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, C22.159(C23×D7), C23.110(C22×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
Generators and relations for C24⋊4D14
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 >
Subgroups: 1388 in 260 conjugacy classes, 91 normal (12 characteristic)
C1, C2, C2, C4, C22, C22, C7, C2×C4, C2×C4, D4, Q8, C23, C23, C23, D7, C14, C14, C42, C22⋊C4, C22⋊C4, C2×D4, C2×D4, C2×Q8, C24, C24, Dic7, C28, D14, C2×C14, C2×C14, C22≀C2, C22≀C2, C4.4D4, Dic14, C2×Dic7, C7⋊D4, C2×C28, C7×D4, C22×D7, C22×D7, C22×C14, C22×C14, C22×C14, C24⋊C22, C4×Dic7, D14⋊C4, C23.D7, C7×C22⋊C4, C2×Dic14, C2×C7⋊D4, D4×C14, C23×D7, C23×C14, Dic7.D4, C28.17D4, C23⋊D14, C24⋊D7, C7×C22≀C2, C24⋊4D14
Quotients: C1, C2, C22, C23, D7, C24, D14, 2+ 1+4, C22×D7, C24⋊C22, C23×D7, D4⋊6D14, C24⋊4D14
►On 112 points
Generators in S112
(1 79)(2 73)(3 81)(4 75)(5 83)(6 77)(7 71)(8 54)(9 48)(10 56)(11 50)(12 44)(13 52)(14 46)(15 82)(16 76)(17 84)(18 78)(19 72)(20 80)(21 74)(22 53)(23 47)(24 55)(25 49)(26 43)(27 51)(28 45)(29 103)(30 97)(31 105)(32 85)(33 107)(34 87)(35 109)(36 89)(37 111)(38 91)(39 99)(40 93)(41 101)(42 95)(57 108)(58 88)(59 110)(60 90)(61 112)(62 92)(63 100)(64 94)(65 102)(66 96)(67 104)(68 98)(69 106)(70 86)
(1 35)(2 29)(3 37)(4 31)(5 39)(6 33)(7 41)(8 40)(9 34)(10 42)(11 36)(12 30)(13 38)(14 32)(15 68)(16 62)(17 70)(18 64)(19 58)(20 66)(21 60)(22 69)(23 63)(24 57)(25 65)(26 59)(27 67)(28 61)(43 110)(44 97)(45 112)(46 85)(47 100)(48 87)(49 102)(50 89)(51 104)(52 91)(53 106)(54 93)(55 108)(56 95)(71 101)(72 88)(73 103)(74 90)(75 105)(76 92)(77 107)(78 94)(79 109)(80 96)(81 111)(82 98)(83 99)(84 86)
(1 19)(2 20)(3 21)(4 15)(5 16)(6 17)(7 18)(8 23)(9 24)(10 25)(11 26)(12 27)(13 28)(14 22)(29 66)(30 67)(31 68)(32 69)(33 70)(34 57)(35 58)(36 59)(37 60)(38 61)(39 62)(40 63)(41 64)(42 65)(43 50)(44 51)(45 52)(46 53)(47 54)(48 55)(49 56)(71 78)(72 79)(73 80)(74 81)(75 82)(76 83)(77 84)(85 106)(86 107)(87 108)(88 109)(89 110)(90 111)(91 112)(92 99)(93 100)(94 101)(95 102)(96 103)(97 104)(98 105)
(1 10)(2 11)(3 12)(4 13)(5 14)(6 8)(7 9)(15 28)(16 22)(17 23)(18 24)(19 25)(20 26)(21 27)(29 36)(30 37)(31 38)(32 39)(33 40)(34 41)(35 42)(43 80)(44 81)(45 82)(46 83)(47 84)(48 71)(49 72)(50 73)(51 74)(52 75)(53 76)(54 77)(55 78)(56 79)(57 64)(58 65)(59 66)(60 67)(61 68)(62 69)(63 70)(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 24)(2 23)(3 22)(4 28)(5 27)(6 26)(7 25)(8 20)(9 19)(10 18)(11 17)(12 16)(13 15)(14 21)(29 40)(30 39)(31 38)(32 37)(33 36)(34 35)(41 42)(43 47)(44 46)(48 56)(49 55)(50 54)(51 53)(57 58)(59 70)(60 69)(61 68)(62 67)(63 66)(64 65)(71 79)(72 78)(73 77)(74 76)(80 84)(81 83)(85 104)(86 103)(87 102)(88 101)(89 100)(90 99)(91 112)(92 111)(93 110)(94 109)(95 108)(96 107)(97 106)(98 105)
