184,125,158,26,214,118,208)(20,190,119,164,27,220,126,200)(21,196,113,156,28,212,120,206)(29,65,36,87,73,105,80,50)(30,93,81,111,74,56,37,57)(31,63,38,85,75,103,82,48)(32,91,83,109,76,54,39,69)(33,61,40,97,77,101,84,46)(34,89,71,107,78,52,41,67)(35,59,42,95,79,99,72,44)(43,148,112,141,94,135,58,128)(45,146,100,153,96,133,60,140)(47,144,102,151,98,131,62,138)(49,142,104,149,86,129,64,136)(51,154,106,147,88,127,66,134)(53,152,108,145,90,139,68,132)(55,150,110,143,92,137,70,130) );
G=PermutationGroup([[(1,60,28,107),(2,68,22,101),(3,62,23,109),(4,70,24,103),(5,64,25,111),(6,58,26,105),(7,66,27,99),(8,108,15,61),(9,102,16,69),(10,110,17,63),(11,104,18,57),(12,112,19,65),(13,106,20,59),(14,100,21,67),(29,158,148,191),(30,222,149,209),(31,160,150,193),(32,224,151,197),(33,162,152,195),(34,212,153,199),(35,164,154,183),(36,214,141,201),(37,166,142,185),(38,216,143,203),(39,168,144,187),(40,218,145,205),(41,156,146,189),(42,220,147,207),(43,118,50,176),(44,170,51,126),(45,120,52,178),(46,172,53,114),(47,122,54,180),(48,174,55,116),(49,124,56,182),(71,206,133,219),(72,190,134,157),(73,208,135,221),(74,192,136,159),(75,210,137,223),(76,194,138,161),(77,198,139,211),(78,196,140,163),(79,200,127,213),(80,184,128,165),(81,202,129,215),(82,186,130,167),(83,204,131,217),(84,188,132,155),(85,181,92,123),(86,117,93,175),(87,169,94,125),(88,119,95,177),(89,171,96,113),(90,121,97,179),(91,173,98,115)], [(1,120,14,113),(2,114,8,121),(3,122,9,115),(4,116,10,123),(5,124,11,117),(6,118,12,125),(7,126,13,119),(15,179,22,172),(16,173,23,180),(17,181,24,174),(18,175,25,182),(19,169,26,176),(20,177,27,170),(21,171,28,178),(29,141,73,128),(30,129,74,142),(31,143,75,130),(32,131,76,144),(33,145,77,132),(34,133,78,146),(35,147,79,134),(36,135,80,148),(37,149,81,136),(38,137,82,150),(39,151,83,138),(40,139,84,152),(41,153,71,140),(42,127,72,154),(43,65,94,105),(44,106,95,66),(45,67,96,107),(46,108,97,68),(47,69,98,109),(48,110,85,70),(49,57,86,111),(50,112,87,58),(51,59,88,99),(52,100,89,60),(53,61,90,101),(54,102,91,62),(55,63,92,103),(56,104,93,64),(155,162,205,198),(156,199,206,163),(157,164,207,200),(158,201,208,165),(159,166,209,202),(160,203,210,167),(161,168,197,204),(183,220,213,190),(184,191,214,221),(185,222,215,192),(186,193,216,223),(187,224,217,194),(188,195,218,211),(189,212,219,196)], [(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),(197,198,199,200,201,202,203,204,205,206,207,208,209,210),(211,212,213,214,215,216,217,218,219,220,221,222,223,224)], [(1,199,178,219,14,163,171,189),(2,205,172,211,8,155,179,195),(3,197,180,217,9,161,173,187),(4,203,174,223,10,167,181,193),(5,209,182,215,11,159,175,185),(6,201,176,221,12,165,169,191),(7,207,170,213,13,157,177,183),(15,188,121,162,22,218,114,198),(16,194,115,168,23,224,122,204),(17,186,123,160,24,216,116,210),(18,192,117,166,25,222,124,202),(19,184,125,158,26,214,118,208),(20,190,119,164,27,220,126,200),(21,196,113,156,28,212,120,206),(29,65,36,87,73,105,80,50),(30,93,81,111,74,56,37,57),(31,63,38,85,75,103,82,48),(32,91,83,109,76,54,39,69),(33,61,40,97,77,101,84,46),(34,89,71,107,78,52,41,67),(35,59,42,95,79,99,72,44),(43,148,112,141,94,135,58,128),(45,146,100,153,96,133,60,140),(47,144,102,151,98,131,62,138),(49,142,104,149,86,129,64,136),(51,154,106,147,88,127,66,134),(53,152,108,145,90,139,68,132),(55,150,110,143,92,137,70,130)]])
