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## G = C2×C25⋊D5order 500 = 22·53

### Direct product of C2 and C25⋊D5

Aliases: C2×C25⋊D5, C50⋊D5, C10⋊D25, C52D50, C252D10, C52.4D10, (C5×C50)⋊3C2, (C5×C25)⋊4C22, (C5×C10).8D5, C10.2(C5⋊D5), C5.(C2×C5⋊D5), SmallGroup(500,32)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C5×C25 — C2×C25⋊D5
 Chief series C1 — C5 — C52 — C5×C25 — C25⋊D5 — C2×C25⋊D5
 Lower central C5×C25 — C2×C25⋊D5
 Upper central C1 — C2

Generators and relations for C2×C25⋊D5
G = < a,b,c,d | a2=b25=c5=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b-1, dcd=c-1 >

Subgroups: 946 in 70 conjugacy classes, 31 normal (9 characteristic)
C1, C2, C2, C22, C5, C5, D5, C10, C10, D10, C25, C52, D25, C50, C5⋊D5, C5×C10, D50, C2×C5⋊D5, C5×C25, C25⋊D5, C5×C50, C2×C25⋊D5
Quotients: C1, C2, C22, D5, D10, D25, C5⋊D5, D50, C2×C5⋊D5, C25⋊D5, C2×C25⋊D5

Smallest permutation representation of C2×C25⋊D5
On 250 points
Generators in S250
(1 121)(2 122)(3 123)(4 124)(5 125)(6 101)(7 102)(8 103)(9 104)(10 105)(11 106)(12 107)(13 108)(14 109)(15 110)(16 111)(17 112)(18 113)(19 114)(20 115)(21 116)(22 117)(23 118)(24 119)(25 120)(26 198)(27 199)(28 200)(29 176)(30 177)(31 178)(32 179)(33 180)(34 181)(35 182)(36 183)(37 184)(38 185)(39 186)(40 187)(41 188)(42 189)(43 190)(44 191)(45 192)(46 193)(47 194)(48 195)(49 196)(50 197)(51 97)(52 98)(53 99)(54 100)(55 76)(56 77)(57 78)(58 79)(59 80)(60 81)(61 82)(62 83)(63 84)(64 85)(65 86)(66 87)(67 88)(68 89)(69 90)(70 91)(71 92)(72 93)(73 94)(74 95)(75 96)(126 234)(127 235)(128 236)(129 237)(130 238)(131 239)(132 240)(133 241)(134 242)(135 243)(136 244)(137 245)(138 246)(139 247)(140 248)(141 249)(142 250)(143 226)(144 227)(145 228)(146 229)(147 230)(148 231)(149 232)(150 233)(151 218)(152 219)(153 220)(154 221)(155 222)(156 223)(157 224)(158 225)(159 201)(160 202)(161 203)(162 204)(163 205)(164 206)(165 207)(166 208)(167 209)(168 210)(169 211)(170 212)(171 213)(172 214)(173 215)(174 216)(175 217)
(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)(201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225)(226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250)
(1 133 94 29 223)(2 134 95 30 224)(3 135 96 31 225)(4 136 97 32 201)(5 137 98 33 202)(6 138 99 34 203)(7 139 100 35 204)(8 140 76 36 205)(9 141 77 37 206)(10 142 78 38 207)(11 143 79 39 208)(12 144 80 40 209)(13 145 81 41 210)(14 146 82 42 211)(15 147 83 43 212)(16 148 84 44 213)(17 149 85 45 214)(18 150 86 46 215)(19 126 87 47 216)(20 127 88 48 217)(21 128 89 49 218)(22 129 90 50 219)(23 130 91 26 220)(24 131 92 27 221)(25 132 93 28 222)(51 179 159 124 244)(52 180 160 125 245)(53 181 161 101 246)(54 182 162 102 247)(55 183 163 103 248)(56 184 164 104 249)(57 185 165 105 250)(58 186 166 106 226)(59 187 167 107 227)(60 188 168 108 228)(61 189 169 109 229)(62 190 170 110 230)(63 191 171 111 231)(64 192 172 112 232)(65 193 173 113 233)(66 194 174 114 234)(67 195 175 115 235)(68 196 151 116 236)(69 197 152 117 237)(70 198 153 118 238)(71 199 154 119 239)(72 200 155 120 240)(73 176 156 121 241)(74 177 157 122 242)(75 178 158 123 243)
(1 223)(2 222)(3 221)(4 220)(5 219)(6 218)(7 217)(8 216)(9 215)(10 214)(11 213)(12 212)(13 211)(14 210)(15 209)(16 208)(17 207)(18 206)(19 205)(20 204)(21 203)(22 202)(23 201)(24 225)(25 224)(26 136)(27 135)(28 134)(29 133)(30 132)(31 131)(32 130)(33 129)(34 128)(35 127)(36 126)(37 150)(38 149)(39 148)(40 147)(41 146)(42 145)(43 144)(44 143)(45 142)(46 141)(47 140)(48 139)(49 138)(50 137)(51 70)(52 69)(53 68)(54 67)(55 66)(56 65)(57 64)(58 63)(59 62)(60 61)(71 75)(72 74)(76 87)(77 86)(78 85)(79 84)(80 83)(81 82)(88 100)(89 99)(90 98)(91 97)(92 96)(93 95)(101 151)(102 175)(103 174)(104 173)(105 172)(106 171)(107 170)(108 169)(109 168)(110 167)(111 166)(112 165)(113 164)(114 163)(115 162)(116 161)(117 160)(118 159)(119 158)(120 157)(121 156)(122 155)(123 154)(124 153)(125 152)(176 241)(177 240)(178 239)(179 238)(180 237)(181 236)(182 235)(183 234)(184 233)(185 232)(186 231)(187 230)(188 229)(189 228)(190 227)(191 226)(192 250)(193 249)(194 248)(195 247)(196 246)(197 245)(198 244)(199 243)(200 242)

