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), (C2×C28).109C23, (C4×C28).217C22, (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), (C2×Dic7).146C23, (C4×Dic7).165C22, (C22×D7).121C23, C2.40(Q8.10D14), (C2×Dic14).304C22, (C7×C4⋊Q8)⋊18C2, C4⋊C4⋊D7⋊46C2, C4⋊C4⋊7D7⋊43C2, 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
Subgroups: 876 in 212 conjugacy classes, 99 normal (27 characteristic)
C1, C2 [×3], C2 [×2], C4 [×4], C4 [×11], C22, C22 [×6], C7, C2×C4 [×3], C2×C4 [×4], C2×C4 [×10], D4 [×2], Q8 [×6], C23 [×2], D7 [×2], C14 [×3], C42, C42 [×6], C22⋊C4 [×10], C4⋊C4 [×4], C4⋊C4 [×8], C22×C4 [×2], C2×D4, C2×Q8 [×2], C2×Q8, Dic7 [×6], C28 [×4], C28 [×5], D14 [×6], C2×C14, C42⋊C2 [×2], C4×D4, C4×Q8 [×3], C22⋊Q8 [×2], C4.4D4 [×2], C42⋊2C2 [×4], C4⋊Q8, Dic14 [×2], C4×D7 [×4], D28 [×2], C2×Dic7 [×6], C2×C28 [×3], C2×C28 [×4], C7×Q8 [×4], C22×D7 [×2], C22.50C24, C4×Dic7 [×6], Dic7⋊C4 [×2], C4⋊Dic7 [×2], C4⋊Dic7 [×4], D14⋊C4 [×10], C4×C28, C7×C4⋊C4 [×4], C2×Dic14, C2×C4×D7 [×2], C2×D28, Q8×C14 [×2], C4×Dic14, C4×D28, C4⋊C4⋊7D7 [×2], D14⋊2Q8 [×2], C4⋊C4⋊D7 [×4], Q8×Dic7 [×2], C28.23D4 [×2], C7×C4⋊Q8, C42.177D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×4], C24, D14 [×7], C2×C4○D4 [×2], 2- (1+4), C22×D7 [×7], C22.50C24, D4⋊2D7 [×2], Q8⋊2D7 [×2], C23×D7, C2×D4⋊2D7, C2×Q8⋊2D7, Q8.10D14, C42.177D14
Generators and relations
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 >
►On 224 points
Generators in S224
(1 41 195 114)(2 115 196 42)(3 43 169 116)(4 117 170 44)(5 45 171 118)(6 119 172 46)(7 47 173 120)(8 121 174 48)(9 49 175 122)(10 123 176 50)(11 51 177 124)(12 125 178 52)(13 53 179 126)(14 127 180 54)(15 55 181 128)(16 129 182 56)(17 29 183 130)(18 131 184 30)(19 31 185 132)(20 133 186 32)(21 33 187 134)(22 135 188 34)(23 35 189 136)(24 137 190 36)(25 37 191 138)(26 139 192 38)(27 39 193 140)(28 113 194 40)(57 216 156 89)(58 90 157 217)(59 218 158 91)(60 92 159 219)(61 220 160 93)(62 94 161 221)(63 222 162 95)(64 96 163 223)(65 224 164 97)(66 98 165 197)(67 198 166 99)(68 100 167 199)(69 200 168 101)(70 102 141 201)(71 202 142 103)(72 104 143 203)(73 204 144 105)(74 106 145 205)(75 206 146 107)(76 108 147 207)(77 208 148 109)(78 110 149 209)(79 210 150 111)(80 112 151 211)(81 212 152 85)(82 86 153 213)(83 214 154 87)(84 88 155 215)
(1 205 181 92)(2 93 182 206)(3 207 183 94)(4 95 184 208)(5 209 185 96)(6 97 186 210)(7 211 187 98)(8 99 188 212)(9 213 189 100)(10 101 190 214)(11 215 191 102)(12 103 192 216)(13 217 193 104)(14 105 194 218)(15 219 195 106)(16 107 196 220)(17 221 169 108)(18 109 170 222)(19 223 171 110)(20 111 172 224)(21 197 173 112)(22 85 174 198)(23 199 175 86)(24 87 176 200)(25 201 177 88)(26 89 178 202)(27 203 179 90)(28 91 180 204)(29 62 116 147)(30 148 117 63)(31 64 118 149)(32 150 119 65)(33 66 120 151)(34 152 121 67)(35 68 122 153)(36 154 123 69)(37 70 124 155)(38 156 125 71)(39 72 126 157)(40 158 127 73)(41 74 128 159)(42 160 129 75)(43 76 130 161)(44 162 131 77)(45 78 132 163)(46 164 133 79)(47 80 134 165)(48 166 135 81)(49 82 136 167)(50 168 137 83)(51 84 138 141)(52 142 139 57)(53 58 140 143)(54 144 113 59)(55 60 114 145)(56 146 115 61)
