metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24⋊3D14, C14.262+ (1+4), C7⋊2(D42), C7⋊D4⋊4D4, D14⋊6(C2×D4), C22⋊3(D4×D7), (C2×D4)⋊18D14, C22≀C2⋊3D7, Dic7⋊3(C2×D4), C22⋊D28⋊9C2, C23⋊D14⋊4C2, C28⋊D4⋊11C2, C22⋊C4⋊24D14, (D4×C14)⋊7C22, D14⋊D4⋊13C2, D14⋊C4⋊11C22, Dic7⋊4D4⋊2C2, Dic7⋊D4⋊2C2, (C2×D28)⋊19C22, (C2×C28).28C23, Dic7⋊C4⋊9C22, C14.56(C22×D4), (C23×D7)⋊7C22, (C2×C14).134C24, (C23×C14)⋊10C22, (C4×Dic7)⋊14C22, C2.28(D4⋊6D14), C23.D7⋊15C22, (C22×D7).53C23, C23.108(C22×D7), C22.155(C23×D7), (C22×C14).181C23, (C2×Dic7).221C23, (C22×Dic7)⋊13C22, (C2×D4×D7)⋊7C2, C2.29(C2×D4×D7), (C2×C14)⋊6(C2×D4), (C2×C4×D7)⋊7C22, (C7×C22≀C2)⋊5C2, (C22×C7⋊D4)⋊8C2, (C2×C7⋊D4)⋊39C22, (C7×C22⋊C4)⋊5C22, (C2×C4).28(C22×D7), SmallGroup(448,1043)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 2476 in 428 conjugacy classes, 115 normal (27 characteristic)
C1, C2, C2 [×2], C2 [×12], C4 [×9], C22, C22 [×4], C22 [×40], C7, C2×C4, C2×C4 [×2], C2×C4 [×12], D4 [×34], C23 [×2], C23 [×2], C23 [×24], D7 [×6], C14, C14 [×2], C14 [×6], C42, C22⋊C4, C22⋊C4 [×2], C22⋊C4 [×5], C4⋊C4 [×2], C22×C4 [×4], C2×D4, C2×D4 [×2], C2×D4 [×29], C24, C24 [×3], Dic7 [×4], Dic7 [×2], C28 [×3], D14 [×4], D14 [×22], C2×C14, C2×C14 [×4], C2×C14 [×14], C4×D4 [×2], C22≀C2, C22≀C2 [×3], C4⋊D4 [×4], C4⋊1D4, C22×D4 [×4], C4×D7 [×4], D28 [×5], C2×Dic7 [×4], C2×Dic7 [×4], C7⋊D4 [×8], C7⋊D4 [×16], C2×C28, C2×C28 [×2], C7×D4 [×5], C22×D7 [×4], C22×D7 [×15], C22×C14 [×2], C22×C14 [×2], C22×C14 [×5], D42, C4×Dic7, Dic7⋊C4 [×2], D14⋊C4 [×4], C23.D7, C7×C22⋊C4, C7×C22⋊C4 [×2], C2×C4×D7 [×2], C2×D28, C2×D28 [×2], D4×D7 [×8], C22×Dic7 [×2], C2×C7⋊D4 [×10], C2×C7⋊D4 [×8], D4×C14, D4×C14 [×2], C23×D7, C23×D7 [×2], C23×C14, Dic7⋊4D4 [×2], C22⋊D28 [×2], D14⋊D4 [×2], C23⋊D14, Dic7⋊D4 [×2], C28⋊D4, C7×C22≀C2, C2×D4×D7 [×2], C22×C7⋊D4 [×2], C24⋊3D14
Quotients:
C1, C2 [×15], C22 [×35], D4 [×8], C23 [×15], D7, C2×D4 [×12], C24, D14 [×7], C22×D4 [×2], 2+ (1+4), C22×D7 [×7], D42, D4×D7 [×4], C23×D7, C2×D4×D7 [×2], D4⋊6D14, C24⋊3D14
Generators and relations
G = < a,b,c,d,e,f | a2=b2=c2=d2=e14=f2=1, ab=ba, eae-1=faf=ac=ca, ad=da, fbf=bc=cb, ebe-1=bd=db, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef=e-1 >
►On 112 points
Generators in S112
(1 74)(2 82)(3 76)(4 84)(5 78)(6 72)(7 80)(8 95)(9 89)(10 97)(11 91)(12 85)(13 93)(14 87)(15 94)(16 88)(17 96)(18 90)(19 98)(20 92)(21 86)(22 71)(23 79)(24 73)(25 81)(26 75)(27 83)(28 77)(29 108)(30 69)(31 110)(32 57)(33 112)(34 59)(35 100)(36 61)(37 102)(38 63)(39 104)(40 65)(41 106)(42 67)(43 109)(44 70)(45 111)(46 58)(47 99)(48 60)(49 101)(50 62)(51 103)(52 64)(53 105)(54 66)(55 107)(56 68)
