metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.41D14, C14.902+ (1+4), (C2×C28)⋊14D4, C28⋊2D4⋊40C2, C28⋊D4⋊29C2, C28.252(C2×D4), (C22×D4)⋊11D7, (C2×D4).230D14, (C2×D28)⋊57C22, C24⋊D7⋊13C2, C4⋊Dic7⋊78C22, C28.17D4⋊28C2, (C2×C14).300C24, (C2×C28).545C23, C7⋊6(C22.29C24), (C4×Dic7)⋊42C22, C14.147(C22×D4), (C22×C4).272D14, C2.93(D4⋊6D14), C23.D7⋊39C22, (C2×Dic14)⋊68C22, (D4×C14).271C22, (C23×C14).79C22, C23.136(C22×D7), C22.313(C23×D7), C23.21D14⋊33C2, (C22×C14).234C23, (C22×C28).277C22, (C2×Dic7).155C23, (C22×D7).131C23, (D4×C2×C14)⋊7C2, (C2×C4)⋊6(C7⋊D4), (C2×C4×D7)⋊31C22, C4.97(C2×C7⋊D4), (C2×C4○D28)⋊29C2, (C2×C14).583(C2×D4), (C2×C7⋊D4)⋊28C22, C22.36(C2×C7⋊D4), C2.20(C22×C7⋊D4), (C2×C4).628(C22×D7), SmallGroup(448,1258)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1492 in 334 conjugacy classes, 111 normal (21 characteristic)
C1, C2, C2 [×2], C2 [×8], C4 [×4], C4 [×6], C22, C22 [×2], C22 [×28], C7, C2×C4 [×2], C2×C4 [×4], C2×C4 [×10], D4 [×22], Q8 [×2], C23, C23 [×4], C23 [×10], D7 [×2], C14, C14 [×2], C14 [×6], C42 [×2], C22⋊C4 [×10], C4⋊C4 [×2], C22×C4, C22×C4 [×2], C2×D4 [×4], C2×D4 [×15], C2×Q8, C4○D4 [×4], C24 [×2], Dic7 [×6], C28 [×4], D14 [×6], C2×C14, C2×C14 [×2], C2×C14 [×22], C42⋊C2, C22≀C2 [×4], C4⋊D4 [×4], C4.4D4 [×2], C4⋊1D4 [×2], C22×D4, C2×C4○D4, Dic14 [×2], C4×D7 [×4], D28 [×2], C2×Dic7 [×6], C7⋊D4 [×12], C2×C28 [×2], C2×C28 [×4], C7×D4 [×8], C22×D7 [×2], C22×C14, C22×C14 [×4], C22×C14 [×8], C22.29C24, C4×Dic7 [×2], C4⋊Dic7 [×2], C23.D7 [×10], C2×Dic14, C2×C4×D7 [×2], C2×D28, C4○D28 [×4], C2×C7⋊D4 [×10], C22×C28, D4×C14 [×4], D4×C14 [×4], C23×C14 [×2], C23.21D14, C28.17D4 [×2], C28⋊2D4 [×4], C28⋊D4 [×2], C24⋊D7 [×4], C2×C4○D28, D4×C2×C14, C24.41D14
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C24, D14 [×7], C22×D4, 2+ (1+4) [×2], C7⋊D4 [×4], C22×D7 [×7], C22.29C24, C2×C7⋊D4 [×6], C23×D7, D4⋊6D14 [×2], C22×C7⋊D4, C24.41D14
Generators and relations
G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e14=f2=d, ab=ba, ac=ca, eae-1=ad=da, faf-1=acd, bc=cb, fbf-1=bd=db, be=eb, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=e13 >
►On 112 points
Generators in S112
(1 8)(2 23)(3 10)(4 25)(5 12)(6 27)(7 14)(9 16)(11 18)(13 20)(15 22)(17 24)(19 26)(21 28)(29 90)(30 105)(31 92)(32 107)(33 94)(34 109)(35 96)(36 111)(37 98)(38 85)(39 100)(40 87)(41 102)(42 89)(43 104)(44 91)(45 106)(46 93)(47 108)(48 95)(49 110)(50 97)(51 112)(52 99)(53 86)(54 101)(55 88)(56 103)(57 64)(58 79)(59 66)(60 81)(61 68)(62 83)(63 70)(65 72)(67 74)(69 76)(71 78)(73 80)(75 82)(77 84)
