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⋊4D4⋊4C2, Dic7⋊D4⋊5C2, (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, C2.31(D4⋊6D14), C23.D7⋊17C22, 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, C23.177(C22×D7), C22.158(C23×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
Subgroups: 1100 in 250 conjugacy classes, 95 normal (91 characteristic)
C1, C2 [×3], C2 [×6], C4 [×10], C22, C22 [×2], C22 [×18], C7, C2×C4 [×3], C2×C4 [×11], D4 [×9], Q8, C23 [×4], C23 [×5], D7, C14 [×3], C14 [×5], C42 [×2], C22⋊C4 [×3], C22⋊C4 [×11], C4⋊C4 [×6], C22×C4 [×4], C2×D4 [×3], C2×D4 [×4], C2×Q8, C24, Dic7 [×7], C28 [×3], D14 [×3], C2×C14, C2×C14 [×2], C2×C14 [×15], C2×C22⋊C4, C4×D4 [×2], C22≀C2, C22≀C2, C4⋊D4 [×3], C22⋊Q8, C22.D4 [×2], C4.4D4 [×2], C42⋊2C2 [×2], Dic14, C4×D7, C2×Dic7 [×7], C2×Dic7 [×3], C7⋊D4 [×5], C2×C28 [×3], C7×D4 [×4], C22×D7, C22×C14 [×4], C22×C14 [×4], C22.32C24, C4×Dic7 [×2], Dic7⋊C4 [×4], C4⋊Dic7 [×2], D14⋊C4 [×2], C23.D7 [×9], C7×C22⋊C4 [×3], C2×Dic14, C2×C4×D7, C22×Dic7 [×3], C2×C7⋊D4 [×4], D4×C14 [×3], C23×C14, C22⋊Dic14, C23.D14 [×2], Dic7⋊4D4, D14.D4, Dic7.D4, D4×Dic7, C23.18D14, C28.17D4, C28⋊2D4, Dic7⋊D4 [×2], C2×C23.D7, C24⋊D7, C7×C22≀C2, C24.35D14
Quotients:
C1, C2 [×15], C22 [×35], C23 [×15], D7, C4○D4 [×2], C24, D14 [×7], C2×C4○D4, 2+ (1+4) [×2], C22×D7 [×7], C22.32C24, D4⋊2D7 [×2], C23×D7, C2×D4⋊2D7, D4⋊6D14 [×2], C24.35D14
Generators and relations
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 >
►On 112 points
Generators in S112
(2 101)(4 103)(6 105)(8 107)(10 109)(12 111)(14 85)(16 87)(18 89)(20 91)(22 93)(24 95)(26 97)(28 99)(29 43)(30 78)(31 45)(32 80)(33 47)(34 82)(35 49)(36 84)(37 51)(38 58)(39 53)(40 60)(41 55)(42 62)(44 64)(46 66)(48 68)(50 70)(52 72)(54 74)(56 76)(57 71)(59 73)(61 75)(63 77)(65 79)(67 81)(69 83)
(1 15)(3 17)(5 19)(7 21)(9 23)(11 25)(13 27)(29 77)(30 64)(31 79)(32 66)(33 81)(34 68)(35 83)(36 70)(37 57)(38 72)(39 59)(40 74)(41 61)(42 76)(43 63)(44 78)(45 65)(46 80)(47 67)(48 82)(49 69)(50 84)(51 71)(52 58)(53 73)(54 60)(55 75)(56 62)(86 100)(88 102)(90 104)(92 106)(94 108)(96 110)(98 112)
(1 100)(2 101)(3 102)(4 103)(5 104)(6 105)(7 106)(8 107)(9 108)(10 109)(11 110)(12 111)(13 112)(14 85)(15 86)(16 87)(17 88)(18 89)(19 90)(20 91)(21 92)(22 93)(23 94)(24 95)(25 96)(26 97)(27 98)(28 99)(29 63)(30 64)(31 65)(32 66)(33 67)(34 68)(35 69)(36 70)(37 71)(38 72)(39 73)(40 74)(41 75)(42 76)(43 77)(44 78)(45 79)(46 80)(47 81)(48 82)(49 83)(50 84)(51 57)(52 58)(53 59)(54 60)(55 61)(56 62)