(1 104)(2 112)(3 106)(4 100)(5 108)(6 102)(7 110)(8 107)(9 101)(10 109)(11 103)(12 111)(13 105)(14 99)(15 59)(16 67)(17 61)(18 69)(19 63)(20 57)(21 65)(22 68)(23 62)(24 70)(25 64)(26 58)(27 66)(28 60)(29 78)(30 90)(31 80)(32 92)(33 82)(34 94)(35 84)(36 96)(37 72)(38 98)(39 74)(40 86)(41 76)(42 88)(43 97)(44 73)(45 85)(46 75)(47 87)(48 77)(49 89)(50 79)(51 91)(52 81)(53 93)(54 83)(55 95)(56 71)
(1 25)(2 26)(3 27)(4 28)(5 22)(6 23)(7 24)(8 16)(9 17)(10 18)(11 19)(12 20)(13 21)(14 15)(29 56)(30 43)(31 44)(32 45)(33 46)(34 47)(35 48)(36 49)(37 50)(38 51)(39 52)(40 53)(41 54)(42 55)(57 111)(58 112)(59 99)(60 100)(61 101)(62 102)(63 103)(64 104)(65 105)(66 106)(67 107)(68 108)(69 109)(70 110)(71 78)(72 79)(73 80)(74 81)(75 82)(76 83)(77 84)(85 92)(86 93)(87 94)(88 95)(89 96)(90 97)(91 98)
(1 12)(2 13)(3 14)(4 8)(5 9)(6 10)(7 11)(15 27)(16 28)(17 22)(18 23)(19 24)(20 25)(21 26)(29 49)(30 50)(31 51)(32 52)(33 53)(34 54)(35 55)(36 56)(37 43)(38 44)(39 45)(40 46)(41 47)(42 48)(57 64)(58 65)(59 66)(60 67)(61 68)(62 69)(63 70)(71 96)(72 97)(73 98)(74 85)(75 86)(76 87)(77 88)(78 89)(79 90)(80 91)(81 92)(82 93)(83 94)(84 95)(99 106)(100 107)(101 108)(102 109)(103 110)(104 111)(105 112)
(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)
(1 18)(2 17)(3 16)(4 15)(5 21)(6 20)(7 19)(8 27)(9 26)(10 25)(11 24)(12 23)(13 22)(14 28)(29 40)(30 39)(31 38)(32 37)(33 36)(34 35)(41 42)(43 52)(44 51)(45 50)(46 49)(47 48)(53 56)(54 55)(57 62)(58 61)(59 60)(63 70)(64 69)(65 68)(66 67)(71 86)(72 85)(73 98)(74 97)(75 96)(76 95)(77 94)(78 93)(79 92)(80 91)(81 90)(82 89)(83 88)(84 87)(99 100)(101 112)(102 111)(103 110)(104 109)(105 108)(106 107)
G:=sub<Sym(112)| (1,74)(2,82)(3,76)(4,84)(5,78)(6,72)(7,80)(8,95)(9,89)(10,97)(11,91)(12,85)(13,93)(14,87)(15,94)(16,88)(17,96)(18,90)(19,98)(20,92)(21,86)(22,71)(23,79)(24,73)(25,81)(26,75)(27,83)(28,77)(29,108)(30,69)(31,110)(32,57)(33,112)(34,59)(35,100)(36,61)(37,102)(38,63)(39,104)(40,65)(41,106)(42,67)(43,109)(44,70)(45,111)(46,58)(47,99)(48,60)(49,101)(50,62)(51,103)(52,64)(53,105)(54,66)(55,107)(56,68), (1,104)(2,112)(3,106)(4,100)(5,108)(6,102)(7,110)(8,107)(9,101)(10,109)(11,103)(12,111)(13,105)(14,99)(15,59)(16,67)(17,61)(18,69)(19,63)(20,57)(21,65)(22,68)(23,62)(24,70)(25,64)(26,58)(27,66)(28,60)(29,78)(30,90)(31,80)(32,92)(33,82)(34,94)(35,84)(36,96)(37,72)(38,98)(39,74)(40,86)(41,76)(42,88)(43,97)(44,73)(45,85)(46,75)(47,87)(48,77)(49,89)(50,79)(51,91)(52,81)(53,93)(54,83)(55,95)(56,71), (1,25)(2