metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.34D14, C14.282+ 1+4, (C2×D4)⋊6D14, C22≀C2⋊5D7, C22⋊C4⋊7D14, (C2×Dic7)⋊8D4, C23⋊D14⋊6C2, C28⋊D4⋊12C2, (D4×C14)⋊9C22, C24⋊D7⋊7C2, Dic7.4(C2×D4), C22⋊D28⋊10C2, D14⋊D4⋊14C2, C22.41(D4×D7), D14⋊C4⋊13C22, Dic7⋊D4⋊4C2, (C2×D28)⋊20C22, (C2×C28).30C23, C14.58(C22×D4), (C2×C14).136C24, Dic7⋊C4⋊11C22, C7⋊2(C22.29C24), (C4×Dic7)⋊16C22, C2.30(D4⋊6D14), C23.D7⋊16C22, Dic7.D4⋊13C2, (C2×Dic14)⋊21C22, C23.11D14⋊3C2, (C23×C14).69C22, (C22×C14).10C23, (C2×Dic7).61C23, (C23×D7).44C22, (C22×D7).55C23, C23.109(C22×D7), C22.157(C23×D7), (C22×Dic7)⋊15C22, C2.31(C2×D4×D7), (C2×C4×D7)⋊9C22, (C7×C22≀C2)⋊7C2, (C2×D4⋊2D7)⋊7C2, (C2×C14).55(C2×D4), (C2×C7⋊D4)⋊9C22, (C22×C7⋊D4)⋊10C2, (C7×C22⋊C4)⋊7C22, (C2×C4).30(C22×D7), SmallGroup(448,1045)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for C24.34D14
G = < a,b,c,d,e,f | a2=b2=c2=d2=e14=1, f2=d, ab=ba, eae-1=faf-1=ac=ca, ad=da, bc=cb, ebe-1=bd=db, fbf-1=bcd, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=de-1 >
Subgroups: 1804 in 334 conjugacy classes, 103 normal (39 characteristic)
C1, C2, C2, C2, C4, C22, C22, C22, C7, C2×C4, C2×C4, C2×C4, D4, Q8, C23, C23, C23, D7, C14, C14, C14, C42, C22⋊C4, C22⋊C4, C22⋊C4, C4⋊C4, C22×C4, C2×D4, C2×D4, C2×D4, C2×Q8, C4○D4, C24, C24, Dic7, Dic7, C28, D14, C2×C14, C2×C14, C2×C14, C42⋊C2, C22≀C2, C22≀C2, C4⋊D4, C4.4D4, C4⋊1D4, C22×D4, C2×C4○D4, Dic14, C4×D7, D28, C2×Dic7, C2×Dic7, C2×Dic7, C7⋊D4, C2×C28, C2×C28, C7×D4, C22×D7, C22×D7, C22×D7, C22×C14, C22×C14, C22×C14, C22.29C24, C4×Dic7, Dic7⋊C4, D14⋊C4, C23.D7, C23.D7, C7×C22⋊C4, C7×C22⋊C4, C2×Dic14, C2×C4×D7, C2×D28, D4⋊2D7, C22×Dic7, C2×C7⋊D4, C2×C7⋊D4, C2×C7⋊D4, D4×C14, D4×C14, C23×D7, C23×C14, C23.11D14, C22⋊D28, D14⋊D4, Dic7.D4, C23⋊D14, Dic7⋊D4, C28⋊D4, C24⋊D7, C7×C22≀C2, C2×D4⋊2D7, C22×C7⋊D4, C24.34D14
Quotients: C1, C2, C22, D4, C23, D7, C2×D4, C24, D14, C22×D4, 2+ 1+4, C22×D7, C22.29C24, D4×D7, C23×D7, C2×D4×D7, D4⋊6D14, C24.34D14
►On 112 points
Generators in S112
(1 75)(2 64)(3 77)(4 66)(5 79)(6 68)(7 81)(8 70)(9 83)(10 58)(11 71)(12 60)(13 73)(14 62)(15 32)(16 55)(17 34)(18 43)(19 36)(20 45)(21 38)(22 47)(23 40)(24 49)(25 42)(26 51)(27 30)(28 53)(29 111)(31 99)(33 101)(35 103)(37 105)(39 107)(41 109)(44 104)(46 106)(48 108)(50 110)(52 112)(54 100)(56 102)(57 88)(59 90)(61 92)(63 94)(65 96)(67 98)(69 86)(72 91)(74 93)(76 95)(78 97)(80 85)(82 87)(84 89)
(1 104)(2 45)(3 106)(4 47)(5 108)(6 49)(7 110)(8 51)(9 112)(10 53)(11 100)(12 55)(13 102)(14 43)(15 90)(16 60)(17 92)(18 62)(19 94)(20 64)(21 96)(22 66)(23 98)(24 68)(25 86)(26 70)(27 88)(28 58)(29 87)(30 57)(31 89)(32 59)(33 91)(34 61)(35 93)(36 63)(37 95)(38 65)(39 97)(40 67)(41 85)(42 69)(44 75)(46 77)(48 79)(50 81)(52 83)(54 71)(56 73)(72 101)(74 103)(76 105)(78 107)(80 109)(82 111)(84 99)
