metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C42.177D14, C14.392- 1+4, C4⋊Q8⋊15D7, C4⋊C4.221D14, (Q8×Dic7)⋊24C2, (C4×D28).28C2, D14⋊2Q8⋊45C2, (C4×Dic14)⋊54C2, (C2×Q8).149D14, C28.139(C4○D4), C4.19(D4⋊2D7), (C4×C28).217C22, (C2×C28).109C23, (C2×C14).276C24, C4.41(Q8⋊2D7), C28.23D4.8C2, D14⋊C4.155C22, (C2×D28).274C22, C4⋊Dic7.386C22, (Q8×C14).143C22, C22.297(C23×D7), Dic7⋊C4.168C22, C7⋊8(C22.50C24), (C4×Dic7).165C22, (C2×Dic7).146C23, (C22×D7).121C23, C2.40(Q8.10D14), (C2×Dic14).304C22, (C7×C4⋊Q8)⋊18C2, C4⋊C4⋊7D7⋊43C2, C4⋊C4⋊D7⋊46C2, C14.123(C2×C4○D4), C2.66(C2×D4⋊2D7), C2.31(C2×Q8⋊2D7), (C2×C4×D7).149C22, (C7×C4⋊C4).219C22, (C2×C4).601(C22×D7), SmallGroup(448,1185)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C42.177D14
G = < a,b,c,d | a4=b4=1, c14=a2b2, d2=a2, ab=ba, cac-1=dad-1=a-1, cbc-1=b-1, dbd-1=a2b, dcd-1=b2c13 >
Subgroups: 876 in 212 conjugacy classes, 99 normal (27 characteristic)
C1, C2, C2, C4, C4, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, D7, C14, C42, C42, C22⋊C4, C4⋊C4, C4⋊C4, C22×C4, C2×D4, C2×Q8, C2×Q8, Dic7, C28, C28, D14, C2×C14, C42⋊C2, C4×D4, C4×Q8, C22⋊Q8, C4.4D4, C42⋊2C2, C4⋊Q8, Dic14, C4×D7, D28, C2×Dic7, C2×C28, C2×C28, C7×Q8, C22×D7, C22.50C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, C4⋊Dic7, D14⋊C4, C4×C28, C7×C4⋊C4, C2×Dic14, C2×C4×D7, C2×D28, Q8×C14, C4×Dic14, C4×D28, C4⋊C4⋊7D7, D14⋊2Q8, C4⋊C4⋊D7, Q8×Dic7, C28.23D4, C7×C4⋊Q8, C42.177D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2- 1+4, C22×D7, C22.50C24, D4⋊2D7, Q8⋊2D7, C23×D7, C2×D4⋊2D7, C2×Q8⋊2D7, Q8.10D14, C42.177D14
►On 224 points
Generators in S224
(1 185 111 70)(2 71 112 186)(3 187 85 72)(4 73 86 188)(5 189 87 74)(6 75 88 190)(7 191 89 76)(8 77 90 192)(9 193 91 78)(10 79 92 194)(11 195 93 80)(12 81 94 196)(13 169 95 82)(14 83 96 170)(15 171 97 84)(16 57 98 172)(17 173 99 58)(18 59 100 174)(19 175 101 60)(20 61 102 176)(21 177 103 62)(22 63 104 178)(23 179 105 64)(24 65 106 180)(25 181 107 66)(26 67 108 182)(27 183 109 68)(28 69 110 184)(29 220 159 117)(30 118 160 221)(31 222 161 119)(32 120 162 223)(33 224 163 121)(34 122 164 197)(35 198 165 123)(36 124 166 199)(37 200 167 125)(38 126 168 201)(39 202 141 127)(40 128 142 203)(41 204 143 129)(42 130 144 205)(43 206 145 131)(44 132 146 207)(45 208 147 133)(46 134 148 209)(47 210 149 135)(48 136 150 211)(49 212 151 137)(50 138 152 213)(51 214 153 139)(52 140 154 215)(53 216 155 113)(54 114 156 217)(55 218 157 115)(56 116 158 219)
(1 151 97 35)(2 36 98 152)(3 153 99 37)(4 38 100 154)(5 155 101 39)(6 40 102 156)(7 157 103 41)(8 42 104 158)(9 159 105 43)(10 44 106 160)(11 161 107 45)(12 46 108 162)(13 163 109 47)(14 48 110 164)(15 165 111 49)(16 50 112 166)(17 167 85 51)(18 52 86 168)(19 141 87 53)(20 54 88 142)(21 143 89 55)(22 56 90 144)(23 145 91 29)(24 30 92 146)(25 147 93 31)(26 32 94 148)(27 149 95 33)(28 34 96 150)(57 138 186 199)(58 200 187 139)(59 140 188 201)(60 202 189 113)(61 114 190 203)(62 204 191 115)(63 116 192 205)(64 206 193 117)(65 118 194 207)(66 208 195 119)(67 120 196 209)(68 210 169 121)(69 122 170 211)(70 212 171 123)(71 124 172 213)(72 214 173 125)(73 126 174 215)(74 216 175 127)(75 128 176 217)(76 218 177 129)(77 130 178 219)(78 220 179 131)(79 132 180 221)(80 222 181 133)(81 134 182 223)(82 224 183 135)(83 136 184 197)(84 198 185 137)
