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G = C2×C28.23D4  order 448 = 26·7

Direct product of C2 and C28.23D4

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C2×C28.23D4, (C2×Q8)⋊29D14, (C22×Q8)⋊6D7, C28.259(C2×D4), (C2×C28).215D4, D14⋊C4⋊74C22, C14⋊4(C4.4D4), (Q8×C14)⋊36C22, (C2×C14).306C24, (C2×C28).646C23, (C4×Dic7)⋊69C22, (C22×D28).19C2, C14.154(C22×D4), (C22×C4).385D14, (C2×D28).278C22, (C23×D7).78C22, C23.342(C22×D7), C22.317(C23×D7), (C22×C28).439C22, (C22×C14).424C23, C22.40(Q8⋊2D7), (C2×Dic7).289C23, (C22×D7).133C23, (C22×Dic7).234C22, (Q8×C2×C14)⋊5C2, C7⋊5(C2×C4.4D4), (C2×C4×Dic7)⋊13C2, C4.28(C2×C7⋊D4), (C2×D14⋊C4)⋊43C2, C14.128(C2×C4○D4), (C2×C14).589(C2×D4), C2.35(C2×Q8⋊2D7), C2.27(C22×C7⋊D4), (C2×C4).157(C7⋊D4), (C2×C4).243(C22×D7), C22.117(C2×C7⋊D4), (C2×C14).201(C4○D4), SmallGroup(448,1267)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C2×C14 — C2×C28.23D4
Chief series
C1 — C7 — C14 — C2×C14 — C22×D7 — C23×D7 — C22×D28 — C2×C28.23D4
Lower central
C7 — C2×C14 — C2×C28.23D4

Subgroups: 1652 in 330 conjugacy classes, 127 normal (15 characteristic)
C1, C2, C2 [×6], C2 [×4], C4 [×4], C4 [×8], C22, C22 [×6], C22 [×20], C7, C2×C4 [×10], C2×C4 [×12], D4 [×8], Q8 [×8], C23, C23 [×16], D7 [×4], C14, C14 [×6], C42 [×4], C22⋊C4 [×16], C22×C4, C22×C4 [×2], C22×C4 [×2], C2×D4 [×8], C2×Q8 [×4], C2×Q8 [×4], C24 [×2], Dic7 [×4], C28 [×4], C28 [×4], D14 [×20], C2×C14, C2×C14 [×6], C2×C42, C2×C22⋊C4 [×4], C4.4D4 [×8], C22×D4, C22×Q8, D28 [×8], C2×Dic7 [×4], C2×Dic7 [×4], C2×C28 [×10], C2×C28 [×4], C7×Q8 [×8], C22×D7 [×4], C22×D7 [×12], C22×C14, C2×C4.4D4, C4×Dic7 [×4], D14⋊C4 [×16], C2×D28 [×4], C2×D28 [×4], C22×Dic7 [×2], C22×C28, C22×C28 [×2], Q8×C14 [×4], Q8×C14 [×4], C23×D7 [×2], C2×C4×Dic7, C2×D14⋊C4 [×4], C28.23D4 [×8], C22×D28, Q8×C2×C14, C2×C28.23D4

Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C4○D4 [×4], C24, D14 [×7], C4.4D4 [×4], C22×D4, C2×C4○D4 [×2], C7⋊D4 [×4], C22×D7 [×7], C2×C4.4D4, Q8⋊2D7 [×4], C2×C7⋊D4 [×6], C23×D7, C28.23D4 [×4], C2×Q8⋊2D7 [×2], C22×C7⋊D4, C2×C28.23D4

Generators and relations
 G = < a,b,c,d | a2=b28=c4=d2=1, ab=ba, ac=ca, ad=da, cbc-1=b13, dbd=b-1, dcd=b14c-1 >

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

(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)

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

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

Matrix representation ►G ⊆ GL6(𝔽29)

2800000
0280000
0028000
0002800
000010
000001
,
070000
4110000
00232700
004600
0000223
0000190
,
070000
2500000
0012000
0001200
00002028
0000249
,
0220000
400000
00232700
003600
000018
0000028

G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[0,4,0,0,0,0,7,11,0,0,0,0,0,0,23,4,0,0,0,0,27,6,0,0,0,0,0,0,22,19,0,0,0,0,3,0],[0,25,0,0,0,0,7,0,0,0,0,0,0,0,12,0,0,0,0,0,0,12,0,0,0,0,0,0,20,24,0,0,0,0,28,9],[0,4,0,0,0,0,22,0,0,0,0,0,0,0,23,3,0,0,0,0,27,6,0,0,0,0,0,0,1,0,0,0,0,0,8,28] >;
 

88 conjugacy classes

class 1 2A···2G2H2I2J2K4A4B4C4D4E4F4G4H4I···4P7A7B7C14A···14U28A···28AJ
order12···22222444444444···477714···1428···28
size11···1282828282222444414···142222···24···4

88 irreducible representations

dim1111112222224
type+++++++++++
imageC1C2C2C2C2C2D4D7C4○D4D14D14C7⋊D4Q8⋊2D7
kernelC2×C28.23D4C2×C4×Dic7C2×D14⋊C4C28.23D4C22×D28Q8×C2×C14C2×C28C22×Q8C2×C14C22×C4C2×Q8C2×C4C22
# reps1148114389122412

In GAP, Magma, Sage, TeX 

C_2\times C_{28}._{23}D_4
 
% in TeX
 
G:=Group("C2xC28.23D4");
 
// GroupNames label
 
G:=SmallGroup(448,1267);
 
// by ID
 
G=gap.SmallGroup(448,1267);
 
# by ID
 
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,184,675,297,136,18822]);
 
// Polycyclic
 
G:=Group<a,b,c,d|a^2=b^28=c^4=d^2=1,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=b^13,d*b*d=b^-1,d*c*d=b^14*c^-1>;
 
// generators/relations
 

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