metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24.33D14, C14.272+ (1+4), C7⋊D4⋊5D4, (C2×D4)⋊19D14, C7⋊4(D4⋊5D4), C22≀C2⋊4D7, C22⋊C4⋊6D14, C23⋊D14⋊5C2, C28⋊2D4⋊13C2, (D4×Dic7)⋊12C2, D14.16(C2×D4), (D4×C14)⋊8C22, C22.11(D4×D7), D14⋊C4⋊12C22, Dic7⋊4D4⋊3C2, Dic7⋊D4⋊3C2, (C2×C28).29C23, C4⋊Dic7⋊26C22, Dic7.19(C2×D4), C14.57(C22×D4), D14.D4⋊13C2, C22⋊4(D4⋊2D7), C23.7(C22×D7), (C2×C14).135C24, Dic7⋊C4⋊10C22, (C4×Dic7)⋊15C22, (C22×C14).9C23, C23.D7⋊50C22, C2.29(D4⋊6D14), C22⋊Dic14⋊13C2, Dic7.D4⋊12C2, (C2×Dic14)⋊20C22, C22.D28⋊10C2, (C23×C14).68C22, (C23×D7).43C22, (C22×D7).54C23, C22.156(C23×D7), (C2×Dic7).222C23, (C22×Dic7)⋊14C22, C2.30(C2×D4×D7), (C2×C4×D7)⋊8C22, (D7×C22⋊C4)⋊3C2, (C7×C22≀C2)⋊6C2, (C2×D4⋊2D7)⋊6C2, C14.77(C2×C4○D4), (C2×C14).54(C2×D4), (C22×C7⋊D4)⋊9C2, (C2×C7⋊D4)⋊8C22, (C2×C14)⋊10(C4○D4), C2.28(C2×D4⋊2D7), (C7×C22⋊C4)⋊6C22, (C2×C23.D7)⋊20C2, (C2×C4).29(C22×D7), SmallGroup(448,1044)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1644 in 334 conjugacy classes, 107 normal (91 characteristic)
C1, C2 [×3], C2 [×9], C4 [×10], C22, C22 [×4], C22 [×25], C7, C2×C4 [×3], C2×C4 [×16], D4 [×18], Q8 [×2], C23 [×4], C23 [×12], D7 [×3], C14 [×3], C14 [×6], C42, C22⋊C4 [×3], C22⋊C4 [×9], C4⋊C4 [×4], C22×C4 [×6], C2×D4 [×3], C2×D4 [×10], C2×Q8, C4○D4 [×4], C24, C24, Dic7 [×2], Dic7 [×5], C28 [×3], D14 [×2], D14 [×9], C2×C14, C2×C14 [×4], C2×C14 [×14], C2×C22⋊C4 [×2], C4×D4 [×2], C22≀C2, C22≀C2, C4⋊D4 [×3], C22⋊Q8, C22.D4 [×2], C4.4D4, C22×D4, C2×C4○D4, Dic14 [×2], C4×D7 [×3], C2×Dic7 [×6], C2×Dic7 [×7], C7⋊D4 [×4], C7⋊D4 [×9], C2×C28 [×3], C7×D4 [×5], C22×D7 [×2], C22×D7 [×5], C22×C14 [×4], C22×C14 [×5], D4⋊5D4, C4×Dic7, Dic7⋊C4 [×2], C4⋊Dic7 [×2], D14⋊C4 [×4], C23.D7 [×5], C7×C22⋊C4 [×3], C2×Dic14, C2×C4×D7 [×2], D4⋊2D7 [×4], C22×Dic7 [×4], C2×C7⋊D4 [×6], C2×C7⋊D4 [×4], D4×C14 [×3], C23×D7, C23×C14, C22⋊Dic14, D7×C22⋊C4, Dic7⋊4D4, D14.D4, Dic7.D4, C22.D28, D4×Dic7, C23⋊D14, C28⋊2D4, Dic7⋊D4 [×2], C2×C23.D7, C7×C22≀C2, C2×D4⋊2D7, C22×C7⋊D4, C24.33D14
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C4○D4 [×2], C24, D14 [×7], C22×D4, C2×C4○D4, 2+ (1+4), C22×D7 [×7], D4⋊5D4, D4×D7 [×2], D4⋊2D7 [×2], C23×D7, C2×D4×D7, C2×D4⋊2D7, D4⋊6D14, C24.33D14
Generators and relations
G = < a,b,c,d,e,f | a2=b2=c2=d2=1, e14=f2=d, ab=ba, eae-1=faf-1=ac=ca, ad=da, fbf-1=bc=cb, ebe-1=bd=db, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef-1=e13 >
►On 112 points
Generators in S112
(2 57)(4 59)(6 61)(8 63)(10 65)(12 67)(14 69)(16 71)(18 73)(20 75)(22 77)(24 79)(26 81)(28 83)(29 96)(31 98)(33 100)(35 102)(37 104)(39 106)(41 108)(43 110)(45 112)(47 86)(49 88)(51 90)(53 92)(55 94)
