metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24⋊4D14, C14.302+ (1+4), C22≀C2⋊7D7, C22⋊C4⋊8D14, C23⋊D14⋊7C2, (C2×D4).87D14, C24⋊D7⋊9C2, D14⋊C4⋊15C22, (C2×C28).32C23, (C23×D7)⋊8C22, C28.17D4⋊13C2, (C2×C14).138C24, (C23×C14)⋊11C22, C7⋊1(C24⋊C22), (C4×Dic7)⋊18C22, C2.32(D4⋊6D14), C23.D7⋊18C22, Dic7.D4⋊15C2, (C2×Dic14)⋊23C22, (D4×C14).112C22, (C2×Dic7).63C23, (C22×D7).57C23, C23.110(C22×D7), C22.159(C23×D7), (C22×C14).183C23, (C7×C22≀C2)⋊9C2, (C7×C22⋊C4)⋊8C22, (C2×C4).32(C22×D7), (C2×C7⋊D4).22C22, SmallGroup(448,1047)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1388 in 260 conjugacy classes, 91 normal (12 characteristic)
C1, C2 [×3], C2 [×6], C4 [×9], C22, C22 [×26], C7, C2×C4 [×3], C2×C4 [×6], D4 [×9], Q8 [×3], C23, C23 [×3], C23 [×8], D7 [×2], C14 [×3], C14 [×4], C42 [×3], C22⋊C4 [×3], C22⋊C4 [×15], C2×D4 [×3], C2×D4 [×6], C2×Q8 [×3], C24, C24, Dic7 [×6], C28 [×3], D14 [×10], C2×C14, C2×C14 [×16], C22≀C2, C22≀C2 [×5], C4.4D4 [×9], Dic14 [×3], C2×Dic7 [×6], C7⋊D4 [×6], C2×C28 [×3], C7×D4 [×3], C22×D7 [×2], C22×D7 [×3], C22×C14, C22×C14 [×3], C22×C14 [×3], C24⋊C22, C4×Dic7 [×3], D14⋊C4 [×6], C23.D7 [×9], C7×C22⋊C4 [×3], C2×Dic14 [×3], C2×C7⋊D4 [×6], D4×C14 [×3], C23×D7, C23×C14, Dic7.D4 [×6], C28.17D4 [×3], C23⋊D14 [×3], C24⋊D7 [×2], C7×C22≀C2, C24⋊4D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C24, D14 [×7], 2+ (1+4) [×3], C22×D7 [×7], C24⋊C22, C23×D7, D4⋊6D14 [×3], C24⋊4D14
Generators and relations
G = < a,b,c,d,e,f | a2=b2=c2=d2=e14=f2=1, ab=ba, eae-1=ac=ca, ad=da, faf=acd, 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
(1 112)(2 106)(3 100)(4 108)(5 102)(6 110)(7 104)(8 71)(9 79)(10 73)(11 81)(12 75)(13 83)(14 77)(15 111)(16 105)(17 99)(18 107)(19 101)(20 109)(21 103)(22 84)(23 78)(24 72)(25 80)(26 74)(27 82)(28 76)(29 68)(30 55)(31 70)(32 43)(33 58)(34 45)(35 60)(36 47)(37 62)(38 49)(39 64)(40 51)(41 66)(42 53)(44 86)(46 88)(48 90)(50 92)(52 94)(54 96)(56 98)(57 85)(59 87)(61 89)(63 91)(65 93)(67 95)(69 97)
(1 60)(2 68)(3 62)(4 70)(5 64)(6 58)(7 66)(8 61)(9 69)(10 63)(11 57)(12 65)(13 59)(14 67)(15 52)(16 46)(17 54)(18 48)(19 56)(20 50)(21 44)(22 53)(23 47)(24 55)(25 49)(26 43)(27 51)(28 45)(29 106)(30 72)(31 108)(32 74)(33 110)(34 76)(35 112)(36 78)(37 100)(38 80)(39 102)(40 82)(41 104)(42 84)(71 89)(73 91)(75 93)(77 95)(79 97)(81 85)(83 87)(86 103)(88 105)(90 107)(92 109)(94 111)(96 99)(98 101)