(1 59)(2 60)(3 61)(4 62)(5 63)(6 64)(7 65)(8 66)(9 67)(10 68)(11 69)(12 70)(13 71)(14 72)(15 73)(16 74)(17 75)(18 76)(19 77)(20 78)(21 79)(22 80)(23 81)(24 82)(25 83)(26 84)(27 57)(28 58)(29 97)(30 98)(31 99)(32 100)(33 101)(34 102)(35 103)(36 104)(37 105)(38 106)(39 107)(40 108)(41 109)(42 110)(43 111)(44 112)(45 85)(46 86)(47 87)(48 88)(49 89)(50 90)(51 91)(52 92)(53 93)(54 94)(55 95)(56 96)
(1 59)(2 60)(3 61)(4 62)(5 63)(6 64)(7 65)(8 66)(9 67)(10 68)(11 69)(12 70)(13 71)(14 72)(15 73)(16 74)(17 75)(18 76)(19 77)(20 78)(21 79)(22 80)(23 81)(24 82)(25 83)(26 84)(27 57)(28 58)(29 111)(30 112)(31 85)(32 86)(33 87)(34 88)(35 89)(36 90)(37 91)(38 92)(39 93)(40 94)(41 95)(42 96)(43 97)(44 98)(45 99)(46 100)(47 101)(48 102)(49 103)(50 104)(51 105)(52 106)(53 107)(54 108)(55 109)(56 110)
(1 15)(2 16)(3 17)(4 18)(5 19)(6 20)(7 21)(8 22)(9 23)(10 24)(11 25)(12 26)(13 27)(14 28)(29 43)(30 44)(31 45)(32 46)(33 47)(34 48)(35 49)(36 50)(37 51)(38 52)(39 53)(40 54)(41 55)(42 56)(57 71)(58 72)(59 73)(60 74)(61 75)(62 76)(63 77)(64 78)(65 79)(66 80)(67 81)(68 82)(69 83)(70 84)(85 99)(86 100)(87 101)(88 102)(89 103)(90 104)(91 105)(92 106)(93 107)(94 108)(95 109)(96 110)(97 111)(98 112)
(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)
(1 110 15 96)(2 95 16 109)(3 108 17 94)(4 93 18 107)(5 106 19 92)(6 91 20 105)(7 104 21 90)(8 89 22 103)(9 102 23 88)(10 87 24 101)(11 100 25 86)(12 85 26 99)(13 98 27 112)(14 111 28 97)(29 58 43 72)(30 71 44 57)(31 84 45 70)(32 69 46 83)(33 82 47 68)(34 67 48 81)(35 80 49 66)(36 65 50 79)(37 78 51 64)(38 63 52 77)(39 76 53 62)(40 61 54 75)(41 74 55 60)(42 59 56 73)
G:=sub<Sym(112)| (1,8)(2,23)(3,10)(4,25)(5,12)(6,27)(7,14)(9,16)(11,18)(13,20)(15,22)(17,24)(19,26)(21,28)(29,90)(30,105)(31,92)(32,107)(33,94)(34,109)(35,96)(36,111)(37,98)(38,85)(39,100)(40,87)(41,102)(42,89)(43,104)(44,91)(45,106)(46,93)(47,108)(48,95)(49,110)(50,97)(51,112)(52,99)(53,86)(54,101)(55,88)(56,103)(57,64)(58,79)(59,66)(60,81)(61,68)(62,83)(63,70)(65,72)(67,74)(69,76)(71,78)(73,80)(75,82)(77,84), (1,59)(2,60)(3,61)(4,62)(5,63)(6,64)(7,65)(8,66)(9,67)(10,68)(11,69)(12,70)(13,71)(14,72)(15,73)(16,74)(17,75)(18,76)(19,77)(20,78)(21,79)(22,80)(23,81)(24,82)(25,83)(26,84)(27,57)(28,58)(29,97)(30,98)(31,99)(32,100)(33,101)(34,102)(35,103)(36,104)(37,105)(38,106)(39,107)(40,108)(41,109)(42,110)(43,111)(44,112)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(51,91)(52,92