(1 111)(2 98)(3 85)(4 100)(5 87)(6 102)(7 89)(8 104)(9 91)(10 106)(11 93)(12 108)(13 95)(14 110)(15 97)(16 112)(17 99)(18 86)(19 101)(20 88)(21 103)(22 90)(23 105)(24 92)(25 107)(26 94)(27 109)(28 96)(29 83)(30 70)(31 57)(32 72)(33 59)(34 74)(35 61)(36 76)(37 63)(38 78)(39 65)(40 80)(41 67)(42 82)(43 69)(44 84)(45 71)(46 58)(47 73)(48 60)(49 75)(50 62)(51 77)(52 64)(53 79)(54 66)(55 81)(56 68)
(1 84)(2 57)(3 58)(4 59)(5 60)(6 61)(7 62)(8 63)(9 64)(10 65)(11 66)(12 67)(13 68)(14 69)(15 70)(16 71)(17 72)(18 73)(19 74)(20 75)(21 76)(22 77)(23 78)(24 79)(25 80)(26 81)(27 82)(28 83)(29 96)(30 97)(31 98)(32 99)(33 100)(34 101)(35 102)(36 103)(37 104)(38 105)(39 106)(40 107)(41 108)(42 109)(43 110)(44 111)(45 112)(46 85)(47 86)(48 87)(49 88)(50 89)(51 90)(52 91)(53 92)(54 93)(55 94)(56 95)
(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 28 15 14)(2 13 16 27)(3 26 17 12)(4 11 18 25)(5 24 19 10)(6 9 20 23)(7 22 21 8)(29 97 43 111)(30 110 44 96)(31 95 45 109)(32 108 46 94)(33 93 47 107)(34 106 48 92)(35 91 49 105)(36 104 50 90)(37 89 51 103)(38 102 52 88)(39 87 53 101)(40 100 54 86)(41 85 55 99)(42 98 56 112)(57 68 71 82)(58 81 72 67)(59 66 73 80)(60 79 74 65)(61 64 75 78)(62 77 76 63)(69 84 83 70)
G:=sub<Sym(112)| (2,57)(4,59)(6,61)(8,63)(10,65)(12,67)(14,69)(16,71)(18,73)(20,75)(22,77)(24,79)(26,81)(28,83)(29,96)(31,98)(33,100)(35,102)(37,104)(39,106)(41,108)(43,110)(45,112)(47,86)(49,88)(51,90)(53,92)(55,94), (1,111)(2,98)(3,85)(4,100)(5,87)(6,102)(7,89)(8,104)(9,91)(10,106)(11,93)(12,108)(13,95)(14,110)(15,97)(16,112)(17,99)(18,86)(19,101)(20,88)(21,103)(22,90)(23,105)(24,92)(25,107)(26,94)(27,109)(28,96)(29,83)(30,70)(31,57)(32,72)(33,59)(34,74)(35,61)(36,76)(37,63)(38,78)(39,65)(40,80)(41,67)(42,82)(43,69)(44,84)(45,71)(46,58)(47,73)(48,60)(49,75)(50,62)(51,77)(52,64)(53,79)(54,66)(55,81)(56,68), (1,84)(2,57)(3,58)(4,59)(5,60)(6,61)(7,62)(8,63)(9,64)(10,65)(11,66)(12,67)(13,68)(14,69)(15,70)(16,71)(17,72)(18,73)(19,74)(20,75)(21,76)(22,77)(23,78)(24,79)(25,80)(26,81)(27,82)(28,83)(29,96)(30,97)(31,98)(32,99)(33,100)(34,101)(35,102)(36,103)(37,104)(38,105)(39,106)(40,107)(41,108)(42,109)(43,110)(44,111)(45,112)(46,85)(47,86)(48,87)(49,88)(50,89)(51,90)(52,91)(53,92)(54,93)(55,94)(56,95), (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), (1,28,15,14)(2,13,16,27)(3,26,17,12)(4,11,18,25)(5,24,19,10)(6,9,20,23)(7,22,21,8)(29,97,43,111)(30,110,44,96)(31,95,45,109)(32,108,46,94)(33,93,47,107)(34,106,48,92)(35,91,49,105)(36,104,50,90)(37,89,51,103)(38,102,52,88)(39,87,53,101)(40,100,54,86)(41,85,55,99)(42,98,56,112)(57,68,71,82)(58,81,72,67)(59,66,73,80)(60,79,74,65)(61,64,75,78)(62,77,76,63)(69,84,83,70)>;