(1 16)(2 17)(3 18)(4 19)(5 20)(6 21)(7 15)(8 23)(9 24)(10 25)(11 26)(12 27)(13 28)(14 22)(29 96)(30 97)(31 98)(32 85)(33 86)(34 87)(35 88)(36 89)(37 90)(38 91)(39 92)(40 93)(41 94)(42 95)(43 57)(44 58)(45 59)(46 60)(47 61)(48 62)(49 63)(50 64)(51 65)(52 66)(53 67)(54 68)(55 69)(56 70)(71 78)(72 79)(73 80)(74 81)(75 82)(76 83)(77 84)(99 106)(100 107)(101 108)(102 109)(103 110)(104 111)(105 112)
(1 14)(2 8)(3 9)(4 10)(5 11)(6 12)(7 13)(15 28)(16 22)(17 23)(18 24)(19 25)(20 26)(21 27)(29 89)(30 90)(31 91)(32 92)(33 93)(34 94)(35 95)(36 96)(37 97)(38 98)(39 85)(40 86)(41 87)(42 88)(43 50)(44 51)(45 52)(46 53)(47 54)(48 55)(49 56)(57 64)(58 65)(59 66)(60 67)(61 68)(62 69)(63 70)(71 106)(72 107)(73 108)(74 109)(75 110)(76 111)(77 112)(78 99)(79 100)(80 101)(81 102)(82 103)(83 104)(84 105)
(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 28)(2 27)(3 26)(4 25)(5 24)(6 23)(7 22)(8 21)(9 20)(10 19)(11 18)(12 17)(13 16)(14 15)(29 86)(30 85)(31 98)(32 97)(33 96)(34 95)(35 94)(36 93)(37 92)(38 91)(39 90)(40 89)(41 88)(42 87)(43 48)(44 47)(45 46)(49 56)(50 55)(51 54)(52 53)(57 62)(58 61)(59 60)(63 70)(64 69)(65 68)(66 67)(71 75)(72 74)(76 84)(77 83)(78 82)(79 81)(99 103)(100 102)(104 112)(105 111)(106 110)(107 109)
G:=sub<Sym(112)| (1,112)(2,106)(3,100)(4,108)(5,102)(6,110)(7,104)(8,71)(9,79)(10,73)(11,81)(12,75)(13,83)(14,77)(15,111)(16,105)(17,99)(18,107)(19,101)(20,109)(21,103)(22,84)(23,78)(24,72)(25,80)(26,74)(27,82)(28,76)(29,68)(30,55)(31,70)(32,43)(33,58)(34,45)(35,60)(36,47)(37,62)(38,49)(39,64)(40,51)(41,66)(42,53)(44,86)(46,88)(48,90)(50,92)(52,94)(54,96)(56,98)(57,85)(59,87)(61,89)(63,91)(65,93)(67,95)(69,97), (1,60)(2,68)(3,62)(4,70)(5,64)(6,58)(7,66)(8,61)(9,69)(10,63)(11,57)(12,65)(13,59)(14,67)(15,52)(16,46)(17,54)(18,48)(19,56)(20,50)(21,44)(22,53)(23,47)(24,55)(25,49)(26,43)(27,51)(28,45)(29,106)(30,72)(31,108)(32,74)(33,110)(34,76)(35,112)(36,78)(37,100)(38,80)(39,102)(40,82)(41,104)(42,84)(71,89)(73,91)(75,93)(77,95)(79,97)(81,85)(83,87)(86,103)(88,105)(90,107)(92,109)(94,111)(96,99)(98,101), (1,16)(2,17)(3,18)(4,19)(5,20)(6,21)(7,15)(8,23)(9,24)(10,25)(11,26)(12,27)(13,28)(14,22)(29,96)(30,97)(31,98)(32,85)(33,86)(34,87)(35,88)(36,89)(37,90)(38,91)(39,92)(40,93)(41,94)(42,95)(43,57)(44,58)(45,59)(46,60)(47,61)(48,62)(49,63)(50,64)(51,65)(52,66)(53,67)(54,68)(55,69)(56,70)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112), (1,14)(2,8)(3,9)(4,10)(5,11)(6,12)(7,13)(15,28)(16,22)(17,23)(18,24)(19,25)(20,26)(21,27)(29,89)(30,90)(31,91)(32,92)(33,93)(34,94)(35,95)(36,96)(37,97)(38,98)(39,85)(40,86)(41,87)(42,88)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(71,106)(72,107)(73,108)(74,109)(75,110)(76,111)(77,112)(78,99)(79,100)(80,101)(81,102)(82,103