(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 40 15 54)(2 53 16 39)(3 38 17 52)(4 51 18 37)(5 36 19 50)(6 49 20 35)(7 34 21 48)(8 47 22 33)(9 32 23 46)(10 45 24 31)(11 30 25 44)(12 43 26 29)(13 56 27 42)(14 41 28 55)(57 89 71 103)(58 102 72 88)(59 87 73 101)(60 100 74 86)(61 85 75 99)(62 98 76 112)(63 111 77 97)(64 96 78 110)(65 109 79 95)(66 94 80 108)(67 107 81 93)(68 92 82 106)(69 105 83 91)(70 90 84 104)
G:=sub<Sym(112)| (2,101)(4,103)(6,105)(8,107)(10,109)(12,111)(14,85)(16,87)(18,89)(20,91)(22,93)(24,95)(26,97)(28,99)(29,43)(30,78)(31,45)(32,80)(33,47)(34,82)(35,49)(36,84)(37,51)(38,58)(39,53)(40,60)(41,55)(42,62)(44,64)(46,66)(48,68)(50,70)(52,72)(54,74)(56,76)(57,71)(59,73)(61,75)(63,77)(65,79)(67,81)(69,83), (1,15)(3,17)(5,19)(7,21)(9,23)(11,25)(13,27)(29,77)(30,64)(31,79)(32,66)(33,81)(34,68)(35,83)(36,70)(37,57)(38,72)(39,59)(40,74)(41,61)(42,76)(43,63)(44,78)(45,65)(46,80)(47,67)(48,82)(49,69)(50,84)(51,71)(52,58)(53,73)(54,60)(55,75)(56,62)(86,100)(88,102)(90,104)(92,106)(94,108)(96,110)(98,112), (1,100)(2,101)(3,102)(4,103)(5,104)(6,105)(7,106)(8,107)(9,108)(10,109)(11,110)(12,111)(13,112)(14,85)(15,86)(16,87)(17,88)(18,89)(19,90)(20,91)(21,92)(22,93)(23,94)(24,95)(25,96)(26,97)(27,98)(28,99)(29,63)(30,64)(31,65)(32,66)(33,67)(34,68)(35,69)(36,70)(37,71)(38,72)(39,73)(40,74)(41,75)(42,76)(43,77)(44,78)(45,79)(46,80)(47,81)(48,82)(49,83)(50,84)(51,57)(52,58)(53,59)(54,60)(55,61)(56,62), (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), (1,40,15,54)(2,53,16,39)(3,38,17,52)(4,51,18,37)(5,36,19,50)(6,49,20,35)(7,34,21,48)(8,47,22,33)(9,32,23,46)(10,45,24,31)(11,30,25,44)(12,43,26,29)(13,56,27,42)(14,41,28,55)(57,89,71,103)(58,102,72,88)(59,87,73,101)(60,100,74,86)(61,85,75,99)(62,98,76,112)(63,111,77,97)(64,96,78,110)(65,109,79,95)(66,94,80,108)(67,107,81,93)(68,92,82,106)(69,105,83,91)(70,90,84,104)>;
G:=Group( (2,101)(4,103)(6,105)(8,107)(10,109)(12,111)(14,85)(16,87)(18,89)(20,91)(22,93)(24,95)(26,97)(28,99)(29,43)(30,78)(31,45)(32,80)(33,47)(34,82)(35,49)(36,84)(37,51)(38,58)(39,53)(40,60)(41,55)(42,62)(44,64)(46,66)(48,68)(50,70)(52,72)(54,74)(56,76)(57,71)(59,73)(61,75)(63,77)(65,79)(67,81)(69,83), (1,15)(3,17)(5,19)(7,21)(9,23)(11,25)(13,27)(29,77)(30,64)(31,79)(32,66)(33,81)(34,68)(35,83)(36,70)(37,57)(38,72)(39,59)(40,74)(41,61)(42,76)(43,63)(44,78)(45,65)(46,80)(47,67)(48,82)(49,69)(50,84)(51,71)(52,58)(53,73)(54,60)(55,75)(56,62)(86,100)(88,102)(90,104)(92,106)(94,108)(96,110)(98,112), (1,100)(2,101)(3,102)(4,103)(5,104)(6,105)(7,106)(8,107)(9,108)(10,109)(11,110)(12,111)(13,112)(14,85)(15,86)(16,87)(17,88)(18,89)(19,90)(20