G:=Group( (2,57)(4,59)(6,61)(8,63)(10,65)(12,67)(14,69)(16,71)(18,73)(20,75)(22,77)(24,79)(26,81)(28,83)(29,96)(31,98)(33,100)(35,102)(37,104)(39,106)(41,108)(43,110)(45,112)(47,86)(49,88)(51,90)(53,92)(55,94), (1,111)(2,98)(3,85)(4,100)(5,87)(6,102)(7,89)(8,104)(9,91)(10,106)(11,93)(12,108)(13,95)(14,110)(15,97)(16,112)(17,99)(18,86)(19,101)(20,88)(21,103)(22,90)(23,105)(24,92)(25,107)(26,94)(27,109)(28,96)(29,83)(30,70)(31,57)(32,72)(33,59)(34,74)(35,61)(36,76)(37,63)(38,78)(39,65)(40,80)(41,67)(42,82)(43,69)(44,84)(45,71)(46,58)(47,73)(48,60)(49,75)(50,62)(51,77)(52,64)(53,79)(54,66)(55,81)(56,68), (1,84)(2,57)(3,58)(4,59)(5,60)(6,61)(7,62)(8,63)(9,64)(10,65)(11,66)(12,67)(13,68)(14,69)(15,70)(16,71)(17,72)(18,73)(19,74)(20,75)(21,76)(22,77)(23,78)(24,79)(25,80)(26,81)(27,82)(28,83)(29,96)(30,97)(31,98)(32,99)(33,100)(34,101)(35,102)(36,103)(37,104)(38,105)(39,106)(40,107)(41,108)(42,109)(43,110)(44,111)(45,112)(46,85)(47,86)(48,87)(49,88)(50,89)(51,90)(52,91)(53,92)(54,93)(55,94)(56,95), (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), (1,28,15,14)(2,13,16,27)(3,26,17,12)(4,11,18,25)(5,24,19,10)(6,9,20,23)(7,22,21,8)(29,97,43,111)(30,110,44,96)(31,95,45,109)(32,108,46,94)(33,93,47,107)(34,106,48,92)(35,91,49,105)(36,104,50,90)(37,89,51,103)(38,102,52,88)(39,87,53,101)(40,100,54,86)(41,85,55,99)(42,98,56,112)(57,68,71,82)(58,81,72,67)(59,66,73,80)(60,79,74,65)(61,64,75,78)(62,77,76,63)(69,84,83,70) );
G=PermutationGroup([(2,57),(4,59),(6,61),(8,63),(10,65),(12,67),(14,69),(16,71),(18,73),(20,75),(22,77),(24,79),(26,81),(28,83),(29,96),(31,98),(33,100),(35,102),(37,104),(39,106),(41,108),(43,110),(45,112),(47,86),(49,88),(51,90),(53,92),(55,94)], [(1,111),(2,98),(3,85),(4,100),(5,87),(6,102),(7,89),(8,104),(9,91),(10,106),(11,93),(12,108),(13,95),(14,110),(15,97),(16,112),(17,99),(18,86),(19,101),(20,88),(21,103),(22,90),(23,105),(24,92),(25,107),(26,94),(27,109),(28,96),(29,83),(30,70),(31,57),(32,72),(33,59),(34,74),(35,61),(36,76),(37,63),(38,78),(39,65),(40,80),(41,67),(42,82),(43,69),(44,84),(45,71),(46,58),(47,73),(48,60),(49,75),(50,62),(51,77),(52,64),(53,79),(54,66),(55,81),(56,68)], [(1,84),(2,57),(3,58),(4,59),(5,60),(6,61),(7,62),(8,63),(9,64),(10,65),(11,66),(12,67),(13,68),(14,69),(15,70),(16,71),(17,72),(18,73),(19,74),(20,75),(21,76),(22,77),(23,78),(24,79),(25,80),(26,81),(27,82),(28,83),(29,96),(30,97),(31,98),(32,99),(33,100),(34,101),(35,102),(36,103),(37,104),(38,105),(39,106),(40,107),(41,108),(42,109),(43,110),(44,111),(45,112),(46,85),(47,86),(48,87),(49,88),(50,89),(51,90),(52,91),(53,92),(54,93),(55,94),(56,95)], [(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)], [(1,28,15,14),(2,13,16,27),(3,26,17,12),(4,11,18,25),(5,24,19,10),(6,9,20,23),(7,22,21,8),(29,97,43,111),(30,110,44,96),(31,95,45,109),(32,108,46,94),(33,93,47,107),(34,106,48,92),(35,91,49,105),(36,104,50,90),(37,89,51,103),(38,102,52,88),(39,87,53,101),(40,100,54,86),(41,85,55,99),(42,98,56,112),(57,68,71,82),(58,81,72,67),(59,66,73,80),(60,79,74,65),(61,64,75,78),(62,77,76,63),(69,84,83,70)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 28 | 0 | 0 | 0 | 0 | 0 |