G:=sub<Sym(250)| (1,121)(2,122)(3,123)(4,124)(5,125)(6,101)(7,102)(8,103)(9,104)(10,105)(11,106)(12,107)(13,108)(14,109)(15,110)(16,111)(17,112)(18,113)(19,114)(20,115)(21,116)(22,117)(23,118)(24,119)(25,120)(26,198)(27,199)(28,200)(29,176)(30,177)(31,178)(32,179)(33,180)(34,181)(35,182)(36,183)(37,184)(38,185)(39,186)(40,187)(41,188)(42,189)(43,190)(44,191)(45,192)(46,193)(47,194)(48,195)(49,196)(50,197)(51,97)(52,98)(53,99)(54,100)(55,76)(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)(65,86)(66,87)(67,88)(68,89)(69,90)(70,91)(71,92)(72,93)(73,94)(74,95)(75,96)(126,234)(127,235)(128,236)(129,237)(130,238)(131,239)(132,240)(133,241)(134,242)(135,243)(136,244)(137,245)(138,246)(139,247)(140,248)(141,249)(142,250)(143,226)(144,227)(145,228)(146,229)(147,230)(148,231)(149,232)(150,233)(151,218)(152,219)(153,220)(154,221)(155,222)(156,223)(157,224)(158,225)(159,201)(160,202)(161,203)(162,204)(163,205)(164,206)(165,207)(166,208)(167,209)(168,210)(169,211)(170,212)(171,213)(172,214)(173,215)(174,216)(175,217), (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)(201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225)(226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250), (1,133,94,29,223)(2,134,95,30,224)(3,135,96,31,225)(4,136,97,32,201)(5,137,98,33,202)(6,138,99,34,203)(7,139,100,35,204)(8,140,76,36,205)(9,141,77,37,206)(10,142,78,38,207)(11,143,79,39,208)(12,144,80,40,209)(13,145,81,41,210)(14,146,82,42,211)(15,147,83,43,212)(16,148,84,44,213)(17,149,85,45,214)(18,150,86,46,215)(19,126,87,47,216)(20,127,88,48,217)(21,128,89,49,218)(22,129,90,50,219)(23,130,91,26,220)(24,131,92,27,221)(25,132,93,28,222)(51,179,159,124,244)(52,180,160,125,245)(53,181,161,101,246)(54,182,162,102,247)(55,183,163,103,248)(56,184,164,104,249)(57,185,165,105,250)(58,186,166,106,226)(59,187,167,107,227)(60,188,168,108,228)(61,189,169,109,229)(62,190,170,110,230)(63,191,171,111,231)(64,192,172,112,232)(65,193,173,113,233)(66,194,174,114,234)(67,195,175,115,235)(68,196,151,116,236)(69,197,152,117,237)(70,198,153,118,238)(71,199,154,119,239)(72,200,155,120,240)(73,176,156,121,241)(74,177,157,122,242)(75,178,158,123,243), (1,223)(2,222)(3,221)(4,220)(5,219)(6,218)(7,217)(8,216)(9,215)(10,214)(11,213)(12,212)(13,211)(14,210)(15,209)(16,208)(17,207)(18,206)(19,205)(20,204)(21,203)(22,202)(23,201)(24,225)(25,224)(26,136)(27,135)(28,134)(29,133)(30,132)(31,131)(32,130)(33,129)(34,128)(35,127)(36,126)(37,150)(38,149)(39,148)(40,147)(41,146)(42,145)(43,144)(44,143)(45,142)(46,141)(47,140)(48,139)(49,138)(50,137)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61)(71,75)(72,74)(76,87)(77,86)(78,85)(79,84)(80,83)(81,82)(88,100)(89,99)(90,98)(91,97)(92,96)(93,95)(101,151)(102,175)(103,174)(104,173)(105,172)(106,171)(107,170)(108,169)(109,168)(110,167)(111,166)(112,165)(113,164)(114,163)(115,162)(116,161)(117,160)(118,159)(119,158)(120,157)(121,156)(122,155)(123,154)(124,153)(125,152)(176,241)(177,240)(178,239)(179,238)(180,237)(181,236)(182,235)(183,234)(184,233)(185,232)(186,231)(187,230)(188,229)(189,228)(190,227)(191,226)(192,250)(193,249)(194,248)(195,247)(196,246)(197,245)(198,244)(199,243)(200,242)>;