G:=sub<Sym(112)| (1,79)(2,73)(3,81)(4,75)(5,83)(6,77)(7,71)(8,54)(9,48)(10,56)(11,50)(12,44)(13,52)(14,46)(15,82)(16,76)(17,84)(18,78)(19,72)(20,80)(21,74)(22,53)(23,47)(24,55)(25,49)(26,43)(27,51)(28,45)(29,103)(30,97)(31,105)(32,85)(33,107)(34,87)(35,109)(36,89)(37,111)(38,91)(39,99)(40,93)(41,101)(42,95)(57,108)(58,88)(59,110)(60,90)(61,112)(62,92)(63,100)(64,94)(65,102)(66,96)(67,104)(68,98)(69,106)(70,86), (1,35)(2,29)(3,37)(4,31)(5,39)(6,33)(7,41)(8,40)(9,34)(10,42)(11,36)(12,30)(13,38)(14,32)(15,68)(16,62)(17,70)(18,64)(19,58)(20,66)(21,60)(22,69)(23,63)(24,57)(25,65)(26,59)(27,67)(28,61)(43,110)(44,97)(45,112)(46,85)(47,100)(48,87)(49,102)(50,89)(51,104)(52,91)(53,106)(54,93)(55,108)(56,95)(71,101)(72,88)(73,103)(74,90)(75,105)(76,92)(77,107)(78,94)(79,109)(80,96)(81,111)(82,98)(83,99)(84,86), (1,19)(2,20)(3,21)(4,15)(5,16)(6,17)(7,18)(8,23)(9,24)(10,25)(11,26)(12,27)(13,28)(14,22)(29,66)(30,67)(31,68)(32,69)(33,70)(34,57)(35,58)(36,59)(37,60)(38,61)(39,62)(40,63)(41,64)(42,65)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(85,106)(86,107)(87,108)(88,109)(89,110)(90,111)(91,112)(92,99)(93,100)(94,101)(95,102)(96,103)(97,104)(98,105), (1,10)(2,11)(3,12)(4,13)(5,14)(6,8)(7,9)(15,28)(16,22)(17,23)(18,24)(19,25)(20,26)(21,27)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,80)(44,81)(45,82)(46,83)(47,84)(48,71)(49,72)(50,73)(51,74)(52,75)(53,76)(54,77)(55,78)(56,79)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(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), (1,24)(2,23)(3,22)(4,28)(5,27)(6,26)(7,25)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)(14,21)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)(41,42)(43,47)(44,46)(48,56)(49,55)(50,54)(51,53)(57,58)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)(71,79)(72,78)(73,77)(74,76)(80,84)(81,83)(85,104)(86,103)(87,102)(88,101)(89,100)(90,99)(91,112)(92,111)(93,110)(94,109)(95,108)(96,107)(97,106)(98,105)>;
G:=Group( (1,79)(2,73)(3,81)(4,75)(5,83)(6,77)(7,71)(8,54)(9,48)(10,56)(11,50)(12,44)(13,52)(14,46)(15,82)(16,76)(17,84)(18,78)(19,72)(20,80)(21,74)(22,53)(23,47)(24,55)(25,49)(26,43)(27,51)(28,45)(29,103)(30,97)(31,105)(32,85)(33,107)(34,87)(35,109)(36,89)(37,111)(38,91)(39,99)(40,93)(41,101)(42,95)(57,108)(58,88)(59,110)(60,90)(61,112)(62,92)(63,100)(64,94)(65,102)(66,96)(67,104)(68,98)(69,106)(70,86), (1,35)(2,29)(3,37)(4,31)(5,39)(6,33)(7,41)(8,40)(9,34)(10,42)(11,36)(12,30)(13,38)(14,32)(15,68)(16,62)(17,70)(18,64)(19,58)(20,66)(21,60)(22,69)(23,63)(24,57)(25,65)(26,59)(27,67)(28,61)(43,110)(44,97)(45,112)(46,85)(47,100)(48,87)(49,102)(50,89)(51,104)(52,91)(53,106)(54,93)(55,108)(56,95)(71,101)(72,88)(73,103)(74,90)(75,105)(76,92)(77,107)(78,94)(79,109)(80,96)(81,111)(82,98)(83,99)(84,86), (1,19)(2,20)(3,21)(4,15)(5,16)(6,17)(7,18)(8,23)(9,24)(10,25)(11,26)(12,27)(13,28)(14,22)(29,66)(30,67)(31,68)(32,69)(33,70)(34,57)(35,58)(36,59)(37,60)(38,61)(39,62)(40,63)(41,64)(42,65)(43,50)(44,51)(45,52)(46,53)(47,54)(48,55)(49,56)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(85,106)(86,107)(87,108)(88,109)(89,110)(90,111)(91,112)(92,99)(93,100)(94,101)(95,102)(96,103)(97,104)(98,105), (1,10)(2,11)(3,12)(4,13)(5,14)(6,8)(7,9)(15,28)(16,22)(17,23)(18,24)(19,25)(20,26)(21,27)(29,36)(30,37)(31,38)(32,39)(33,40)(34,41)(35,42)(43,80)(44,81)(45