)(83,104)(84,105), (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), (1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(29,86)(30,85)(31,98)(32,97)(33,96)(34,95)(35,94)(36,93)(37,92)(38,91)(39,90)(40,89)(41,88)(42,87)(43,48)(44,47)(45,46)(49,56)(50,55)(51,54)(52,53)(57,62)(58,61)(59,60)(63,70)(64,69)(65,68)(66,67)(71,75)(72,74)(76,84)(77,83)(78,82)(79,81)(99,103)(100,102)(104,112)(105,111)(106,110)(107,109)>;
G:=Group( (1,112)(2,106)(3,100)(4,108)(5,102)(6,110)(7,104)(8,71)(9,79)(10,73)(11,81)(12,75)(13,83)(14,77)(15,111)(16,105)(17,99)(18,107)(19,101)(20,109)(21,103)(22,84)(23,78)(24,72)(25,80)(26,74)(27,82)(28,76)(29,68)(30,55)(31,70)(32,43)(33,58)(34,45)(35,60)(36,47)(37,62)(38,49)(39,64)(40,51)(41,66)(42,53)(44,86)(46,88)(48,90)(50,92)(52,94)(54,96)(56,98)(57,85)(59,87)(61,89)(63,91)(65,93)(67,95)(69,97), (1,60)(2,68)(3,62)(4,70)(5,64)(6,58)(7,66)(8,61)(9,69)(10,63)(11,57)(12,65)(13,59)(14,67)(15,52)(16,46)(17,54)(18,48)(19,56)(20,50)(21,44)(22,53)(23,47)(24,55)(25,49)(26,43)(27,51)(28,45)(29,106)(30,72)(31,108)(32,74)(33,110)(34,76)(35,112)(36,78)(37,100)(38,80)(39,102)(40,82)(41,104)(42,84)(71,89)(73,91)(75,93)(77,95)(79,97)(81,85)(83,87)(86,103)(88,105)(90,107)(92,109)(94,111)(96,99)(98,101), (1,16)(2,17)(3,18)(4,19)(5,20)(6,21)(7,15)(8,23)(9,24)(10,25)(11,26)(12,27)(13,28)(14,22)(29,96)(30,97)(31,98)(32,85)(33,86)(34,87)(35,88)(36,89)(37,90)(38,91)(39,92)(40,93)(41,94)(42,95)(43,57)(44,58)(45,59)(46,60)(47,61)(48,62)(49,63)(50,64)(51,65)(52,66)(53,67)(54,68)(55,69)(56,70)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112), (1,14)(2,8)(3,9)(4,10)(5,11)(6,12)(7,13)(15,28)(16,22)(17,23)(18,24)(19,25)(20,26)(21,27)(29,89)(30,90)(31,91)(32,92)(33,93)(34,94)(35,95)(36,96)(37,97)(38,98)(39,85)(40,86)(41,87)(42,88)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(71,106)(72,107)(73,108)(74,109)(75,110)(76,111)(77,112)(78,99)(79,100)(80,101)(81,102)(82,103)(83,104)(84,105), (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), (1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(29,86)(30,85)(31,98)(32,97)(33,96)(34,95)(35,94)(36,93)(37,92)(38,91)(39,90)(40,89)(41,88)(42,87)(43,48)(44,47)(45,46)(49,56)(50,55)(51,54)(52,53)(57,62)(58,61)(59,60)(63,70)(64,69)(65,68)(66,67)(71,75)(72,74)(76,84)(77,83)(78,82)(79,81)(99,103)(100,102)(104,112)(105,111)(106,110)(107,109) );