,26)(3,27)(4,28)(5,22)(6,23)(7,24)(8,16)(9,17)(10,18)(11,19)(12,20)(13,21)(14,15)(29,56)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52)(40,53)(41,54)(42,55)(57,111)(58,112)(59,99)(60,100)(61,101)(62,102)(63,103)(64,104)(65,105)(66,106)(67,107)(68,108)(69,109)(70,110)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(85,92)(86,93)(87,94)(88,95)(89,96)(90,97)(91,98), (1,12)(2,13)(3,14)(4,8)(5,9)(6,10)(7,11)(15,27)(16,28)(17,22)(18,23)(19,24)(20,25)(21,26)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,43)(38,44)(39,45)(40,46)(41,47)(42,48)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(71,96)(72,97)(73,98)(74,85)(75,86)(76,87)(77,88)(78,89)(79,90)(80,91)(81,92)(82,93)(83,94)(84,95)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112), (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), (1,18)(2,17)(3,16)(4,15)(5,21)(6,20)(7,19)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,28)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)(41,42)(43,52)(44,51)(45,50)(46,49)(47,48)(53,56)(54,55)(57,62)(58,61)(59,60)(63,70)(64,69)(65,68)(66,67)(71,86)(72,85)(73,98)(74,97)(75,96)(76,95)(77,94)(78,93)(79,92)(80,91)(81,90)(82,89)(83,88)(84,87)(99,100)(101,112)(102,111)(103,110)(104,109)(105,108)(106,107)>;
G:=Group( (1,74)(2,82)(3,76)(4,84)(5,78)(6,72)(7,80)(8,95)(9,89)(10,97)(11,91)(12,85)(13,93)(14,87)(15,94)(16,88)(17,96)(18,90)(19,98)(20,92)(21,86)(22,71)(23,79)(24,73)(25,81)(26,75)(27,83)(28,77)(29,108)(30,69)(31,110)(32,57)(33,112)(34,59)(35,100)(36,61)(37,102)(38,63)(39,104)(40,65)(41,106)(42,67)(43,109)(44,70)(45,111)(46,58)(47,99)(48,60)(49,101)(50,62)(51,103)(52,64)(53,105)(54,66)(55,107)(56,68), (1,104)(2,112)(3,106)(4,100)(5,108)(6,102)(7,110)(8,107)(9,101)(10,109)(11,103)(12,111)(13,105)(14,99)(15,59)(16,67)(17,61)(18,69)(19,63)(20,57)(21,65)(22,68)(23,62)(24,70)(25,64)(26,58)(27,66)(28,60)(29,78)(30,90)(31,80)(32,92)(33,82)(34,94)(35,84)(36,96)(37,72)(38,98)(39,74)(40,86)(41,76)(42,88)(43,97)(44,73)(45,85)(46,75)(47,87)(48,77)(49,89)(50,79)(51,91)(52,81)(53,93)(54,83)(55,95)(56,71), (1,25)(2,26)(3,27)(4,28)(5,22)(6,23)(7,24)(8,16)(9,17)(10,18)(11,19)(12,20)(13,21)(14,15)(29,56)(30,43)(31,44)(32,45)(33,46)(34,47)(35,48)(36,49)(37,50)(38,51)(39,52)(40,53)(41,54)(42,55)(57,111)(58,112)(59,99)(60,100)(61,101)(62,102)(63,103)(64,104)(65,105)(66,106)(67,107)(68,108)(69,109)(70,110)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(85,92)(86,93)(87,94)(88,95)(89,96)(90,97)(91,98), (1,12)(2,13)(3,14)(4,8)(5,9)(6,10)(7,11)(15,27)(16,28)(17,22)(18,23)(19,24)(20,