)(53,93)(54,94)(55,95)(56,96), (1,59)(2,60)(3,61)(4,62)(5,63)(6,64)(7,65)(8,66)(9,67)(10,68)(11,69)(12,70)(13,71)(14,72)(15,73)(16,74)(17,75)(18,76)(19,77)(20,78)(21,79)(22,80)(23,81)(24,82)(25,83)(26,84)(27,57)(28,58)(29,111)(30,112)(31,85)(32,86)(33,87)(34,88)(35,89)(36,90)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,103)(50,104)(51,105)(52,106)(53,107)(54,108)(55,109)(56,110), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112), (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), (1,110,15,96)(2,95,16,109)(3,108,17,94)(4,93,18,107)(5,106,19,92)(6,91,20,105)(7,104,21,90)(8,89,22,103)(9,102,23,88)(10,87,24,101)(11,100,25,86)(12,85,26,99)(13,98,27,112)(14,111,28,97)(29,58,43,72)(30,71,44,57)(31,84,45,70)(32,69,46,83)(33,82,47,68)(34,67,48,81)(35,80,49,66)(36,65,50,79)(37,78,51,64)(38,63,52,77)(39,76,53,62)(40,61,54,75)(41,74,55,60)(42,59,56,73)>;
G:=Group( (1,8)(2,23)(3,10)(4,25)(5,12)(6,27)(7,14)(9,16)(11,18)(13,20)(15,22)(17,24)(19,26)(21,28)(29,90)(30,105)(31,92)(32,107)(33,94)(34,109)(35,96)(36,111)(37,98)(38,85)(39,100)(40,87)(41,102)(42,89)(43,104)(44,91)(45,106)(46,93)(47,108)(48,95)(49,110)(50,97)(51,112)(52,99)(53,86)(54,101)(55,88)(56,103)(57,64)(58,79)(59,66)(60,81)(61,68)(62,83)(63,70)(65,72)(67,74)(69,76)(71,78)(73,80)(75,82)(77,84), (1,59)(2,60)(3,61)(4,62)(5,63)(6,64)(7,65)(8,66)(9,67)(10,68)(11,69)(12,70)(13,71)(14,72)(15,73)(16,74)(17,75)(18,76)(19,77)(20,78)(21,79)(22,80)(23,81)(24,82)(25,83)(26,84)(27,57)(28,58)(29,97)(30,98)(31,99)(32,100)(33,101)(34,102)(35,103)(36,104)(37,105)(38,106)(39,107)(40,108)(41,109)(42,110)(43,111)(44,112)(45,85)(46,86)(47,87)(48,88)(49,89)(50,90)(51,91)(52,92)(53,93)(54,94)(55,95)(56,96), (1,59)(2,60)(3,61)(4,62)(5,63)(6,64)(7,65)(8,66)(9,67)(10,68)(11,69)(12,70)(13,71)(14,72)(15,73)(16,74)(17,75)(18,76)(19,77)(20,78)(21,79)(22,80)(23,81)(24,82)(25,83)(26,84)(27,57)(28,58)(29,111)(30,112)(31,85)(32,86)(33,87)(34,88)(35,89)(36,90)(37,91)(38,92)(39,93)(40,94)(41,95)(42,96)(43,97)(44,98)(45,99)(46,100)(47,101)(48,102)(49,103)(50,104)(51,105)(52,106)(53,107)(54,108)(55,109)(56,110), (1,15)(2,16)(3,17)(4,18)(5,19)(6,20)(7,21)(8,22)(9,23)(10,24)(11,25)(12,26)(13,27)(14,28)(29,43)(30,44)(31,45)(32,46)(33,47)(34,48)(35,49)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,71)(58,72)(59,73)(60,74)(61,75)(62,76)(63,77)(64,78)(65,79)(66,80)(67,81)(68,82)(69,83)(70,84)(85,99)(86,100)(87,101)(88,102)(89,103)(90,104)(91,105)(92,106)(93,107)(94,108)(95,109)(96,110)(97,111)(98