G=PermutationGroup([(1,112),(2,106),(3,100),(4,108),(5,102),(6,110),(7,104),(8,71),(9,79),(10,73),(11,81),(12,75),(13,83),(14,77),(15,111),(16,105),(17,99),(18,107),(19,101),(20,109),(21,103),(22,84),(23,78),(24,72),(25,80),(26,74),(27,82),(28,76),(29,68),(30,55),(31,70),(32,43),(33,58),(34,45),(35,60),(36,47),(37,62),(38,49),(39,64),(40,51),(41,66),(42,53),(44,86),(46,88),(48,90),(50,92),(52,94),(54,96),(56,98),(57,85),(59,87),(61,89),(63,91),(65,93),(67,95),(69,97)], [(1,60),(2,68),(3,62),(4,70),(5,64),(6,58),(7,66),(8,61),(9,69),(10,63),(11,57),(12,65),(13,59),(14,67),(15,52),(16,46),(17,54),(18,48),(19,56),(20,50),(21,44),(22,53),(23,47),(24,55),(25,49),(26,43),(27,51),(28,45),(29,106),(30,72),(31,108),(32,74),(33,110),(34,76),(35,112),(36,78),(37,100),(38,80),(39,102),(40,82),(41,104),(42,84),(71,89),(73,91),(75,93),(77,95),(79,97),(81,85),(83,87),(86,103),(88,105),(90,107),(92,109),(94,111),(96,99),(98,101)], [(1,16),(2,17),(3,18),(4,19),(5,20),(6,21),(7,15),(8,23),(9,24),(10,25),(11,26),(12,27),(13,28),(14,22),(29,96),(30,97),(31,98),(32,85),(33,86),(34,87),(35,88),(36,89),(37,90),(38,91),(39,92),(40,93),(41,94),(42,95),(43,57),(44,58),(45,59),(46,60),(47,61),(48,62),(49,63),(50,64),(51,65),(52,66),(53,67),(54,68),(55,69),(56,70),(71,78),(72,79),(73,80),(74,81),(75,82),(76,83),(77,84),(99,106),(100,107),(101,108),(102,109),(103,110),(104,111),(105,112)], [(1,14),(2,8),(3,9),(4,10),(5,11),(6,12),(7,13),(15,28),(16,22),(17,23),(18,24),(19,25),(20,26),(21,27),(29,89),(30,90),(31,91),(32,92),(33,93),(34,94),(35,95),(36,96),(37,97),(38,98),(39,85),(40,86),(41,87),(42,88),(43,50),(44,51),(45,52),(46,53),(47,54),(48,55),(49,56),(57,64),(58,65),(59,66),(60,67),(61,68),(62,69),(63,70),(71,106),(72,107),(73,108),(74,109),(75,110),(76,111),(77,112),(78,99),(79,100),(80,101),(81,102),(82,103),(83,104),(84,105)], [(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)], [(1,28),(2,27),(3,26),(4,25),(5,24),(6,23),(7,22),(8,21),(9,20),(10,19),(11,18),(12,17),(13,16),(14,15),(29,86),(30,85),(31,98),(32,97),(33,96),(34,95),(35,94),(36,93),(37,92),(38,91),(39,90),(40,89),(41,88),(42,87),(43,48),(44,47),(45,46),(49,56),(50,55),(51,54),(52,53),(57,62),(58,61),(59,60),(63,70),(64,69),(65,68),(66,67),(71,75),(72,74),(76,84),(77,83),(78,82),(79,81),(99,103),(100,102),(104,112),(105,111),(106,110),(107,109)])
Matrix representation ►G ⊆ GL8(𝔽29)
| 0 | 0 | 5 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 24 | 0 | 0 | 0 | 0 |
| 5 | 13 | 0 | 0 | 0 | 0 | 0 | 0 |
| 16 | 24 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 2 | 6 | 1 | 0 |
| 0 | 0 | 0 | 0 | 10 | 1 | 0 | 1 |
| 0 | 0 | 0 | 0 | 24 | 11 | 27 | 23 |