(1 94)(2 95)(3 96)(4 97)(5 98)(6 85)(7 86)(8 87)(9 88)(10 89)(11 90)(12 91)(13 92)(14 93)(15 100)(16 101)(17 102)(18 103)(19 104)(20 105)(21 106)(22 107)(23 108)(24 109)(25 110)(26 111)(27 112)(28 99)(29 51)(30 52)(31 53)(32 54)(33 55)(34 56)(35 43)(36 44)(37 45)(38 46)(39 47)(40 48)(41 49)(42 50)(57 83)(58 84)(59 71)(60 72)(61 73)(62 74)(63 75)(64 76)(65 77)(66 78)(67 79)(68 80)(69 81)(70 82)
(1 75)(2 76)(3 77)(4 78)(5 79)(6 80)(7 81)(8 82)(9 83)(10 84)(11 71)(12 72)(13 73)(14 74)(15 32)(16 33)(17 34)(18 35)(19 36)(20 37)(21 38)(22 39)(23 40)(24 41)(25 42)(26 29)(27 30)(28 31)(43 103)(44 104)(45 105)(46 106)(47 107)(48 108)(49 109)(50 110)(51 111)(52 112)(53 99)(54 100)(55 101)(56 102)(57 88)(58 89)(59 90)(60 91)(61 92)(62 93)(63 94)(64 95)(65 96)(66 97)(67 98)(68 85)(69 86)(70 87)
(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 14 75 74)(2 73 76 13)(3 12 77 72)(4 71 78 11)(5 10 79 84)(6 83 80 9)(7 8 81 82)(15 107 32 47)(16 46 33 106)(17 105 34 45)(18 44 35 104)(19 103 36 43)(20 56 37 102)(21 101 38 55)(22 54 39 100)(23 99 40 53)(24 52 41 112)(25 111 42 51)(26 50 29 110)(27 109 30 49)(28 48 31 108)(57 68 88 85)(58 98 89 67)(59 66 90 97)(60 96 91 65)(61 64 92 95)(62 94 93 63)(69 70 86 87)
G:=sub<Sym(112)| (1,75)(2,64)(3,77)(4,66)(5,79)(6,68)(7,81)(8,70)(9,83)(10,58)(11,71)(12,60)(13,73)(14,62)(15,32)(16,55)(17,34)(18,43)(19,36)(20,45)(21,38)(22,47)(23,40)(24,49)(25,42)(26,51)(27,30)(28,53)(29,111)(31,99)(33,101)(35,103)(37,105)(39,107)(41,109)(44,104)(46,106)(48,108)(50,110)(52,112)(54,100)(56,102)(57,88)(59,90)(61,92)(63,94)(65,96)(67,98)(69,86)(72,91)(74,93)(76,95)(78,97)(80,85)(82,87)(84,89), (1,104)(2,45)(3,106)(4,47)(5,108)(6,49)(7,110)(8,51)(9,112)(10,53)(11,100)(12,55)(13,102)(14,43)(15,90)(16,60)(17,92)(18,62)(19,94)(20,64)(21,96)(22,66)(23,98)(24,68)(25,86)(26,70)(27,88)(28,58)(29,87)(30,57)(31,89)(32,59)(33,91)(34,61)(35,93)(36,63)(37,95)(38,65)(39,97)(40,67)(41,85)(42,69)(44,75)(46,77)(48,79)(50,81)(52,83)(54,71)(56,73)(72,101)(74,103)(76,105)(78,107)(80,109)(82,111)(84,99), (1,94)(2,95)(3,96)(4,97)(5,98)(6,85)(7,86)(8,87)(9,88)(10,89)(11,90)(12,91)(13,92)(14,93)(15,100)(16,101)(17,102)(18,103)(19,104)(20,105)(21,106)(22,107)(23,108)(24,109)(25,110)(26,111)(27,112)(28,99)(29,51)(30,52)(31,53)(32,54)(33,55)(34,56)(35,43)(36,44)(37,45)(38,46)(39,47)(40,48)(41,49)(42,50)(57,83)(58,84)(59,71)(60,72)(61,73)(62,74)(63,75)(64,76)(65,77)(66,78)(67,79)(68,80)(69,81)(70,82), (1,75)(2,76)(3,77)(4,78)(5,79)(6,80)(7,81)(8,82)(9,83)(10,84)(11,71)(12,72)(13,73)(14,74)(15,32)(16,33)(17,34)(18,35)(19,36)(20,37)(21,38)(22,39)(23,40)(24,41)(25,42)(26,29)(27,30)(28,31)(