(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)
(1 136 111 211)(2 210 112 135)(3 134 85 209)(4 208 86 133)(5 132 87 207)(6 206 88 131)(7 130 89 205)(8 204 90 129)(9 128 91 203)(10 202 92 127)(11 126 93 201)(12 200 94 125)(13 124 95 199)(14 198 96 123)(15 122 97 197)(16 224 98 121)(17 120 99 223)(18 222 100 119)(19 118 101 221)(20 220 102 117)(21 116 103 219)(22 218 104 115)(23 114 105 217)(24 216 106 113)(25 140 107 215)(26 214 108 139)(27 138 109 213)(28 212 110 137)(29 176 159 61)(30 60 160 175)(31 174 161 59)(32 58 162 173)(33 172 163 57)(34 84 164 171)(35 170 165 83)(36 82 166 169)(37 196 167 81)(38 80 168 195)(39 194 141 79)(40 78 142 193)(41 192 143 77)(42 76 144 191)(43 190 145 75)(44 74 146 189)(45 188 147 73)(46 72 148 187)(47 186 149 71)(48 70 150 185)(49 184 151 69)(50 68 152 183)(51 182 153 67)(52 66 154 181)(53 180 155 65)(54 64 156 179)(55 178 157 63)(56 62 158 177)
G:=sub<Sym(224)| (1,185,111,70)(2,71,112,186)(3,187,85,72)(4,73,86,188)(5,189,87,74)(6,75,88,190)(7,191,89,76)(8,77,90,192)(9,193,91,78)(10,79,92,194)(11,195,93,80)(12,81,94,196)(13,169,95,82)(14,83,96,170)(15,171,97,84)(16,57,98,172)(17,173,99,58)(18,59,100,174)(19,175,101,60)(20,61,102,176)(21,177,103,62)(22,63,104,178)(23,179,105,64)(24,65,106,180)(25,181,107,66)(26,67,108,182)(27,183,109,68)(28,69,110,184)(29,220,159,117)(30,118,160,221)(31,222,161,119)(32,120,162,223)(33,224,163,121)(34,122,164,197)(35,198,165,123)(36,124,166,199)(37,200,167,125)(38,126,168,201)(39,202,141,127)(40,128,142,203)(41,204,143,129)(42,130,144,205)(43,206,145,131)(44,132,146,207)(45,208,147,133)(46,134,148,209)(47,210,149,135)(48,136,150,211)(49,212,151,137)(50,138,152,213)(51,214,153,139)(52,140,154,215)(53,216,155,113)(54,114,156,217)(55,218,157,115)(56,116,158,219), (1,151,97,35)(2,36,98,152)(3,153,99,37)(4,38,100,154)(5,155,101,39)(6,40,102,156)(7,157,103,41)(8,42,104,158)(9,159,105,43)(10,44,106,160)(11,161,107,45)(12,46,108,162)(13,163,109,47)(14,48,110,164)(15,165,111,49)(16,50,112,166)(17,167,85,51)(18,52,86,168)(19,141,87,53)(20,54,88,142)(21,143,89,55)(22,56,90,144)(23,145,91,29)(24,30,92,146)(25,147,93,31)(26,32,94,148)(27,149,95,33)(28,34,96,150)(57,138,186,199)(58,200,187,139)(59,140,188,201)(60,202,189,113)(61,114,190,203)(62,204,191,115)(63,116,192,205)(64,206,193,117)(65,118,194,207)(66,208,195,119)(67,120,196,209)(68,210,169,121)(69,122,170,211)(70,212,171,123)(71,124,172,213)(72,214,173,125)(73,126,174,215)(74,216,175,127)(75,128,176,217