G:=Group( (1,121)(2,122)(3,123)(4,124)(5,125)(6,101)(7,102)(8,103)(9,104)(10,105)(11,106)(12,107)(13,108)(14,109)(15,110)(16,111)(17,112)(18,113)(19,114)(20,115)(21,116)(22,117)(23,118)(24,119)(25,120)(26,198)(27,199)(28,200)(29,176)(30,177)(31,178)(32,179)(33,180)(34,181)(35,182)(36,183)(37,184)(38,185)(39,186)(40,187)(41,188)(42,189)(43,190)(44,191)(45,192)(46,193)(47,194)(48,195)(49,196)(50,197)(51,97)(52,98)(53,99)(54,100)(55,76)(56,77)(57,78)(58,79)(59,80)(60,81)(61,82)(62,83)(63,84)(64,85)(65,86)(66,87)(67,88)(68,89)(69,90)(70,91)(71,92)(72,93)(73,94)(74,95)(75,96)(126,234)(127,235)(128,236)(129,237)(130,238)(131,239)(132,240)(133,241)(134,242)(135,243)(136,244)(137,245)(138,246)(139,247)(140,248)(141,249)(142,250)(143,226)(144,227)(145,228)(146,229)(147,230)(148,231)(149,232)(150,233)(151,218)(152,219)(153,220)(154,221)(155,222)(156,223)(157,224)(158,225)(159,201)(160,202)(161,203)(162,204)(163,205)(164,206)(165,207)(166,208)(167,209)(168,210)(169,211)(170,212)(171,213)(172,214)(173,215)(174,216)(175,217), (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)(201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225)(226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250), (1,133,94,29,223)(2,134,95,30,224)(3,135,96,31,225)(4,136,97,32,201)(5,137,98,33,202)(6,138,99,34,203)(7,139,100,35,204)(8,140,76,36,205)(9,141,77,37,206)(10,142,78,38,207)(11,143,79,39,208)(12,144,80,40,209)(13,145,81,41,210)(14,146,82,42,211)(15,147,83,43,212)(16,148,84,44,213)(17,149,85,45,214)(18,150,86,46,215)(19,126,87,47,216)(20,127,88,48,217)(21,128,89,49,218)(22,129,90,50,219)(23,130,91,26,220)(24,131,92,27,221)(25,132,93,28,222)(51,179,159,124,244)(52,180,160,125,245)(53,181,161,101,246)(54,182,162,102,247)(55,183,163,103,248)(56,184,164,104,249)(57,185,165,105,250)(58,186,166,106,226)(59,187,167,107,227)(60,188,168,108,228)(61,189,169,109,229)(62,190,170,110,230)(63,191,171,111,231)(64,192,172,112,232)(65,193,173,113,233)(66,194,174,114,234)(67,195,175,115,235)(68,196,151,116,236)(69,197,152,117,237)(70,198,153,118,238)(71,199,154,119,239)(72,200,155,120,240)(73,176,156,121,241)(74,177,157,122,242)(75,178,158,123,243), (1,223)(2,222)(3,221)(4,220)(5,219)(6,218)(7,217)(8,216)(9,215)(10,214)(11,213)(12,212)(13,211)(14,210)(15,209)(16,208)(17,207)(18,206)(19,205)(20,204)(21,203)(22,202)(23,201)(24,225)(25,224)(26,136)(27,135)(28,134)(29,133)(30,132)(31,131)(32,130)(33,129)(34,128)(35,127)(36,126)(37,150)(38,149)(39,148)(40,147)(41,146)(42,145)(43,144)(44,143)(45,142)(46,141)(47,140)(48,139)(49,138)(50,137)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61)(71,75)(72,74)(76,87)(77,86)(78,85)(79,84)(80,83)(81,82)(88,100)(89,99)(90,98)(91,97)(92,96)(93,95)(101,151)(102,175)(103,174)(104,173)(105,172)(106,171)(107,170)(108,169)(109,168)(110,167)(111,166)(112,165)(113,164)(114,163)(115,162)(116,161)(117,160)(118,159)(119,158)(120,157)(121,156)(122,155)(123,154)(124,153)(125,152)(176,241)(177,240)(178,239)(179,238)(180,237)(181,236)(182,235)(183,234)(184,233)(185,232)(186,231)(187,230)(188,229)(189,228)(190,227)(191,226)(192,250)(193,249)(194,248)(195,247)(196,246)(197,245)(198,244)(199,243)(200,242) );

