metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: C24⋊7D14, C14.892+ (1+4), (C2×D4)⋊40D14, (C22×D4)⋊10D7, (C22×C4)⋊28D14, (C22×C14)⋊13D4, C7⋊5(C23⋊3D4), C23⋊4(C7⋊D4), C23⋊D14⋊30C2, D14⋊C4⋊36C22, (D4×C14)⋊58C22, C24⋊D7⋊12C2, Dic7⋊D4⋊41C2, (C2×C28).644C23, (C2×C14).299C24, Dic7⋊C4⋊38C22, (C22×C28)⋊44C22, (C23×C14)⋊14C22, C14.146(C22×D4), (C23×D7)⋊15C22, C23.D7⋊64C22, C2.92(D4⋊6D14), C22.312(C23×D7), C23.206(C22×D7), C23.23D14⋊28C2, C23.18D14⋊29C2, (C22×C14).233C23, (C2×Dic7).154C23, (C22×Dic7)⋊34C22, (C22×D7).130C23, (D4×C2×C14)⋊17C2, (C2×C14).582(C2×D4), (C22×C7⋊D4)⋊17C2, (C2×C7⋊D4)⋊48C22, (C2×C23.D7)⋊30C2, C22.20(C2×C7⋊D4), C2.19(C22×C7⋊D4), (C2×C4).238(C22×D7), SmallGroup(448,1257)
Series: Derived ►Chief ►Lower central ►Upper central
Subgroups: 1620 in 346 conjugacy classes, 111 normal (25 characteristic)
C1, C2, C2 [×2], C2 [×10], C4 [×8], C22, C22 [×6], C22 [×30], C7, C2×C4 [×2], C2×C4 [×12], D4 [×20], C23 [×3], C23 [×6], C23 [×12], D7 [×2], C14, C14 [×2], C14 [×8], C22⋊C4 [×12], C4⋊C4 [×4], C22×C4, C22×C4 [×3], C2×D4 [×4], C2×D4 [×16], C24 [×2], C24, Dic7 [×6], C28 [×2], D14 [×10], C2×C14, C2×C14 [×6], C2×C14 [×20], C2×C22⋊C4, C22≀C2 [×4], C4⋊D4 [×4], C22.D4 [×4], C22×D4, C22×D4, C2×Dic7 [×6], C2×Dic7 [×4], C7⋊D4 [×12], C2×C28 [×2], C2×C28 [×2], C7×D4 [×8], C22×D7 [×2], C22×D7 [×4], C22×C14 [×3], C22×C14 [×6], C22×C14 [×6], C23⋊3D4, Dic7⋊C4 [×4], D14⋊C4 [×4], C23.D7 [×8], C22×Dic7, C22×Dic7 [×2], C2×C7⋊D4 [×8], C2×C7⋊D4 [×4], C22×C28, D4×C14 [×4], D4×C14 [×4], C23×D7, C23×C14 [×2], C23.23D14 [×2], C23.18D14 [×2], C23⋊D14 [×2], Dic7⋊D4 [×4], C2×C23.D7, C24⋊D7 [×2], C22×C7⋊D4, D4×C2×C14, C24⋊7D14
Quotients:
C1, C2 [×15], C22 [×35], D4 [×4], C23 [×15], D7, C2×D4 [×6], C24, D14 [×7], C22×D4, 2+ (1+4) [×2], C7⋊D4 [×4], C22×D7 [×7], C23⋊3D4, C2×C7⋊D4 [×6], C23×D7, D4⋊6D14 [×2], C22×C7⋊D4, C24⋊7D14
Generators and relations
G = < a,b,c,d,e,f | a2=b2=c2=d2=e14=f2=1, ab=ba, ac=ca, faf=ad=da, ae=ea, bc=cb, ebe-1=bd=db, fbf=bcd, cd=dc, ce=ec, cf=fc, de=ed, df=fd, fef=e-1 >
►On 112 points
Generators in S112
(1 19)(2 20)(3 21)(4 15)(5 16)(6 17)(7 18)(8 47)(9 48)(10 49)(11 43)(12 44)(13 45)(14 46)(22 51)(23 52)(24 53)(25 54)(26 55)(27 56)(28 50)(29 40)(30 41)(31 42)(32 36)(33 37)(34 38)(35 39)(57 95)(58 96)(59 97)(60 98)(61 85)(62 86)(63 87)(64 88)(65 89)(66 90)(67 91)(68 92)(69 93)(70 94)(71 104)(72 105)(73 106)(74 107)(75 108)(76 109)(77 110)(78 111)(79 112)(80 99)(81 100)(82 101)(83 102)(84 103)
(1 59)(2 67)(3 61)(4 69)(5 63)(6 57)(7 65)(8 62)(9 70)(10 64)(11 58)(12 66)(13 60)(14 68)(15 93)(16 87)(17 95)(18 89)(19 97)(20 91)(21 85)(22 79)(23 73)(24 81)(25 75)(26 83)(27 77)(28 71)(29 82)(30 76)(31 84)(32 78)(33 72)(34 80)(35 74)(36 111)(37 105)(38 99)(39 107)(40 101)(41 109)(42 103)(43 96)(44 90)(45 98)(46 92)(47 86)(48 94)(49 88)(50 104)(51 112)(52 106)(53 100)(54 108)(55 102)(56 110)