43,103)(44,104)(45,105)(46,106)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,99)(54,100)(55,101)(56,102)(57,88)(58,89)(59,90)(60,91)(61,92)(62,93)(63,94)(64,95)(65,96)(66,97)(67,98)(68,85)(69,86)(70,87), (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), (1,14,75,74)(2,73,76,13)(3,12,77,72)(4,71,78,11)(5,10,79,84)(6,83,80,9)(7,8,81,82)(15,107,32,47)(16,46,33,106)(17,105,34,45)(18,44,35,104)(19,103,36,43)(20,56,37,102)(21,101,38,55)(22,54,39,100)(23,99,40,53)(24,52,41,112)(25,111,42,51)(26,50,29,110)(27,109,30,49)(28,48,31,108)(57,68,88,85)(58,98,89,67)(59,66,90,97)(60,96,91,65)(61,64,92,95)(62,94,93,63)(69,70,86,87)>;
G:=Group( (1,75)(2,64)(3,77)(4,66)(5,79)(6,68)(7,81)(8,70)(9,83)(10,58)(11,71)(12,60)(13,73)(14,62)(15,32)(16,55)(17,34)(18,43)(19,36)(20,45)(21,38)(22,47)(23,40)(24,49)(25,42)(26,51)(27,30)(28,53)(29,111)(31,99)(33,101)(35,103)(37,105)(39,107)(41,109)(44,104)(46,106)(48,108)(50,110)(52,112)(54,100)(56,102)(57,88)(59,90)(61,92)(63,94)(65,96)(67,98)(69,86)(72,91)(74,93)(76,95)(78,97)(80,85)(82,87)(84,89), (1,104)(2,45)(3,106)(4,47)(5,108)(6,49)(7,110)(8,51)(9,112)(10,53)(11,100)(12,55)(13,102)(14,43)(15,90)(16,60)(17,92)(18,62)(19,94)(20,64)(21,96)(22,66)(23,98)(24,68)(25,86)(26,70)(27,88)(28,58)(29,87)(30,57)(31,89)(32,59)(33,91)(34,61)(35,93)(36,63)(37,95)(38,65)(39,97)(40,67)(41,85)(42,69)(44,75)(46,77)(48,79)(50,81)(52,83)(54,71)(56,73)(72,101)(74,103)(76,105)(78,107)(80,109)(82,111)(84,99), (1,94)(2,95)(3,96)(4,97)(5,98)(6,85)(7,86)(8,87)(9,88)(10,89)(11,90)(12,91)(13,92)(14,93)(15,100)(16,101)(17,102)(18,103)(19,104)(20,105)(21,106)(22,107)(23,108)(24,109)(25,110)(26,111)(27,112)(28,99)(29,51)(30,52)(31,53)(32,54)(33,55)(34,56)(35,43)(36,44)(37,45)(38,46)(39,47)(40,48)(41,49)(42,50)(57,83)(58,84)(59,71)(60,72)(61,73)(62,74)(63,75)(64,76)(65,77)(66,78)(67,79)(68,80)(69,81)(70,82), (1,75)(2,76)(3,77)(4,78)(5,79)(6,80)(7,81)(8,82)(9,83)(10,84)(11,71)(12,72)(13,73)(14,74)(15,32)(16,33)(17,34)(18,35)(19,36)(20,37)(21,38)(22,39)(23,40)(24,41)(25,42)(26,29)(27,30)(28,31)(43,103)(44,104)(45,105)(46,106)(47,107)(48,108)(49,109)(50,110)(51,111)(52,112)(53,99)(54,100)(55,101)(56,102)(57,88)(58,89)(59,90)(60,91)(61,92)(62,93)(63,94)(64,95)(65,96)(66,97)(67,98)(68,85)(69,86)(70,87), (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), (1,14,75,74)(2,73,76,13)(3,12,77,72)(4,71,78,11)(5,10,79,84)(6,83,80,9)(7,8,81,82)(15,107,32,47)(16,46,33,106)(17,105,34,45)(18,44,35,104)(19,103,36,43)(20,56,37,102)(21,101,38,55)(22,54,39,100)(23,99,40,53)(24,52,41,112)(25,111,42,51)(26,50,29,110)(27,109,30,49)(28,48,31,108)(57,68,88,85)(58,98,89,67)(59,66,90,97)(60,96,91,65)(61,64,92,95)(62,94,93,63)(69,70,86,87) );