| 0 | 0 | 0 | 0 | 28 | 27 | 19 | 28 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 25 | 14 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 4 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 25 | 25 | 14 |
| 0 | 0 | 0 | 0 | 23 | 11 | 1 | 4 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 28 |
| 28 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 26 | 21 | 0 | 0 | 0 | 0 | 0 | 0 |
| 8 | 21 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 3 | 8 | 0 | 0 | 0 | 0 |
| 0 | 0 | 21 | 8 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 10 | 0 | 0 |
| 0 | 0 | 0 | 0 | 9 | 23 | 0 | 0 |
| 0 | 0 | 0 | 0 | 13 | 10 | 20 | 19 |
| 0 | 0 | 0 | 0 | 1 | 3 | 20 | 6 |
| 21 | 26 | 0 | 0 | 0 | 0 | 0 | 0 |
| 21 | 8 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 8 | 21 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 22 | 22 | 0 | 0 |
| 0 | 0 | 0 | 0 | 11 | 7 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 21 | 7 | 7 |
| 0 | 0 | 0 | 0 | 25 | 19 | 18 | 22 |
G:=sub<GL(8,GF(29))| [0,0,5,16,0,0,0,0,0,0,13,24,0,0,0,0,5,16,0,0,0,0,0,0,13,24,0,0,0,0,0,0,0,0,0,0,2,10,24,28,0,0,0,0,6,1,11,27,0,0,0,0,1,0,27,19,0,0,0,0,0,1,23,28],[0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,25,1,18,23,0,0,0,0,14,4,25,11,0,0,0,0,0,0,25,1,0,0,0,0,0,0,14,4],[28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[26,8,0,0,0,0,0,0,21,21,0,0,0,0,0,0,0,0,3,21,0,0,0,0,0,0,8,8,0,0,0,0,0,0,0,0,9,9,13,1,0,0,0,0,10,23,10,3,0,0,0,0,0,0,20,20,0,0,0,0,0,0,19,6],[21,21,0,0,0,0,0,0,26,8,0,0,0,0,0,0,0,0,8,8,0,0,0,0,0,0,3,21,0,0,0,0,0,0,0,0,22,11,3,25,0,0,0,0,22,7,21,19,0,0,0,0,0,0,7,18,0,0,0,0,0,0,7,22] >;
61 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | ··· | 4I | 7A | 7B | 7C | 14A | ··· | 14I | 14J | ··· | 14AA | 14AB | 14AC | 14AD | 28A | ··· | 28I |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 4 | 4 | 4 | 4 | 28 | 28 | 4 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | 8 | 8 | 8 | ··· | 8 |
61 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | D7 | D14 | D14 | D14 | 2+ (1+4) | D4⋊6D14 |
| kernel | C24⋊4D14 | Dic7.D4 | C28.17D4 | C23⋊D14 | C24⋊D7 | C7×C22≀C2 | C22≀C2 | C22⋊C4 | C2×D4 | C24 | C14 | C2 |
| # reps | 1 | 6 | 3 | 3 | 2 | 1 | 3 | 9 | 9 | 3 | 3 | 18 |
In GAP, Magma, Sage, TeX
C_2^4\rtimes_4D_{14} % in TeX
G:=Group("C2^4:4D14"); // GroupNames label
G:=SmallGroup(448,1047);
// by ID
G=gap.SmallGroup(448,1047);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,219,1571,570,18822]);
// 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=a*c=c*a,a*d=d*a,f*a*f=a*c*d,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
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