(1 19)(2 20)(3 21)(4 15)(5 16)(6 17)(7 18)(8 47)(9 48)(10 49)(11 43)(12 44)(13 45)(14 46)(22 37)(23 38)(24 39)(25 40)(26 41)(27 42)(28 36)(29 54)(30 55)(31 56)(32 50)(33 51)(34 52)(35 53)(57 95)(58 96)(59 97)(60 98)(61 85)(62 86)(63 87)(64 88)(65 89)(66 90)(67 91)(68 92)(69 93)(70 94)(71 111)(72 112)(73 99)(74 100)(75 101)(76 102)(77 103)(78 104)(79 105)(80 106)(81 107)(82 108)(83 109)(84 110)
(1 12)(2 13)(3 14)(4 8)(5 9)(6 10)(7 11)(15 47)(16 48)(17 49)(18 43)(19 44)(20 45)(21 46)(22 33)(23 34)(24 35)(25 29)(26 30)(27 31)(28 32)(36 50)(37 51)(38 52)(39 53)(40 54)(41 55)(42 56)(57 64)(58 65)(59 66)(60 67)(61 68)(62 69)(63 70)(71 78)(72 79)(73 80)(74 81)(75 82)(76 83)(77 84)(85 92)(86 93)(87 94)(88 95)(89 96)(90 97)(91 98)(99 106)(100 107)(101 108)(102 109)(103 110)(104 111)(105 112)
(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 25)(2 24)(3 23)(4 22)(5 28)(6 27)(7 26)(8 33)(9 32)(10 31)(11 30)(12 29)(13 35)(14 34)(15 37)(16 36)(17 42)(18 41)(19 40)(20 39)(21 38)(43 55)(44 54)(45 53)(46 52)(47 51)(48 50)(49 56)(57 110)(58 109)(59 108)(60 107)(61 106)(62 105)(63 104)(64 103)(65 102)(66 101)(67 100)(68 99)(69 112)(70 111)(71 94)(72 93)(73 92)(74 91)(75 90)(76 89)(77 88)(78 87)(79 86)(80 85)(81 98)(82 97)(83 96)(84 95)
G:=sub<Sym(112)| (1,19)(2,20)(3,21)(4,15)(5,16)(6,17)(7,18)(8,47)(9,48)(10,49)(11,43)(12,44)(13,45)(14,46)(22,51)(23,52)(24,53)(25,54)(26,55)(27,56)(28,50)(29,40)(30,41)(31,42)(32,36)(33,37)(34,38)(35,39)(57,95)(58,96)(59,97)(60,98)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,104)(72,105)(73,106)(74,107)(75,108)(76,109)(77,110)(78,111)(79,112)(80,99)(81,100)(82,101)(83,102)(84,103), (1,59)(2,67)(3,61)(4,69)(5,63)(6,57)(7,65)(8,62)(9,70)(10,64)(11,58)(12,66)(13,60)(14,68)(15,93)(16,87)(17,95)(18,89)(19,97)(20,91)(21,85)(22,79)(23,73)(24,81)(25,75)(26,83)(27,77)(28,71)(29,82)(30,76)(31,84)(32,78)(33,72)(34,80)(35,74)(36,111)(37,105)(38,99)(39,107)(40,101)(41,109)(42,103)(43,96)(44,90)(45,98)(46,92)(47,86)(48,94)(49,88)(50,104)(51,112)(52,106)(53,100)(54,108)(55,102)(56,110), (1,19)(2,20)(3,21)(4,15)(5,16)(6,17)(7,18)(8,47)(9,48)(10,49)(11,43)(12,44)(13,45)(14,46)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,36)(29,54)(30,55)(31,56)(32,50)(33,51)(34,52)(35,53)(57,95)(58,96)(59,97)(60,98)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,111)(72,112)(73,99)(74,100)(75,101)(76,102)(77,103)(78,104)(79,105)(80,106)(81,107)(82,108)(83,109)(84,110), (1,12)(2,13)(3,14)(4,8)(5,9)(6,10)(7,11)(15,47)(16,48)(17,49)(18,43)(19,44)(20,45)(21,46)(22,33)(23,34)(24,35)(25,29)(26,30)(27,31)(28,32)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(85,92)(86,93)(87,94)(88,95)(89