G=PermutationGroup([[(1,75),(2,64),(3,77),(4,66),(5,79),(6,68),(7,81),(8,70),(9,83),(10,58),(11,71),(12,60),(13,73),(14,62),(15,32),(16,55),(17,34),(18,43),(19,36),(20,45),(21,38),(22,47),(23,40),(24,49),(25,42),(26,51),(27,30),(28,53),(29,111),(31,99),(33,101),(35,103),(37,105),(39,107),(41,109),(44,104),(46,106),(48,108),(50,110),(52,112),(54,100),(56,102),(57,88),(59,90),(61,92),(63,94),(65,96),(67,98),(69,86),(72,91),(74,93),(76,95),(78,97),(80,85),(82,87),(84,89)], [(1,104),(2,45),(3,106),(4,47),(5,108),(6,49),(7,110),(8,51),(9,112),(10,53),(11,100),(12,55),(13,102),(14,43),(15,90),(16,60),(17,92),(18,62),(19,94),(20,64),(21,96),(22,66),(23,98),(24,68),(25,86),(26,70),(27,88),(28,58),(29,87),(30,57),(31,89),(32,59),(33,91),(34,61),(35,93),(36,63),(37,95),(38,65),(39,97),(40,67),(41,85),(42,69),(44,75),(46,77),(48,79),(50,81),(52,83),(54,71),(56,73),(72,101),(74,103),(76,105),(78,107),(80,109),(82,111),(84,99)], [(1,94),(2,95),(3,96),(4,97),(5,98),(6,85),(7,86),(8,87),(9,88),(10,89),(11,90),(12,91),(13,92),(14,93),(15,100),(16,101),(17,102),(18,103),(19,104),(20,105),(21,106),(22,107),(23,108),(24,109),(25,110),(26,111),(27,112),(28,99),(29,51),(30,52),(31,53),(32,54),(33,55),(34,56),(35,43),(36,44),(37,45),(38,46),(39,47),(40,48),(41,49),(42,50),(57,83),(58,84),(59,71),(60,72),(61,73),(62,74),(63,75),(64,76),(65,77),(66,78),(67,79),(68,80),(69,81),(70,82)], [(1,75),(2,76),(3,77),(4,78),(5,79),(6,80),(7,81),(8,82),(9,83),(10,84),(11,71),(12,72),(13,73),(14,74),(15,32),(16,33),(17,34),(18,35),(19,36),(20,37),(21,38),(22,39),(23,40),(24,41),(25,42),(26,29),(27,30),(28,31),(43,103),(44,104),(45,105),(46,106),(47,107),(48,108),(49,109),(50,110),(51,111),(52,112),(53,99),(54,100),(55,101),(56,102),(57,88),(58,89),(59,90),(60,91),(61,92),(62,93),(63,94),(64,95),(65,96),(66,97),(67,98),(68,85),(69,86),(70,87)], [(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)], [(1,14,75,74),(2,73,76,13),(3,12,77,72),(4,71,78,11),(5,10,79,84),(6,83,80,9),(7,8,81,82),(15,107,32,47),(16,46,33,106),(17,105,34,45),(18,44,35,104),(19,103,36,43),(20,56,37,102),(21,101,38,55),(22,54,39,100),(23,99,40,53),(24,52,41,112),(25,111,42,51),(26,50,29,110),(27,109,30,49),(28,48,31,108),(57,68,88,85),(58,98,89,67),(59,66,90,97),(60,96,91,65),(61,64,92,95),(62,94,93,63),(69,70,86,87)]])
64 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 2J | 2K | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 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 | 4 | 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 | 28 | 28 | 4 | 4 | 4 | 14 | 14 | 14 | 14 | 28 | 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 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | D14 | D14 | D14 | 2+ 1+4 | D4×D7 | D4⋊6D14 |