(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 73 195 144)(2 143 196 72)(3 71 169 142)(4 141 170 70)(5 69 171 168)(6 167 172 68)(7 67 173 166)(8 165 174 66)(9 65 175 164)(10 163 176 64)(11 63 177 162)(12 161 178 62)(13 61 179 160)(14 159 180 60)(15 59 181 158)(16 157 182 58)(17 57 183 156)(18 155 184 84)(19 83 185 154)(20 153 186 82)(21 81 187 152)(22 151 188 80)(23 79 189 150)(24 149 190 78)(25 77 191 148)(26 147 192 76)(27 75 193 146)(28 145 194 74)(29 89 130 216)(30 215 131 88)(31 87 132 214)(32 213 133 86)(33 85 134 212)(34 211 135 112)(35 111 136 210)(36 209 137 110)(37 109 138 208)(38 207 139 108)(39 107 140 206)(40 205 113 106)(41 105 114 204)(42 203 115 104)(43 103 116 202)(44 201 117 102)(45 101 118 200)(46 199 119 100)(47 99 120 198)(48 197 121 98)(49 97 122 224)(50 223 123 96)(51 95 124 222)(52 221 125 94)(53 93 126 220)(54 219 127 92)(55 91 128 218)(56 217 129 90)
G:=sub<Sym(224)| (1,41,195,114)(2,115,196,42)(3,43,169,116)(4,117,170,44)(5,45,171,118)(6,119,172,46)(7,47,173,120)(8,121,174,48)(9,49,175,122)(10,123,176,50)(11,51,177,124)(12,125,178,52)(13,53,179,126)(14,127,180,54)(15,55,181,128)(16,129,182,56)(17,29,183,130)(18,131,184,30)(19,31,185,132)(20,133,186,32)(21,33,187,134)(22,135,188,34)(23,35,189,136)(24,137,190,36)(25,37,191,138)(26,139,192,38)(27,39,193,140)(28,113,194,40)(57,216,156,89)(58,90,157,217)(59,218,158,91)(60,92,159,219)(61,220,160,93)(62,94,161,221)(63,222,162,95)(64,96,163,223)(65,224,164,97)(66,98,165,197)(67,198,166,99)(68,100,167,199)(69,200,168,101)(70,102,141,201)(71,202,142,103)(72,104,143,203)(73,204,144,105)(74,106,145,205)(75,206,146,107)(76,108,147,207)(77,208,148,109)(78,110,149,209)(79,210,150,111)(80,112,151,211)(81,212,152,85)(82,86,153,213)(83,214,154,87)(84,88,155,215), (1,205,181,92)(2,93,182,206)(3,207,183,94)(4,95,184,208)(5,209,185,96)(6,97,186,210)(7,211,187,98)(8,99,188,212)(9,213,189,100)(10,101,190,214)(11,215,191,102)(12,103,192,216)(13,217,193,104)(14,105,194,218)(15,219,195,106)(16,107,196,220)(17,221,169,108)(18,109,170,222)(19,223,171,110)(20,111,172,224)(21,197,173,112)(22,85,174,198)(23,199,175,86)(24,87,176,200)(25,201,177,88)(26,89,178,202)(27,203,179,90)(28,91,180,204)(29,62,116,147)(30,148,117,63)(31,64,118,149)(32,150,119,65)(33,66,120,151)(34,152,121,67)(35,68,122,153)(36,154,123,69)(37,70,124,155)(38,156,125,71)(39,72,126,157)(40,158,127,73)(41,74,128,159)(42,160,129,75)(43,76,130,161)(44,162,131,77)(45,78,132,163)(46,164,133,79)(47,80,134,165)(48,166,135,81)(49,82,136,167)(50,168,137,83)(51,84,138,141)(52,142,139,57)(53,58,140,143)(54,144,113,59)(55,60,114,145)(56,146,115,61), (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), (1,73,195,144)(2,143,196,72)(3,71,169,142)(4,141,170,70)(5,69,171,168)(6,167,172,68)(7,67,173,166)(8,165,174,66)(9,65,175,164)(10,163,176,64)(11,63,177,162)(12,161,178,62)(13,61,179,160)(14,159,180,60)(15,59,181,158)(16,157,182,58)(17,57,183,156)(18,155,184,84)(19,83,185,154)(20,153,186,82)(21,81,187,152)(22,151,188,80)(23