,112), (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), (1,110,15,96)(2,95,16,109)(3,108,17,94)(4,93,18,107)(5,106,19,92)(6,91,20,105)(7,104,21,90)(8,89,22,103)(9,102,23,88)(10,87,24,101)(11,100,25,86)(12,85,26,99)(13,98,27,112)(14,111,28,97)(29,58,43,72)(30,71,44,57)(31,84,45,70)(32,69,46,83)(33,82,47,68)(34,67,48,81)(35,80,49,66)(36,65,50,79)(37,78,51,64)(38,63,52,77)(39,76,53,62)(40,61,54,75)(41,74,55,60)(42,59,56,73) );
G=PermutationGroup([(1,8),(2,23),(3,10),(4,25),(5,12),(6,27),(7,14),(9,16),(11,18),(13,20),(15,22),(17,24),(19,26),(21,28),(29,90),(30,105),(31,92),(32,107),(33,94),(34,109),(35,96),(36,111),(37,98),(38,85),(39,100),(40,87),(41,102),(42,89),(43,104),(44,91),(45,106),(46,93),(47,108),(48,95),(49,110),(50,97),(51,112),(52,99),(53,86),(54,101),(55,88),(56,103),(57,64),(58,79),(59,66),(60,81),(61,68),(62,83),(63,70),(65,72),(67,74),(69,76),(71,78),(73,80),(75,82),(77,84)], [(1,59),(2,60),(3,61),(4,62),(5,63),(6,64),(7,65),(8,66),(9,67),(10,68),(11,69),(12,70),(13,71),(14,72),(15,73),(16,74),(17,75),(18,76),(19,77),(20,78),(21,79),(22,80),(23,81),(24,82),(25,83),(26,84),(27,57),(28,58),(29,97),(30,98),(31,99),(32,100),(33,101),(34,102),(35,103),(36,104),(37,105),(38,106),(39,107),(40,108),(41,109),(42,110),(43,111),(44,112),(45,85),(46,86),(47,87),(48,88),(49,89),(50,90),(51,91),(52,92),(53,93),(54,94),(55,95),(56,96)], [(1,59),(2,60),(3,61),(4,62),(5,63),(6,64),(7,65),(8,66),(9,67),(10,68),(11,69),(12,70),(13,71),(14,72),(15,73),(16,74),(17,75),(18,76),(19,77),(20,78),(21,79),(22,80),(23,81),(24,82),(25,83),(26,84),(27,57),(28,58),(29,111),(30,112),(31,85),(32,86),(33,87),(34,88),(35,89),(36,90),(37,91),(38,92),(39,93),(40,94),(41,95),(42,96),(43,97),(44,98),(45,99),(46,100),(47,101),(48,102),(49,103),(50,104),(51,105),(52,106),(53,107),(54,108),(55,109),(56,110)], [(1,15),(2,16),(3,17),(4,18),(5,19),(6,20),(7,21),(8,22),(9,23),(10,24),(11,25),(12,26),(13,27),(14,28),(29,43),(30,44),(31,45),(32,46),(33,47),(34,48),(35,49),(36,50),(37,51),(38,52),(39,53),(40,54),(41,55),(42,56),(57,71),(58,72),(59,73),(60,74),(61,75),(62,76),(63,77),(64,78),(65,79),(66,80),(67,81),(68,82),(69,83),(70,84),(85,99),(86,100),(87,101),(88,102),(89,103),(90,104),(91,105),(92,106),(93,107),(94,108),(95,109),(96,110),(97,111),(98,112)], [(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)], [(1,110,15,96),(2,95,16,109),(3,108,17,94),(4,93,18,107),(5,106,19,92),(6,91,20,105),(7,104,21,90),(8,89,22,103),(9,102,23,88),(10,87,24,101),(11,100,25,86),(12,85,26,99),(13,98,27,112),(14,111,28,97),(29,58,43,72),(30,71,44,57),(31,84,45,70),(32,69,46,83),(33,82,47,68),(34,67,48,81),(35,80,49,66),(36,65,50,79),(37,78,51,64),(38,63,52,77),(39,76,53,62),(40,61,54,75),(41,74,55,60),(42,59,56,73)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 24 | 21 | 0 | 0 |
