metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.35D14, C14.292+ 1+4, C22≀C2⋊6D7, C28⋊2D4⋊14C2, (D4×Dic7)⋊13C2, (C2×D4).86D14, C24⋊D7⋊8C2, C22⋊C4.2D14, D14⋊C4⋊14C22, Dic7⋊D4⋊5C2, Dic7⋊4D4⋊4C2, (C2×C28).31C23, C4⋊Dic7⋊27C22, D14.D4⋊14C2, C28.17D4⋊12C2, (C2×C14).137C24, Dic7⋊C4⋊12C22, C7⋊3(C22.32C24), (C4×Dic7)⋊17C22, C23.D7⋊17C22, C2.31(D4⋊6D14), Dic7.D4⋊14C2, C22⋊Dic14⋊14C2, (C2×Dic14)⋊22C22, (D4×C14).111C22, C23.18D14⋊5C2, C23.D14⋊12C2, (C23×C14).70C22, (C2×Dic7).62C23, (C22×D7).56C23, C22.158(C23×D7), C23.177(C22×D7), C22.10(D4⋊2D7), (C22×C14).182C23, (C22×Dic7)⋊16C22, (C2×C4×D7)⋊10C22, (C7×C22≀C2)⋊8C2, C14.78(C2×C4○D4), C2.29(C2×D4⋊2D7), (C2×C7⋊D4)⋊10C22, (C2×C23.D7)⋊21C2, (C2×C4).31(C22×D7), (C2×C14).44(C4○D4), (C7×C22⋊C4).3C22, SmallGroup(448,1046)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C24.35D14
G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e14=f2=d, ab=ba, eae-1=ac=ca, ad=da, faf-1=acd, bc=cb, ebe-1=bd=db, fbf-1=bcd, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=e13 >
Subgroups: 1100 in 250 conjugacy classes, 95 normal (91 characteristic)
C1, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×D4, C2×Q8, C24, Dic7, C28, D14, C2×C14, C2×C14, C2×C14, C2×C22⋊C4, C4×D4, C22≀C2, C22≀C2, C4⋊D4, C22⋊Q8, C22.D4, C4.4D4, C42⋊2C2, Dic14, C4×D7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C7×D4, C22×D7, C22×C14, C22×C14, C22.32C24, C4×Dic7, Dic7⋊C4, C4⋊Dic7, D14⋊C4, C23.D7, C7×C22⋊C4, C2×Dic14, C2×C4×D7, C22×Dic7, C2×C7⋊D4, D4×C14, C23×C14, C22⋊Dic14, C23.D14, Dic7⋊4D4, D14.D4, Dic7.D4, D4×Dic7, C23.18D14, C28.17D4, C28⋊2D4, Dic7⋊D4, C2×C23.D7, C24⋊D7, C7×C22≀C2, C24.35D14
Quotients: C1, C2, C22, C23, D7, C4○D4, C24, D14, C2×C4○D4, 2+ 1+4, C22×D7, C22.32C24, D4⋊2D7, C23×D7, C2×D4⋊2D7, D4⋊6D14, C24.35D14
►On 112 points
Generators in S112
(2 65)(4 67)(6 69)(8 71)(10 73)(12 75)(14 77)(16 79)(18 81)(20 83)(22 57)(24 59)(26 61)(28 63)(29 43)(30 89)(31 45)(32 91)(33 47)(34 93)(35 49)(36 95)(37 51)(38 97)(39 53)(40 99)(41 55)(42 101)(44 103)(46 105)(48 107)(50 109)(52 111)(54 85)(56 87)(86 100)(88 102)(90 104)(92 106)(94 108)(96 110)(98 112)
(1 15)(3 17)(5 19)(7 21)(9 23)(11 25)(13 27)(29 88)(30 103)(31 90)(32 105)(33 92)(34 107)(35 94)(36 109)(37 96)(38 111)(39 98)(40 85)(41 100)(42 87)(43 102)(44 89)(45 104)(46 91)(47 106)(48 93)(49 108)(50 95)(51 110)(52 97)(53 112)(54 99)(55 86)(56 101)(58 72)(60 74)(62 76)(64 78)(66 80)(68 82)(70 84)
(1 64)(2 65)(3 66)(4 67)(5 68)(6 69)(7 70)(8 71)(9 72)(10 73)(11 74)(12 75)(13 76)(14 77)(15 78)(16 79)(17 80)(18 81)(19 82)(20 83)(21 84)(22 57)(23 58)(24 59)(25 60)(26 61)(27 62)(28 63)(29 102)(30 103)(31 104)(32 105)(33 106)(34 107)(35 108)(36 109)(37 110)(38 111)(39 112)(40 85)(41 86)(42 87)(43 88)(44 89)(45 90)(46 91)(47 92)(48 93)(49 94)(50 95)(51 96)(52 97)(53 98)(54 99)(55 100)(56 101)