25)(21,26)(29,49)(30,50)(31,51)(32,52)(33,53)(34,54)(35,55)(36,56)(37,43)(38,44)(39,45)(40,46)(41,47)(42,48)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(71,96)(72,97)(73,98)(74,85)(75,86)(76,87)(77,88)(78,89)(79,90)(80,91)(81,92)(82,93)(83,94)(84,95)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112), (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), (1,18)(2,17)(3,16)(4,15)(5,21)(6,20)(7,19)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,28)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)(41,42)(43,52)(44,51)(45,50)(46,49)(47,48)(53,56)(54,55)(57,62)(58,61)(59,60)(63,70)(64,69)(65,68)(66,67)(71,86)(72,85)(73,98)(74,97)(75,96)(76,95)(77,94)(78,93)(79,92)(80,91)(81,90)(82,89)(83,88)(84,87)(99,100)(101,112)(102,111)(103,110)(104,109)(105,108)(106,107) );
G=PermutationGroup([(1,74),(2,82),(3,76),(4,84),(5,78),(6,72),(7,80),(8,95),(9,89),(10,97),(11,91),(12,85),(13,93),(14,87),(15,94),(16,88),(17,96),(18,90),(19,98),(20,92),(21,86),(22,71),(23,79),(24,73),(25,81),(26,75),(27,83),(28,77),(29,108),(30,69),(31,110),(32,57),(33,112),(34,59),(35,100),(36,61),(37,102),(38,63),(39,104),(40,65),(41,106),(42,67),(43,109),(44,70),(45,111),(46,58),(47,99),(48,60),(49,101),(50,62),(51,103),(52,64),(53,105),(54,66),(55,107),(56,68)], [(1,104),(2,112),(3,106),(4,100),(5,108),(6,102),(7,110),(8,107),(9,101),(10,109),(11,103),(12,111),(13,105),(14,99),(15,59),(16,67),(17,61),(18,69),(19,63),(20,57),(21,65),(22,68),(23,62),(24,70),(25,64),(26,58),(27,66),(28,60),(29,78),(30,90),(31,80),(32,92),(33,82),(34,94),(35,84),(36,96),(37,72),(38,98),(39,74),(40,86),(41,76),(42,88),(43,97),(44,73),(45,85),(46,75),(47,87),(48,77),(49,89),(50,79),(51,91),(52,81),(53,93),(54,83),(55,95),(56,71)], [(1,25),(2,26),(3,27),(4,28),(5,22),(6,23),(7,24),(8,16),(9,17),(10,18),(11,19),(12,20),(13,21),(14,15),(29,56),(30,43),(31,44),(32,45),(33,46),(34,47),(35,48),(36,49),(37,50),(38,51),(39,52),(40,53),(41,54),(42,55),(57,111),(58,112),(59,99),(60,100),(61,101),(62,102),(63,103),(64,104),(65,105),(66,106),(67,107),(68,108),(69,109),(70,110),(71,78),(72,79),(73,80),(74,81),(75,82),(76,83),(77,84),(85,92),(86,93),(87,94),(88,95),(89,96),(90,97),(91,98)], [(1,12),(2,13),(3,14),(4,8),(5,9),(6,10),(7,11),(15,27),(16,28),(17,22),(18,23),(19,24),(20,25),(21,26),(29,49),(30,50),(31,51),(32,52),(33,53),(34,54),(35,55),(36,56),(37,43),(38,44),(39,45),(40,46),(41,47),(42,48),(57,64),(58,65),(59,66),(60,67),(61,68),(62,69),(63,70),(71,96),(72,97),(73,98),(74,85),(75,86),(76,87),(77,88),(78,89),(79,90),(80,91),(81,