)(76,218,177,129)(77,130,178,219)(78,220,179,131)(79,132,180,221)(80,222,181,133)(81,134,182,223)(82,224,183,135)(83,136,184,197)(84,198,185,137), (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), (1,136,111,211)(2,210,112,135)(3,134,85,209)(4,208,86,133)(5,132,87,207)(6,206,88,131)(7,130,89,205)(8,204,90,129)(9,128,91,203)(10,202,92,127)(11,126,93,201)(12,200,94,125)(13,124,95,199)(14,198,96,123)(15,122,97,197)(16,224,98,121)(17,120,99,223)(18,222,100,119)(19,118,101,221)(20,220,102,117)(21,116,103,219)(22,218,104,115)(23,114,105,217)(24,216,106,113)(25,140,107,215)(26,214,108,139)(27,138,109,213)(28,212,110,137)(29,176,159,61)(30,60,160,175)(31,174,161,59)(32,58,162,173)(33,172,163,57)(34,84,164,171)(35,170,165,83)(36,82,166,169)(37,196,167,81)(38,80,168,195)(39,194,141,79)(40,78,142,193)(41,192,143,77)(42,76,144,191)(43,190,145,75)(44,74,146,189)(45,188,147,73)(46,72,148,187)(47,186,149,71)(48,70,150,185)(49,184,151,69)(50,68,152,183)(51,182,153,67)(52,66,154,181)(53,180,155,65)(54,64,156,179)(55,178,157,63)(56,62,158,177)>;
G:=Group( (1,185,111,70)(2,71,112,186)(3,187,85,72)(4,73,86,188)(5,189,87,74)(6,75,88,190)(7,191,89,76)(8,77,90,192)(9,193,91,78)(10,79,92,194)(11,195,93,80)(12,81,94,196)(13,169,95,82)(14,83,96,170)(15,171,97,84)(16,57,98,172)(17,173,99,58)(18,59,100,174)(19,175,101,60)(20,61,102,176)(21,177,103,62)(22,63,104,178)(23,179,105,64)(24,65,106,180)(25,181,107,66)(26,67,108,182)(27,183,109,68)(28,69,110,184)(29,220,159,117)(30,118,160,221)(31,222,161,119)(32,120,162,223)(33,224,163,121)(34,122,164,197)(35,198,165,123)(36,124,166,199)(37,200,167,125)(38,126,168,201)(39,202,141,127)(40,128,142,203)(41,204,143,129)(42,130,144,205)(43,206,145,131)(44,132,146,207)(45,208,147,133)(46,134,148,209)(47,210,149,135)(48,136,150,211)(49,212,151,137)(50,138,152,213)(51,214,153,139)(52,140,154,215)(53,216,155,113)(54,114,156,217)(55,218,157,115)(56,116,158,219), (1,151,97,35)(2,36,98,152)(3,153,99,37)(4,38,100,154)(5,155,101,39)(6,40,102,156)(7,157,103,41)(8,42,104,158)(9,159,105,43)(10,44,106,160)(11,161,107,45)(12,46,108,162)(13,163,109,47)(14,48,110,164)(15,165,111,49)(16,50,112,166)(17,167,85,51)(18,52,86,168)(19,141,87,53)(20,54,88,142)(21,143,89,55)(22,56,90,144)(23,145,91,29)(24,30,92,146)(25,147,93,31)(26,32,94,148)(27,149,95,33)(28,34,96,150)(57,138,186,199)(58,200,187,139)(59,140,188,201)(60,202,189,113)(61,114,190,203)(62,204,191,115)(63,116,192,205)(64,206,193,117)(65,118,194,207)(66,208,195,119)(67,120,196,209)(68,210,169,121)(69,122,170,211)(70,212,171,123)(71,124,172,213)(72,214,173,125)(73,126,174,215)(74,216,175,127)(75,128,176,217)(76,218,177,129)(77,130,178,219)(78,220,179,131)(79,132,180,221)(80,222,181,133)(81,134,182,223)(82,224,183,135)(83,136,184,197)(84,198,185,137), (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), (1,136,111,211)(2,210,112,135)(3,134,85,209)(4,208,86,133)(5,132,87