(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 91 15 105)(2 104 16 90)(3 89 17 103)(4 102 18 88)(5 87 19 101)(6 100 20 86)(7 85 21 99)(8 98 22 112)(9 111 23 97)(10 96 24 110)(11 109 25 95)(12 94 26 108)(13 107 27 93)(14 92 28 106)(29 81 43 67)(30 66 44 80)(31 79 45 65)(32 64 46 78)(33 77 47 63)(34 62 48 76)(35 75 49 61)(36 60 50 74)(37 73 51 59)(38 58 52 72)(39 71 53 57)(40 84 54 70)(41 69 55 83)(42 82 56 68)
G:=sub<Sym(112)| (2,65)(4,67)(6,69)(8,71)(10,73)(12,75)(14,77)(16,79)(18,81)(20,83)(22,57)(24,59)(26,61)(28,63)(29,43)(30,89)(31,45)(32,91)(33,47)(34,93)(35,49)(36,95)(37,51)(38,97)(39,53)(40,99)(41,55)(42,101)(44,103)(46,105)(48,107)(50,109)(52,111)(54,85)(56,87)(86,100)(88,102)(90,104)(92,106)(94,108)(96,110)(98,112), (1,15)(3,17)(5,19)(7,21)(9,23)(11,25)(13,27)(29,88)(30,103)(31,90)(32,105)(33,92)(34,107)(35,94)(36,109)(37,96)(38,111)(39,98)(40,85)(41,100)(42,87)(43,102)(44,89)(45,104)(46,91)(47,106)(48,93)(49,108)(50,95)(51,110)(52,97)(53,112)(54,99)(55,86)(56,101)(58,72)(60,74)(62,76)(64,78)(66,80)(68,82)(70,84), (1,64)(2,65)(3,66)(4,67)(5,68)(6,69)(7,70)(8,71)(9,72)(10,73)(11,74)(12,75)(13,76)(14,77)(15,78)(16,79)(17,80)(18,81)(19,82)(20,83)(21,84)(22,57)(23,58)(24,59)(25,60)(26,61)(27,62)(28,63)(29,102)(30,103)(31,104)(32,105)(33,106)(34,107)(35,108)(36,109)(37,110)(38,111)(39,112)(40,85)(41,86)(42,87)(43,88)(44,89)(45,90)(46,91)(47,92)(48,93)(49,94)(50,95)(51,96)(52,97)(53,98)(54,99)(55,100)(56,101), (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), (1,91,15,105)(2,104,16,90)(3,89,17,103)(4,102,18,88)(5,87,19,101)(6,100,20,86)(7,85,21,99)(8,98,22,112)(9,111,23,97)(10,96,24,110)(11,109,25,95)(12,94,26,108)(13,107,27,93)(14,92,28,106)(29,81,43,67)(30,66,44,80)(31,79,45,65)(32,64,46,78)(33,77,47,63)(34,62,48,76)(35,75,49,61)(36,60,50,74)(37,73,51,59)(38,58,52,72)(39,71,53,57)(40,84,54,70)(41,69,55,83)(42,82,56,68)>;
G:=Group( (2,65)(4,67)(6,69)(8,71)(10,73)(12,75)(14,77)(16,79)(18,81)(20,83)(22,57)(24,59)(26,61)(28,63)(29,43)(30,89)(31,45)(32,91)(33,47)(34,93)(35,49)(36,95)(37,51)(38,97)(39,53)(40,99)(41,55)(42,101)(44,103)(46,105)(48,107)(50,109)(52,111)(54,85)(56,87)(86,100)(88,102)(90,104)(92,106)(94,108)(96,110)(98,112), (1,15)(3,17)(5,19)(7,21)(9,23)(11,25)(13,27)(29,88)(30,103)(31,90)(32,105)(33,92)(34,107)(35,94)(36,109)(37,96)(38,111)(39,98)(40,85)(41,100)(42,87)(43,102)(44,89)(45,104)(46,91)(47,106)(48,93)(49,108)(50,95)(51,110)(52,97)(53,112)(54,99)(55,86)(56,101)(58,72)(60,74)(62,76)(64,78)(66,80)(68,82)(70,84), (1,64)(2,65)(3,66)(4,67)(5,68)(6,69)(7,70)(8,71)(9,72)(10,73)(11,74)(12,75)(13,76)(14,77)(15,78)(16,79)(17,80)(18,81)(19,82)(20,83)