| 0 | 28 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 28 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 0 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 18 | 24 |
| 0 | 0 | 0 | 0 | 24 | 11 |
| 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 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 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 | 8 | 0 | 0 | 0 | 0 |
| 13 | 2 | 0 | 0 | 0 | 0 |
| 0 | 0 | 28 | 27 | 0 | 0 |
| 0 | 0 | 1 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 12 | 0 |
| 0 | 0 | 0 | 0 | 11 | 17 |
| 26 | 26 | 0 | 0 | 0 | 0 |
| 22 | 3 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 2 | 0 | 0 |
| 0 | 0 | 28 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 17 | 0 |
| 0 | 0 | 0 | 0 | 0 | 17 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,28,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,1,0,0,0,0,0,1,0,0,0,0,0,0,18,24,0,0,0,0,24,11],[1,0,0,0,0,0,0,1,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[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],[9,13,0,0,0,0,8,2,0,0,0,0,0,0,28,1,0,0,0,0,27,1,0,0,0,0,0,0,12,11,0,0,0,0,0,17],[26,22,0,0,0,0,26,3,0,0,0,0,0,0,1,28,0,0,0,0,2,28,0,0,0,0,0,0,17,0,0,0,0,0,0,17] >;
67 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 2J | 2K | 2L | 4A | 4B | 4C | 4D | ··· | 4I | 4J | 4K | 4L | 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 | 2 | 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 | 2 | 2 | 4 | 4 | 14 | 14 | 28 | 4 | 4 | 4 | 14 | ··· | 14 | 28 | 28 | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 8 | 8 | 8 | 8 | ··· | 8 |
67 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | - | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | C4○D4 | D14 | D14 | D14 | 2+ (1+4) | D4×D7 | D4⋊2D7 | D4⋊6D14 |
| kernel | C24.33D14 | C22⋊Dic14 | D7×C22⋊C4 | Dic7⋊4D4 | D14.D4 | Dic7.D4 | C22.D28 | D4×Dic7 | C23⋊D14 | C28⋊2D4 | Dic7⋊D4 | C2×C23.D7 | C7×C22≀C2 | C2×D4⋊2D7 | C22×C7⋊D4 | C7⋊D4 | C22≀C2 | C2×C14 | C22⋊C4 | C2×D4 | C24 | C14 | C22 | C22 | C2 |
| # reps | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 1 | 1 | 4 | 3 | 4 | 9 | 9 | 3 | 1 | 6 | 6 | 6 |
In GAP, Magma, Sage, TeX
C_2^4._{33}D_{14} % in TeX
G:=Group("C2^4.33D14"); // GroupNames label
G:=SmallGroup(448,1044);
// by ID
G=gap.SmallGroup(448,1044);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,219,184,1571,297,18822]);
// 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=f*a*f^-1=a*c=c*a,a*d=d*a,f*b*f^-1=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^-1=e^13>;
// generators/relations
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