,82)(46,83)(47,84)(48,71)(49,72)(50,73)(51,74)(52,75)(53,76)(54,77)(55,78)(56,79)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(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), (1,24)(2,23)(3,22)(4,28)(5,27)(6,26)(7,25)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)(14,21)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)(41,42)(43,47)(44,46)(48,56)(49,55)(50,54)(51,53)(57,58)(59,70)(60,69)(61,68)(62,67)(63,66)(64,65)(71,79)(72,78)(73,77)(74,76)(80,84)(81,83)(85,104)(86,103)(87,102)(88,101)(89,100)(90,99)(91,112)(92,111)(93,110)(94,109)(95,108)(96,107)(97,106)(98,105) );
G=PermutationGroup([[(1,79),(2,73),(3,81),(4,75),(5,83),(6,77),(7,71),(8,54),(9,48),(10,56),(11,50),(12,44),(13,52),(14,46),(15,82),(16,76),(17,84),(18,78),(19,72),(20,80),(21,74),(22,53),(23,47),(24,55),(25,49),(26,43),(27,51),(28,45),(29,103),(30,97),(31,105),(32,85),(33,107),(34,87),(35,109),(36,89),(37,111),(38,91),(39,99),(40,93),(41,101),(42,95),(57,108),(58,88),(59,110),(60,90),(61,112),(62,92),(63,100),(64,94),(65,102),(66,96),(67,104),(68,98),(69,106),(70,86)], [(1,35),(2,29),(3,37),(4,31),(5,39),(6,33),(7,41),(8,40),(9,34),(10,42),(11,36),(12,30),(13,38),(14,32),(15,68),(16,62),(17,70),(18,64),(19,58),(20,66),(21,60),(22,69),(23,63),(24,57),(25,65),(26,59),(27,67),(28,61),(43,110),(44,97),(45,112),(46,85),(47,100),(48,87),(49,102),(50,89),(51,104),(52,91),(53,106),(54,93),(55,108),(56,95),(71,101),(72,88),(73,103),(74,90),(75,105),(76,92),(77,107),(78,94),(79,109),(80,96),(81,111),(82,98),(83,99),(84,86)], [(1,19),(2,20),(3,21),(4,15),(5,16),(6,17),(7,18),(8,23),(9,24),(10,25),(11,26),(12,27),(13,28),(14,22),(29,66),(30,67),(31,68),(32,69),(33,70),(34,57),(35,58),(36,59),(37,60),(38,61),(39,62),(40,63),(41,64),(42,65),(43,50),(44,51),(45,52),(46,53),(47,54),(48,55),(49,56),(71,78),(72,79),(73,80),(74,81),(75,82),(76,83),(77,84),(85,106),(86,107),(87,108),(88,109),(89,110),(90,111),(91,112),(92,99),(93,100),(94,101),(95,102),(96,103),(97,104),(98,105)], [(1,10),(2,11),(3,12),(4,13),(5,14),(6,8),(7,9),(15,28),(16,22),(17,23),(18,24),(19,25),(20,26),(21,27),(29,36),(30,37),(31,38),(32,39),(33,40),(34,41),(35,42),(43,80),(44,81),(45,82),(46,83),(47,84),(48,71),(49,72),(50,73),(51,74),(52,75),(53,76),(54,77),(55,78),(56,79),(57,64),(58,65),(59,66),(60,67),(61,68),(62,69),(63,70),(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)], [(1,24),(2,23),(3,22),(4,28),(5,27),(6,26),(7,25),(8,20),(9,19),(10,18),(11,17),(12,16),(13,15),(14,21),(29,40),(30,39),(31,38),(32,37),(33,36),(34,35),(41,42),(43,47),(44,46),(48,56),(49,55),(50,54),(51,53),(57,58),(59,70),(60,69),(61,68),(62,67),(63,66),(64,65),(71,79),(72,78),(73,77),(74,76),(80,84),(81,83),(85,104),(86,103),(87,102),(88,101),(89,100),(90,99),(91,112),(92,111),(93,110),(94,109),(95,108),(96,107),(97,106),(98,105)]])
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 |
Matrix representation of C24⋊4D14 ►in 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] >;
C24⋊4D14 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