(21,84)(22,57)(23,58)(24,59)(25,60)(26,61)(27,62)(28,63)(29,102)(30,103)(31,104)(32,105)(33,106)(34,107)(35,108)(36,109)(37,110)(38,111)(39,112)(40,85)(41,86)(42,87)(43,88)(44,89)(45,90)(46,91)(47,92)(48,93)(49,94)(50,95)(51,96)(52,97)(53,98)(54,99)(55,100)(56,101), (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), (1,91,15,105)(2,104,16,90)(3,89,17,103)(4,102,18,88)(5,87,19,101)(6,100,20,86)(7,85,21,99)(8,98,22,112)(9,111,23,97)(10,96,24,110)(11,109,25,95)(12,94,26,108)(13,107,27,93)(14,92,28,106)(29,81,43,67)(30,66,44,80)(31,79,45,65)(32,64,46,78)(33,77,47,63)(34,62,48,76)(35,75,49,61)(36,60,50,74)(37,73,51,59)(38,58,52,72)(39,71,53,57)(40,84,54,70)(41,69,55,83)(42,82,56,68) );
G=PermutationGroup([[(2,65),(4,67),(6,69),(8,71),(10,73),(12,75),(14,77),(16,79),(18,81),(20,83),(22,57),(24,59),(26,61),(28,63),(29,43),(30,89),(31,45),(32,91),(33,47),(34,93),(35,49),(36,95),(37,51),(38,97),(39,53),(40,99),(41,55),(42,101),(44,103),(46,105),(48,107),(50,109),(52,111),(54,85),(56,87),(86,100),(88,102),(90,104),(92,106),(94,108),(96,110),(98,112)], [(1,15),(3,17),(5,19),(7,21),(9,23),(11,25),(13,27),(29,88),(30,103),(31,90),(32,105),(33,92),(34,107),(35,94),(36,109),(37,96),(38,111),(39,98),(40,85),(41,100),(42,87),(43,102),(44,89),(45,104),(46,91),(47,106),(48,93),(49,108),(50,95),(51,110),(52,97),(53,112),(54,99),(55,86),(56,101),(58,72),(60,74),(62,76),(64,78),(66,80),(68,82),(70,84)], [(1,64),(2,65),(3,66),(4,67),(5,68),(6,69),(7,70),(8,71),(9,72),(10,73),(11,74),(12,75),(13,76),(14,77),(15,78),(16,79),(17,80),(18,81),(19,82),(20,83),(21,84),(22,57),(23,58),(24,59),(25,60),(26,61),(27,62),(28,63),(29,102),(30,103),(31,104),(32,105),(33,106),(34,107),(35,108),(36,109),(37,110),(38,111),(39,112),(40,85),(41,86),(42,87),(43,88),(44,89),(45,90),(46,91),(47,92),(48,93),(49,94),(50,95),(51,96),(52,97),(53,98),(54,99),(55,100),(56,101)], [(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)], [(1,91,15,105),(2,104,16,90),(3,89,17,103),(4,102,18,88),(5,87,19,101),(6,100,20,86),(7,85,21,99),(8,98,22,112),(9,111,23,97),(10,96,24,110),(11,109,25,95),(12,94,26,108),(13,107,27,93),(14,92,28,106),(29,81,43,67),(30,66,44,80),(31,79,45,65),(32,64,46,78),(33,77,47,63),(34,62,48,76),(35,75,49,61),(36,60,50,74),(37,73,51,59),(38,58,52,72),(39,71,53,57),(40,84,54,70),(41,69,55,83),(42,82,56,68)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | ··· | 4L | 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 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 14 | 14 | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | 2 | 4 | 4 | 4 | 28 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | 8 | 8 | 8 | ··· | 8 |
64 irreducible representations