92),(82,93),(83,94),(84,95),(99,106),(100,107),(101,108),(102,109),(103,110),(104,111),(105,112)], [(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)], [(1,18),(2,17),(3,16),(4,15),(5,21),(6,20),(7,19),(8,27),(9,26),(10,25),(11,24),(12,23),(13,22),(14,28),(29,40),(30,39),(31,38),(32,37),(33,36),(34,35),(41,42),(43,52),(44,51),(45,50),(46,49),(47,48),(53,56),(54,55),(57,62),(58,61),(59,60),(63,70),(64,69),(65,68),(66,67),(71,86),(72,85),(73,98),(74,97),(75,96),(76,95),(77,94),(78,93),(79,92),(80,91),(81,90),(82,89),(83,88),(84,87),(99,100),(101,112),(102,111),(103,110),(104,109),(105,108),(106,107)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 24 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 24 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 1 | 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 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 4 | 10 | 0 | 0 |
| 0 | 0 | 14 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 17 | 1 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 18 | 7 | 0 | 0 |
| 0 | 0 | 16 | 11 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 17 | 1 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,24,28],[0,1,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,24,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,1,0,0,0,0,0,0,4,14,0,0,0,0,10,28,0,0,0,0,0,0,28,17,0,0,0,0,0,1],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,18,16,0,0,0,0,7,11,0,0,0,0,0,0,28,17,0,0,0,0,0,1] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 2J | 2K | 2L | 2M | 2N | 2O | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14AA | 14AB | 14AC | 14AD | 28A | ··· | 28I |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | 8 | 8 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | D14 | D14 | D14 | 2+ (1+4) | D4×D7 | D4⋊6D14 |
| kernel | C24⋊3D14 | Dic7⋊4D4 | C22⋊D28 | D14⋊D4 | C23⋊D14 | Dic7⋊D4 | C28⋊D4 | C7×C22≀C2 | C2×D4×D7 | C22×C7⋊D4 | C7⋊D4 | C22≀C2 | C22⋊C4 | C2×D4 | C24 | C14 | C22 | C2 |
| # reps | 1 | 2 | 2 | 2 | 1 | 2 | 1 | 1 | 2 | 2 | 8 | 3 | 9 | 9 | 3 | 1 | 12 | 6 |
In GAP, Magma, Sage, TeX
C_2^4\rtimes_3D_{14} % in TeX
G:=Group("C2^4:3D14"); // GroupNames label
G:=SmallGroup(448,1043);
// by ID
G=gap.SmallGroup(448,1043);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,219,1571,297,18822]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^14=f^2=1,a*b=b*a,e*a*e^-1=f*a*f=a*c=c*a,a*d=d*a,f*b*f=b*c=c*b,e*b*e^-1=b*d=d*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f=e^-1>;
// generators/relations
×
⋊
ℤ
𝔽
○
≀