G=PermutationGroup([[(1,121),(2,122),(3,123),(4,124),(5,125),(6,101),(7,102),(8,103),(9,104),(10,105),(11,106),(12,107),(13,108),(14,109),(15,110),(16,111),(17,112),(18,113),(19,114),(20,115),(21,116),(22,117),(23,118),(24,119),(25,120),(26,198),(27,199),(28,200),(29,176),(30,177),(31,178),(32,179),(33,180),(34,181),(35,182),(36,183),(37,184),(38,185),(39,186),(40,187),(41,188),(42,189),(43,190),(44,191),(45,192),(46,193),(47,194),(48,195),(49,196),(50,197),(51,97),(52,98),(53,99),(54,100),(55,76),(56,77),(57,78),(58,79),(59,80),(60,81),(61,82),(62,83),(63,84),(64,85),(65,86),(66,87),(67,88),(68,89),(69,90),(70,91),(71,92),(72,93),(73,94),(74,95),(75,96),(126,234),(127,235),(128,236),(129,237),(130,238),(131,239),(132,240),(133,241),(134,242),(135,243),(136,244),(137,245),(138,246),(139,247),(140,248),(141,249),(142,250),(143,226),(144,227),(145,228),(146,229),(147,230),(148,231),(149,232),(150,233),(151,218),(152,219),(153,220),(154,221),(155,222),(156,223),(157,224),(158,225),(159,201),(160,202),(161,203),(162,204),(163,205),(164,206),(165,207),(166,208),(167,209),(168,210),(169,211),(170,212),(171,213),(172,214),(173,215),(174,216),(175,217)], [(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),(201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225),(226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250)], [(1,133,94,29,223),(2,134,95,30,224),(3,135,96,31,225),(4,136,97,32,201),(5,137,98,33,202),(6,138,99,34,203),(7,139,100,35,204),(8,140,76,36,205),(9,141,77,37,206),(10,142,78,38,207),(11,143,79,39,208),(12,144,80,40,209),(13,145,81,41,210),(14,146,82,42,211),(15,147,83,43,212),(16,148,84,44,213),(17,149,85,45,214),(18,150,86,46,215),(19,126,87,47,216),(20,127,88,48,217),(21,128,89,49,218),(22,129,90,50,219),(23,130,91,26,220),(24,131,92,27,221),(25,132,93,28,222),(51,179,159,124,244),(52,180,160,125,245),(53,181,161,101,246),(54,182,162,102,247),(55,183,163,103,248),(56,184,164,104,249),(57,185,165,105,250),(58,186,166,106,226),(59,187,167,107,227),(60,188,168,108,228),(61,189,169,109,229),(62,190,170,110,230),(63,191,171,111,231),(64,192,172,112,232),(65,193,173,113,233),(66,194,174,114,234),(67,195,175,115,235),(68,196,151,116,236),(69,197,152,117,237),(70,198,153,118,238),(71,199,154,119,239),(72,200,155,120,240),(73,176,156,121,241),(74,177,157,122,242),(75,178,158,123,243)], [(1,223),(2,222),(3,221),(4,220),(5,219),(6,218),(7,217),(8,216),(9,215),(10,214),(11,213),(12,212),(13,211),(14,210),(15,209),(16,208),(17,207),(18,206),(19,205),(20,204),(21,203),(22,202),(23,201),(24,225),(25,224),(26,136),(27,135),(28,134),(29,133),(30,132),(31,131),(32,130),(33,129),(34,128),(35,127),(36,126),(37,150),(38,149),(39,148),(40,147),(41,146),(42,145),(43,144),(44,143),(45,142),(46,141),(47,140),(48,139),(49,138),(50,137),(51,70),(52,69),(53,68),(54,67),(55,66),(56,65),(57,64),(58,63),(59,62),(60,61),(71,75),(72,74),(76,87),(77,86),(78,85),(79,84),(80,83),(81,82),(88,100),(89,99),(90,98),(91,97),(92,96),(93,95),(101,151),(102,175),(103,174),(104,173),(105,172),(106,171),(107,170),(108,169),(109,168),(110,167),(111,166),(112,165),(113,164),(114,163),(115,162),(116,161),(117,160),(118,159),(119,158),(120,157),(121,156),(122,155),(123,154),(124,153),(125,152),(176,241),(177,240),(178,239),(179,238),(180,237),(181,236),(182,235),(183,234),(184,233),(185,232),(186,231),(187,230),(188,229),(189,228),(190,227),(191,226),(192,250),(193,249),(194,248),(195,247),(196,246),(197,245),(198,244),(199,243),(200,242)]])