| dim | 1 | 1 | 1 | 1 | 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 | C2 | C2 | C2 | C2 | D7 | C4○D4 | D14 | D14 | D14 | 2+ 1+4 | D4⋊2D7 | D4⋊6D14 |
| kernel | C24.35D14 | C22⋊Dic14 | C23.D14 | Dic7⋊4D4 | D14.D4 | Dic7.D4 | D4×Dic7 | C23.18D14 | C28.17D4 | C28⋊2D4 | Dic7⋊D4 | C2×C23.D7 | C24⋊D7 | C7×C22≀C2 | C22≀C2 | C2×C14 | C22⋊C4 | C2×D4 | C24 | C14 | C22 | C2 |
| # reps | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 3 | 4 | 9 | 9 | 3 | 2 | 6 | 12 |
Matrix representation of C24.35D14 ►in GL8(𝔽29)
| 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 | 26 | 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 | 15 | 28 | 0 |
| 0 | 0 | 0 | 0 | 15 | 0 | 0 | 28 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 1 | 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 | 15 | 28 | 0 |
| 0 | 0 | 0 | 0 | 14 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 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 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 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 |
| 24 | 25 | 0 | 0 | 0 | 0 | 0 | 0 |
| 8 | 12 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 20 | 0 | 0 | 0 | 0 |
| 0 | 0 | 26 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 14 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 0 | 15 | 28 | 0 |
| 14 | 11 | 0 | 0 | 0 | 0 | 0 | 0 |
| 6 | 15 | 0 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 17 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 17 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 23 | 0 | 0 | 24 |
| 0 | 0 | 0 | 0 | 0 | 6 | 5 | 0 |
| 0 | 0 | 0 | 0 | 0 | 10 | 23 | 0 |
| 0 | 0 | 0 | 0 | 19 | 0 | 0 | 6 |
G:=sub<GL(8,GF(29))| [28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,26,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,15,0,0,0,0,0,1,15,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,28,26,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,14,0,0,0,0,0,1,15,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28],[24,8,0,0,0,0,0,0,25,12,0,0,0,0,0,0,0,0,28,26,0,0,0,0,0,0,20,1,0,0,0,0,0,0,0,0,0,28,14,0,0,0,0,0,1,0,0,15,0,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0],[14,6,0,0,0,0,0,0,11,15,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,23,0,0,19,0,0,0,0,0,6,10,0,0,0,0,0,0,5,23,0,0,0,0,0,24,0,0,6] >;
C24.35D14 in GAP, Magma, Sage, TeX
C_2^4._{35}D_{14} % in TeX
G:=Group("C2^4.35D14"); // GroupNames label
G:=SmallGroup(448,1046);
// by ID
G=gap.SmallGroup(448,1046);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,232,758,219,675,570,18822]);
// 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,e*a*e^-1=a*c=c*a,a*d=d*a,f*a*f^-1=a*c*d,b*c=c*b,e*b*e^-1=b*d=d*b,f*b*f^-1=b*c*d,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