,79,189,150)(24,149,190,78)(25,77,191,148)(26,147,192,76)(27,75,193,146)(28,145,194,74)(29,89,130,216)(30,215,131,88)(31,87,132,214)(32,213,133,86)(33,85,134,212)(34,211,135,112)(35,111,136,210)(36,209,137,110)(37,109,138,208)(38,207,139,108)(39,107,140,206)(40,205,113,106)(41,105,114,204)(42,203,115,104)(43,103,116,202)(44,201,117,102)(45,101,118,200)(46,199,119,100)(47,99,120,198)(48,197,121,98)(49,97,122,224)(50,223,123,96)(51,95,124,222)(52,221,125,94)(53,93,126,220)(54,219,127,92)(55,91,128,218)(56,217,129,90)>;
G:=Group( (1,41,195,114)(2,115,196,42)(3,43,169,116)(4,117,170,44)(5,45,171,118)(6,119,172,46)(7,47,173,120)(8,121,174,48)(9,49,175,122)(10,123,176,50)(11,51,177,124)(12,125,178,52)(13,53,179,126)(14,127,180,54)(15,55,181,128)(16,129,182,56)(17,29,183,130)(18,131,184,30)(19,31,185,132)(20,133,186,32)(21,33,187,134)(22,135,188,34)(23,35,189,136)(24,137,190,36)(25,37,191,138)(26,139,192,38)(27,39,193,140)(28,113,194,40)(57,216,156,89)(58,90,157,217)(59,218,158,91)(60,92,159,219)(61,220,160,93)(62,94,161,221)(63,222,162,95)(64,96,163,223)(65,224,164,97)(66,98,165,197)(67,198,166,99)(68,100,167,199)(69,200,168,101)(70,102,141,201)(71,202,142,103)(72,104,143,203)(73,204,144,105)(74,106,145,205)(75,206,146,107)(76,108,147,207)(77,208,148,109)(78,110,149,209)(79,210,150,111)(80,112,151,211)(81,212,152,85)(82,86,153,213)(83,214,154,87)(84,88,155,215), (1,205,181,92)(2,93,182,206)(3,207,183,94)(4,95,184,208)(5,209,185,96)(6,97,186,210)(7,211,187,98)(8,99,188,212)(9,213,189,100)(10,101,190,214)(11,215,191,102)(12,103,192,216)(13,217,193,104)(14,105,194,218)(15,219,195,106)(16,107,196,220)(17,221,169,108)(18,109,170,222)(19,223,171,110)(20,111,172,224)(21,197,173,112)(22,85,174,198)(23,199,175,86)(24,87,176,200)(25,201,177,88)(26,89,178,202)(27,203,179,90)(28,91,180,204)(29,62,116,147)(30,148,117,63)(31,64,118,149)(32,150,119,65)(33,66,120,151)(34,152,121,67)(35,68,122,153)(36,154,123,69)(37,70,124,155)(38,156,125,71)(39,72,126,157)(40,158,127,73)(41,74,128,159)(42,160,129,75)(43,76,130,161)(44,162,131,77)(45,78,132,163)(46,164,133,79)(47,80,134,165)(48,166,135,81)(49,82,136,167)(50,168,137,83)(51,84,138,141)(52,142,139,57)(53,58,140,143)(54,144,113,59)(55,60,114,145)(56,146,115,61), (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), (1,73,195,144)(2,143,196,72)(3,71,169,142)(4,141,170,70)(5,69,171,168)(6,167,172,68)(7,67,173,166)(8,165,174,66)(9,65,175,164)(10,163,176,64)(11,63,177,162)(12,161,178,62)(13,61,179,160)(14,159,180,60)(15,59,181,158)(16,157,182,58)(17,57,183,156)(18,155,184,84)(19,83,185,154)(20,153,186,82)(21,81,187,152)(22,151,188,80)(23,79,189,150)(24,149,190,78)(25,77,191,148)(26,147,192,76)(27,75,193,146)(28,145,194,74)(29,89,130,216)(30,215,131,88)(31,87,132,214)(32,213,133,86)(33,85,134,212)(34,211,135,112)(35,111,136,210)(36,209,137,110)(37,109,138,208)(38,207,139,108)(39,107,140,206)(40,205,113,106)(41,105,114,204)(42,203,115,104)(43,103,116,202)(44,201,117,102)(45,101,118,200)(46,199,119,100)(47,99,120,198)(48,197,121,98)(49,97,122,224)(50,223,123,96)(51,95,124,222)(52,221,125,94)(53,93,126,220)(54,219,127,92)(55,91,128,218)(56,217,129,90) );