| kernel | C24.34D14 | C23.11D14 | C22⋊D28 | D14⋊D4 | Dic7.D4 | C23⋊D14 | Dic7⋊D4 | C28⋊D4 | C24⋊D7 | C7×C22≀C2 | C2×D4⋊2D7 | C22×C7⋊D4 | C2×Dic7 | C22≀C2 | C22⋊C4 | C2×D4 | C24 | C14 | C22 | C2 |
| # reps | 1 | 1 | 1 | 2 | 2 | 1 | 2 | 2 | 1 | 1 | 1 | 1 | 4 | 3 | 9 | 9 | 3 | 2 | 6 | 12 |
Matrix representation of C24.34D14 ►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 | 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 | 9 | 17 | 1 | 0 |
| 0 | 0 | 0 | 0 | 24 | 18 | 0 | 1 |
| 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 | 11 | 16 | 0 | 0 |
| 0 | 0 | 0 | 0 | 7 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 10 | 9 | 24 | 13 |
| 0 | 0 | 0 | 0 | 24 | 1 | 16 | 5 |
| 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 | 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 | 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 |
| 11 | 18 | 12 | 17 | 0 | 0 | 0 | 0 |
| 11 | 21 | 12 | 15 | 0 | 0 | 0 | 0 |
| 17 | 12 | 18 | 11 | 0 | 0 | 0 | 0 |
| 17 | 14 | 18 | 8 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 3 | 4 | 6 | 27 |
| 0 | 0 | 0 | 0 | 26 | 1 | 7 | 8 |
| 0 | 0 | 0 | 0 | 3 | 4 | 15 | 28 |
| 0 | 0 | 0 | 0 | 20 | 5 | 10 | 10 |
| 18 | 11 | 17 | 12 | 0 | 0 | 0 | 0 |
| 21 | 11 | 15 | 12 | 0 | 0 | 0 | 0 |
| 12 | 17 | 11 | 18 | 0 | 0 | 0 | 0 |
| 14 | 17 | 8 | 18 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 24 | 21 | 2 | 23 |
| 0 | 0 | 0 | 0 | 25 | 14 | 21 | 22 |
| 0 | 0 | 0 | 0 | 4 | 20 | 1 | 14 |
| 0 | 0 | 0 | 0 | 11 | 14 | 19 | 19 |
G:=sub<GL(8,GF(29))| [28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,9,24,0,0,0,0,0,28,17,18,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1],[0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,11,7,10,24,0,0,0,0,16,18,9,1,0,0,0,0,0,0,24,16,0,0,0,0,0,0,13,5],[1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28],[28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28,0,0,0,0,0,0,0,0,28],[11,11,17,17,0,0,0,0,18,21,12,14,0,0,0,0,12,12,18,18,0,0,0,0,17,15,11,8,0,0,0,0,0,0,0,0,3,26,3,20,0,0,0,0,4,1,4,5,0,0,0,0,6,7,15,10,0,0,0,0,27,8,28,10],[18,21,12,14,0,0,0,0,11,11,17,17,0,0,0,0,17,15,11,8,0,0,0,0,12,12,18,18,0,0,0,0,0,0,0,0,24,25,4,11,0,0,0,0,21,14,20,14,0,0,0,0,2,21,1,19,0,0,0,0,23,22,14,19] >;
C24.34D14 in GAP, Magma, Sage, TeX
C_2^4._{34}D_{14} % in TeX
G:=Group("C2^4.34D14"); // GroupNames label
G:=SmallGroup(448,1045);
// by ID
G=gap.SmallGroup(448,1045);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,219,675,297,18822]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^2=b^2=c^2=d^2=e^14=1,f^2=d,a*b=b*a,e*a*e^-1=f*a*f^-1=a*c=c*a,a*d=d*a,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=d*e^-1>;
// generators/relations