,91)(21,92)(22,93)(23,94)(24,95)(25,96)(26,97)(27,98)(28,99)(29,63)(30,64)(31,65)(32,66)(33,67)(34,68)(35,69)(36,70)(37,71)(38,72)(39,73)(40,74)(41,75)(42,76)(43,77)(44,78)(45,79)(46,80)(47,81)(48,82)(49,83)(50,84)(51,57)(52,58)(53,59)(54,60)(55,61)(56,62), (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), (1,40,15,54)(2,53,16,39)(3,38,17,52)(4,51,18,37)(5,36,19,50)(6,49,20,35)(7,34,21,48)(8,47,22,33)(9,32,23,46)(10,45,24,31)(11,30,25,44)(12,43,26,29)(13,56,27,42)(14,41,28,55)(57,89,71,103)(58,102,72,88)(59,87,73,101)(60,100,74,86)(61,85,75,99)(62,98,76,112)(63,111,77,97)(64,96,78,110)(65,109,79,95)(66,94,80,108)(67,107,81,93)(68,92,82,106)(69,105,83,91)(70,90,84,104) );
G=PermutationGroup([(2,101),(4,103),(6,105),(8,107),(10,109),(12,111),(14,85),(16,87),(18,89),(20,91),(22,93),(24,95),(26,97),(28,99),(29,43),(30,78),(31,45),(32,80),(33,47),(34,82),(35,49),(36,84),(37,51),(38,58),(39,53),(40,60),(41,55),(42,62),(44,64),(46,66),(48,68),(50,70),(52,72),(54,74),(56,76),(57,71),(59,73),(61,75),(63,77),(65,79),(67,81),(69,83)], [(1,15),(3,17),(5,19),(7,21),(9,23),(11,25),(13,27),(29,77),(30,64),(31,79),(32,66),(33,81),(34,68),(35,83),(36,70),(37,57),(38,72),(39,59),(40,74),(41,61),(42,76),(43,63),(44,78),(45,65),(46,80),(47,67),(48,82),(49,69),(50,84),(51,71),(52,58),(53,73),(54,60),(55,75),(56,62),(86,100),(88,102),(90,104),(92,106),(94,108),(96,110),(98,112)], [(1,100),(2,101),(3,102),(4,103),(5,104),(6,105),(7,106),(8,107),(9,108),(10,109),(11,110),(12,111),(13,112),(14,85),(15,86),(16,87),(17,88),(18,89),(19,90),(20,91),(21,92),(22,93),(23,94),(24,95),(25,96),(26,97),(27,98),(28,99),(29,63),(30,64),(31,65),(32,66),(33,67),(34,68),(35,69),(36,70),(37,71),(38,72),(39,73),(40,74),(41,75),(42,76),(43,77),(44,78),(45,79),(46,80),(47,81),(48,82),(49,83),(50,84),(51,57),(52,58),(53,59),(54,60),(55,61),(56,62)], [(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)], [(1,40,15,54),(2,53,16,39),(3,38,17,52),(4,51,18,37),(5,36,19,50),(6,49,20,35),(7,34,21,48),(8,47,22,33),(9,32,23,46),(10,45,24,31),(11,30,25,44),(12,43,26,29),(13,56,27,42),(14,41,28,55),(57,89,71,103),(58,102,72,88),(59,87,73,101),(60,100,74,86),(61,85,75,99),(62,98,76,112),(63,111,77,97),(64,96,78,110),(65,109,79,95),(66,94,80,108),(67,107,81,93),(68,92,82,106),(69,105,83,91),(70,90,84,104)])
Matrix representation ►G ⊆ 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] >;
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 |
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
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