| 0 | 0 | 3 | 5 | 0 | 0 |
| 0 | 0 | 6 | 16 | 1 | 7 |
| 0 | 0 | 9 | 18 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 4 | 0 | 1 | 0 |
| 0 | 0 | 19 | 0 | 0 | 1 |
| 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 | 28 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 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 | 28 |
| 9 | 0 | 0 | 0 | 0 | 0 |
| 0 | 13 | 0 | 0 | 0 | 0 |
| 0 | 0 | 16 | 14 | 0 | 0 |
| 0 | 0 | 7 | 13 | 0 | 0 |
| 0 | 0 | 3 | 1 | 13 | 4 |
| 0 | 0 | 5 | 12 | 17 | 16 |
| 0 | 16 | 0 | 0 | 0 | 0 |
| 20 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 11 | 0 | 19 | 17 |
| 0 | 0 | 21 | 0 | 22 | 22 |
| 0 | 0 | 21 | 5 | 20 | 24 |
| 0 | 0 | 12 | 20 | 8 | 27 |
G:=sub<GL(6,GF(29))| [1,0,0,0,0,0,0,28,0,0,0,0,0,0,24,3,6,9,0,0,21,5,16,18,0,0,0,0,1,0,0,0,0,0,7,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,4,19,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[9,0,0,0,0,0,0,13,0,0,0,0,0,0,16,7,3,5,0,0,14,13,1,12,0,0,0,0,13,17,0,0,0,0,4,16],[0,20,0,0,0,0,16,0,0,0,0,0,0,0,11,21,21,12,0,0,0,0,5,20,0,0,19,22,20,8,0,0,17,22,24,27] >;
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | ··· | 4J | 7A | 7B | 7C | 14A | ··· | 14U | 14V | ··· | 14AS | 28A | ··· | 28L |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 4 | 28 | 28 | 2 | 2 | 2 | 2 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | D14 | D14 | D14 | C7⋊D4 | 2+ (1+4) | D4⋊6D14 |
| kernel | C24.41D14 | C23.21D14 | C28.17D4 | C28⋊2D4 | C28⋊D4 | C24⋊D7 | C2×C4○D28 | D4×C2×C14 | C2×C28 | C22×D4 | C22×C4 | C2×D4 | C24 | C2×C4 | C14 | C2 |
| # reps | 1 | 1 | 2 | 4 | 2 | 4 | 1 | 1 | 4 | 3 | 3 | 12 | 6 | 24 | 2 | 12 |
In GAP, Magma, Sage, TeX
C_2^4._{41}D_{14} % in TeX
G:=Group("C2^4.41D14"); // GroupNames label
G:=SmallGroup(448,1258);
// by ID
G=gap.SmallGroup(448,1258);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,675,570,18822]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=1,e^14=f^2=d,a*b=b*a,a*c=c*a,e*a*e^-1=a*d=d*a,f*a*f^-1=a*c*d,b*c=c*b,f*b*f^-1=b*d=d*b,b*e=e*b,c*d=d*c,c*e=e*c,c*f=f*c,d*e=e*d,d*f=f*d,f*e*f^-1=e^13>;
// generators/relations
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