,207)(6,206,88,131)(7,130,89,205)(8,204,90,129)(9,128,91,203)(10,202,92,127)(11,126,93,201)(12,200,94,125)(13,124,95,199)(14,198,96,123)(15,122,97,197)(16,224,98,121)(17,120,99,223)(18,222,100,119)(19,118,101,221)(20,220,102,117)(21,116,103,219)(22,218,104,115)(23,114,105,217)(24,216,106,113)(25,140,107,215)(26,214,108,139)(27,138,109,213)(28,212,110,137)(29,176,159,61)(30,60,160,175)(31,174,161,59)(32,58,162,173)(33,172,163,57)(34,84,164,171)(35,170,165,83)(36,82,166,169)(37,196,167,81)(38,80,168,195)(39,194,141,79)(40,78,142,193)(41,192,143,77)(42,76,144,191)(43,190,145,75)(44,74,146,189)(45,188,147,73)(46,72,148,187)(47,186,149,71)(48,70,150,185)(49,184,151,69)(50,68,152,183)(51,182,153,67)(52,66,154,181)(53,180,155,65)(54,64,156,179)(55,178,157,63)(56,62,158,177) );
G=PermutationGroup([[(1,185,111,70),(2,71,112,186),(3,187,85,72),(4,73,86,188),(5,189,87,74),(6,75,88,190),(7,191,89,76),(8,77,90,192),(9,193,91,78),(10,79,92,194),(11,195,93,80),(12,81,94,196),(13,169,95,82),(14,83,96,170),(15,171,97,84),(16,57,98,172),(17,173,99,58),(18,59,100,174),(19,175,101,60),(20,61,102,176),(21,177,103,62),(22,63,104,178),(23,179,105,64),(24,65,106,180),(25,181,107,66),(26,67,108,182),(27,183,109,68),(28,69,110,184),(29,220,159,117),(30,118,160,221),(31,222,161,119),(32,120,162,223),(33,224,163,121),(34,122,164,197),(35,198,165,123),(36,124,166,199),(37,200,167,125),(38,126,168,201),(39,202,141,127),(40,128,142,203),(41,204,143,129),(42,130,144,205),(43,206,145,131),(44,132,146,207),(45,208,147,133),(46,134,148,209),(47,210,149,135),(48,136,150,211),(49,212,151,137),(50,138,152,213),(51,214,153,139),(52,140,154,215),(53,216,155,113),(54,114,156,217),(55,218,157,115),(56,116,158,219)], [(1,151,97,35),(2,36,98,152),(3,153,99,37),(4,38,100,154),(5,155,101,39),(6,40,102,156),(7,157,103,41),(8,42,104,158),(9,159,105,43),(10,44,106,160),(11,161,107,45),(12,46,108,162),(13,163,109,47),(14,48,110,164),(15,165,111,49),(16,50,112,166),(17,167,85,51),(18,52,86,168),(19,141,87,53),(20,54,88,142),(21,143,89,55),(22,56,90,144),(23,145,91,29),(24,30,92,146),(25,147,93,31),(26,32,94,148),(27,149,95,33),(28,34,96,150),(57,138,186,199),(58,200,187,139),(59,140,188,201),(60,202,189,113),(61,114,190,203),(62,204,191,115),(63,116,192,205),(64,206,193,117),(65,118,194,207),(66,208,195,119),(67,120,196,209),(68,210,169,121),(69,122,170,211),(70,212,171,123),(71,124,172,213),(72,214,173,125),(73,126,174,215),(74,216,175,127),(75,128,176,217),(76,218,177,129),(77,130,178,219),(78,220,179,131),(79,132,180,221),(80,222,181,133),(81,134,182,223),(82,224,183,135),(83,136,184,197),(84,198,185,137)], [(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)], [(1,136,111,211),(2,210,112,135),(3,134,85,209),(4,208,86,133),(5,132,87,207),(6,206,88,131),(7,130,89,205),(8,204,90,129),(9,128,91,203),(10,202,92,127),(11,126,93,201),(12,200,94,125),(13,124,95,199),(14,198,96