G=PermutationGroup([(1,41,195,114),(2,115,196,42),(3,43,169,116),(4,117,170,44),(5,45,171,118),(6,119,172,46),(7,47,173,120),(8,121,174,48),(9,49,175,122),(10,123,176,50),(11,51,177,124),(12,125,178,52),(13,53,179,126),(14,127,180,54),(15,55,181,128),(16,129,182,56),(17,29,183,130),(18,131,184,30),(19,31,185,132),(20,133,186,32),(21,33,187,134),(22,135,188,34),(23,35,189,136),(24,137,190,36),(25,37,191,138),(26,139,192,38),(27,39,193,140),(28,113,194,40),(57,216,156,89),(58,90,157,217),(59,218,158,91),(60,92,159,219),(61,220,160,93),(62,94,161,221),(63,222,162,95),(64,96,163,223),(65,224,164,97),(66,98,165,197),(67,198,166,99),(68,100,167,199),(69,200,168,101),(70,102,141,201),(71,202,142,103),(72,104,143,203),(73,204,144,105),(74,106,145,205),(75,206,146,107),(76,108,147,207),(77,208,148,109),(78,110,149,209),(79,210,150,111),(80,112,151,211),(81,212,152,85),(82,86,153,213),(83,214,154,87),(84,88,155,215)], [(1,205,181,92),(2,93,182,206),(3,207,183,94),(4,95,184,208),(5,209,185,96),(6,97,186,210),(7,211,187,98),(8,99,188,212),(9,213,189,100),(10,101,190,214),(11,215,191,102),(12,103,192,216),(13,217,193,104),(14,105,194,218),(15,219,195,106),(16,107,196,220),(17,221,169,108),(18,109,170,222),(19,223,171,110),(20,111,172,224),(21,197,173,112),(22,85,174,198),(23,199,175,86),(24,87,176,200),(25,201,177,88),(26,89,178,202),(27,203,179,90),(28,91,180,204),(29,62,116,147),(30,148,117,63),(31,64,118,149),(32,150,119,65),(33,66,120,151),(34,152,121,67),(35,68,122,153),(36,154,123,69),(37,70,124,155),(38,156,125,71),(39,72,126,157),(40,158,127,73),(41,74,128,159),(42,160,129,75),(43,76,130,161),(44,162,131,77),(45,78,132,163),(46,164,133,79),(47,80,134,165),(48,166,135,81),(49,82,136,167),(50,168,137,83),(51,84,138,141),(52,142,139,57),(53,58,140,143),(54,144,113,59),(55,60,114,145),(56,146,115,61)], [(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)], [(1,73,195,144),(2,143,196,72),(3,71,169,142),(4,141,170,70),(5,69,171,168),(6,167,172,68),(7,67,173,166),(8,165,174,66),(9,65,175,164),(10,163,176,64),(11,63,177,162),(12,161,178,62),(13,61,179,160),(14,159,180,60),(15,59,181,158),(16,157,182,58),(17,57,183,156),(18,155,184,84),(19,83,185,154),(20,153,186,82),(21,81,187,152),(22,151,188,80),(23,79,189,150),(24,149,190,78),(25,77,191,148),(26,147,192,76),(27,75,193,146),(28,145,194,74),(29,89,130,216),(30,215,131,88),(31,87,132,214),(32,213,133,86),(33,85,134,212),(34,211,135,112),(35,111,136,210),(36,209,137,110),(37,109,138,208),(38,207,139,108),(39,107,140,206),(40,205,113,106),(41,105,114,204),(42,203,115,104),(43,103,116,202),(44,201,117,102),(45,101,118,200),(46,199,119,100),(47,99,120,198),(48,197,121,98),(49,97,122,224),(50,223,123,96),(51,95,124,222),(52,221,125,94),(53,93,126,220),(54,219,127,92),(55,91,128,218),(56,217,129,90)])
Matrix representation ►G ⊆ 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] >;
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 |
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
×
⋊
ℤ
𝔽
○
≀