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 7A | 7B | 7C | 8A | 8B | 8C | 8D | 14A | ··· | 14I | 14J | ··· | 14O | 28A | ··· | 28R | 28S | ··· | 28X |
| order | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 8 | 8 | 8 | 8 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 8 | 2 | 2 | 2 | 2 | 4 | 8 | 28 | 28 | 28 | 28 | 2 | 2 | 2 | 28 | 28 | 28 | 28 | 2 | ··· | 2 | 8 | ··· | 8 | 4 | ··· | 4 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | + | - | - | ||||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D4 | D7 | C4○D4 | D14 | D14 | D14 | C4○D8 | C7⋊D4 | C8.C22 | D4×D7 | D4⋊2D7 | D4.8D14 | D4.9D14 |
| kernel | C42.61D14 | C28⋊C8 | D4⋊Dic7 | Q8⋊Dic7 | C4×Dic14 | C2×D4.D7 | C2×C7⋊Q16 | C7×C4.4D4 | Dic14 | C2×C28 | C4.4D4 | C28 | C42 | C2×D4 | C2×Q8 | C14 | C2×C4 | C14 | C4 | C4 | C2 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 3 | 2 | 3 | 3 | 3 | 4 | 12 | 1 | 3 | 3 | 6 | 6 |
Matrix representation of C42.61D14 ►in GL6(𝔽113)
| 15 | 0 | 0 | 0 | 0 | 0 |
| 0 | 15 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 29 | 97 |
| 0 | 0 | 0 | 0 | 95 | 84 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 112 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 112 | 0 | 0 | 0 |
| 0 | 0 | 0 | 112 | 0 | 0 |
| 0 | 0 | 0 | 0 | 112 | 0 |
| 0 | 0 | 0 | 0 | 0 | 112 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 112 | 0 | 0 | 0 | 0 |
| 0 | 0 | 49 | 4 | 0 | 0 |
| 0 | 0 | 0 | 83 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 46 | 112 |
| 82 | 31 | 0 | 0 | 0 | 0 |
| 82 | 82 | 0 | 0 | 0 | 0 |
| 0 | 0 | 60 | 10 | 0 | 0 |
| 0 | 0 | 58 | 53 | 0 | 0 |
| 0 | 0 | 0 | 0 | 29 | 97 |
| 0 | 0 | 0 | 0 | 109 | 84 |
G:=sub<GL(6,GF(113))| [15,0,0,0,0,0,0,15,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,29,95,0,0,0,0,97,84],[0,112,0,0,0,0,1,0,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112,0,0,0,0,0,0,112],[1,0,0,0,0,0,0,112,0,0,0,0,0,0,49,0,0,0,0,0,4,83,0,0,0,0,0,0,1,46,0,0,0,0,0,112],[82,82,0,0,0,0,31,82,0,0,0,0,0,0,60,58,0,0,0,0,10,53,0,0,0,0,0,0,29,109,0,0,0,0,97,84] >;
C42.61D14 in GAP, Magma, Sage, TeX
C_4^2._{61}D_{14} % in TeX
G:=Group("C4^2.61D14"); // GroupNames label
G:=SmallGroup(448,588);
// by ID
G=gap.SmallGroup(448,588);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,112,344,254,219,1123,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=c^14=1,d^2=a^2*b,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1*b^2,c*b*c^-1=b^-1,b*d=d*b,d*c*d^-1=b^-1*c^-1>;
// generators/relations