,123),(15,122,97,197),(16,224,98,121),(17,120,99,223),(18,222,100,119),(19,118,101,221),(20,220,102,117),(21,116,103,219),(22,218,104,115),(23,114,105,217),(24,216,106,113),(25,140,107,215),(26,214,108,139),(27,138,109,213),(28,212,110,137),(29,176,159,61),(30,60,160,175),(31,174,161,59),(32,58,162,173),(33,172,163,57),(34,84,164,171),(35,170,165,83),(36,82,166,169),(37,196,167,81),(38,80,168,195),(39,194,141,79),(40,78,142,193),(41,192,143,77),(42,76,144,191),(43,190,145,75),(44,74,146,189),(45,188,147,73),(46,72,148,187),(47,186,149,71),(48,70,150,185),(49,184,151,69),(50,68,152,183),(51,182,153,67),(52,66,154,181),(53,180,155,65),(54,64,156,179),(55,178,157,63),(56,62,158,177)]])
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 4A | 4B | 4C | 4D | 4E | ··· | 4I | 4J | ··· | 4Q | 4R | 4S | 7A | 7B | 7C | 14A | ··· | 14I | 28A | ··· | 28R | 28S | ··· | 28AD |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 4 | ··· | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 28 | ··· | 28 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 28 | 28 | 2 | 2 | 2 | 2 | 4 | ··· | 4 | 14 | ··· | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | - | - | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | 2- 1+4 | D4⋊2D7 | Q8⋊2D7 | Q8.10D14 |
| kernel | C42.177D14 | C4×Dic14 | C4×D28 | C4⋊C4⋊7D7 | D14⋊2Q8 | C4⋊C4⋊D7 | Q8×Dic7 | C28.23D4 | C7×C4⋊Q8 | C4⋊Q8 | C28 | C42 | C4⋊C4 | C2×Q8 | C14 | C4 | C4 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 4 | 2 | 2 | 1 | 3 | 8 | 3 | 12 | 6 | 1 | 6 | 6 | 6 |
Matrix representation of C42.177D14 ►in GL6(𝔽29)
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 12 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 28 |
| 0 | 0 | 0 | 0 | 2 | 28 |
| 0 | 16 | 0 | 0 | 0 | 0 |
| 20 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 4 | 0 | 0 |
| 0 | 0 | 25 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 24 | 17 |
| 0 | 16 | 0 | 0 | 0 | 0 |
| 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 25 | 25 | 0 | 0 |
| 0 | 0 | 11 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 17 |
| 0 | 0 | 0 | 0 | 24 | 17 |
G:=sub<GL(6,GF(29))| [17,0,0,0,0,0,0,12,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[17,0,0,0,0,0,0,12,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,2,0,0,0,0,28,28],[0,20,0,0,0,0,16,0,0,0,0,0,0,0,4,25,0,0,0,0,4,18,0,0,0,0,0,0,12,24,0,0,0,0,0,17],[0,9,0,0,0,0,16,0,0,0,0,0,0,0,25,11,0,0,0,0,25,4,0,0,0,0,0,0,12,24,0,0,0,0,17,17] >;
C42.177D14 in GAP, Magma, Sage, TeX
C_4^2._{177}D_{14} % in TeX
G:=Group("C4^2.177D14"); // GroupNames label
G:=SmallGroup(448,1185);
// by ID
G=gap.SmallGroup(448,1185);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,120,758,219,268,1571,297,136,18822]);
// Polycyclic
G:=Group<a,b,c,d|a^4=b^4=1,c^14=a^2*b^2,d^2=a^2,a*b=b*a,c*a*c^-1=d*a*d^-1=a^-1,c*b*c^-1=b^-1,d*b*d^-1=a^2*b,d*c*d^-1=b^2*c^13>;
// generators/relations