128 conjugacy classes

 class 1 2A 2B 2C 5A ··· 5L 10A ··· 10L 25A ··· 25AX 50A ··· 50AX order 1 2 2 2 5 ··· 5 10 ··· 10 25 ··· 25 50 ··· 50 size 1 1 125 125 2 ··· 2 2 ··· 2 2 ··· 2 2 ··· 2

128 irreducible representations

 dim 1 1 1 2 2 2 2 2 2 type + + + + + + + + + image C1 C2 C2 D5 D5 D10 D10 D25 D50 kernel C2×C25⋊D5 C25⋊D5 C5×C50 C50 C5×C10 C25 C52 C10 C5 # reps 1 2 1 10 2 10 2 50 50

Matrix representation of C2×C25⋊D5 in GL4(𝔽101) generated by

 1 0 0 0 0 1 0 0 0 0 100 0 0 0 0 100
,
 99 62 0 0 90 88 0 0 0 0 43 93 0 0 8 69
,
 22 23 0 0 79 0 0 0 0 0 1 0 0 0 0 1
,
 79 1 0 0 22 22 0 0 0 0 1 0 0 0 22 100
G:=sub<GL(4,GF(101))| [1,0,0,0,0,1,0,0,0,0,100,0,0,0,0,100],[99,90,0,0,62,88,0,0,0,0,43,8,0,0,93,69],[22,79,0,0,23,0,0,0,0,0,1,0,0,0,0,1],[79,22,0,0,1,22,0,0,0,0,1,22,0,0,0,100] >;

C2×C25⋊D5 in GAP, Magma, Sage, TeX

C_2\times C_{25}\rtimes D_5
% in TeX

G:=Group("C2xC25:D5");
// GroupNames label

G:=SmallGroup(500,32);
// by ID

G=gap.SmallGroup(500,32);
# by ID

G:=PCGroup([5,-2,-2,-5,-5,-5,1742,1512,1603,10004]);
// Polycyclic

G:=Group<a,b,c,d|a^2=b^25=c^5=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,d*b*d=b^-1,d*c*d=c^-1>;
// generators/relations

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