,96)(90,97)(91,98)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112), (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), (1,25)(2,24)(3,23)(4,22)(5,28)(6,27)(7,26)(8,33)(9,32)(10,31)(11,30)(12,29)(13,35)(14,34)(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)(21,38)(43,55)(44,54)(45,53)(46,52)(47,51)(48,50)(49,56)(57,110)(58,109)(59,108)(60,107)(61,106)(62,105)(63,104)(64,103)(65,102)(66,101)(67,100)(68,99)(69,112)(70,111)(71,94)(72,93)(73,92)(74,91)(75,90)(76,89)(77,88)(78,87)(79,86)(80,85)(81,98)(82,97)(83,96)(84,95)>;
G:=Group( (1,19)(2,20)(3,21)(4,15)(5,16)(6,17)(7,18)(8,47)(9,48)(10,49)(11,43)(12,44)(13,45)(14,46)(22,51)(23,52)(24,53)(25,54)(26,55)(27,56)(28,50)(29,40)(30,41)(31,42)(32,36)(33,37)(34,38)(35,39)(57,95)(58,96)(59,97)(60,98)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,104)(72,105)(73,106)(74,107)(75,108)(76,109)(77,110)(78,111)(79,112)(80,99)(81,100)(82,101)(83,102)(84,103), (1,59)(2,67)(3,61)(4,69)(5,63)(6,57)(7,65)(8,62)(9,70)(10,64)(11,58)(12,66)(13,60)(14,68)(15,93)(16,87)(17,95)(18,89)(19,97)(20,91)(21,85)(22,79)(23,73)(24,81)(25,75)(26,83)(27,77)(28,71)(29,82)(30,76)(31,84)(32,78)(33,72)(34,80)(35,74)(36,111)(37,105)(38,99)(39,107)(40,101)(41,109)(42,103)(43,96)(44,90)(45,98)(46,92)(47,86)(48,94)(49,88)(50,104)(51,112)(52,106)(53,100)(54,108)(55,102)(56,110), (1,19)(2,20)(3,21)(4,15)(5,16)(6,17)(7,18)(8,47)(9,48)(10,49)(11,43)(12,44)(13,45)(14,46)(22,37)(23,38)(24,39)(25,40)(26,41)(27,42)(28,36)(29,54)(30,55)(31,56)(32,50)(33,51)(34,52)(35,53)(57,95)(58,96)(59,97)(60,98)(61,85)(62,86)(63,87)(64,88)(65,89)(66,90)(67,91)(68,92)(69,93)(70,94)(71,111)(72,112)(73,99)(74,100)(75,101)(76,102)(77,103)(78,104)(79,105)(80,106)(81,107)(82,108)(83,109)(84,110), (1,12)(2,13)(3,14)(4,8)(5,9)(6,10)(7,11)(15,47)(16,48)(17,49)(18,43)(19,44)(20,45)(21,46)(22,33)(23,34)(24,35)(25,29)(26,30)(27,31)(28,32)(36,50)(37,51)(38,52)(39,53)(40,54)(41,55)(42,56)(57,64)(58,65)(59,66)(60,67)(61,68)(62,69)(63,70)(71,78)(72,79)(73,80)(74,81)(75,82)(76,83)(77,84)(85,92)(86,93)(87,94)(88,95)(89,96)(90,97)(91,98)(99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112), (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), (1,25)(2,24)(3,23)(4,22)(5,28)(6,27)(7,26)(8,33)(9,32)(10,31)(11,30)(12,29)(13,35)(14,34)(15,37)(16,36)(17,42)(18,41)(19,40)(20,39)(21,38)(43,55)(44,54)(45,53)(46,52)(47,51)(48,50)(49,56)(57,110)(58,109)(59,108)(60,107)(61,106)(62,105)(63,104)(64,103)(65,102)(66,101)(67,100)(68,99)(69,112)(70,111)(71,94)(72,93)(73,92)(74,91)(75,90)(76,89)(77,88)(78,87)(79,86)(80,85)(81,98)(82,97)(83,96)(84,95) );
G=PermutationGroup([(1,19),(2,20),(3,21),(4,15),(5,16),(6,17),(7,18),(8,47),(9,48),(10,49),(11,43),(12,44),(13,45),(14,46),(22,51),(23,52),(24,53),(25,54),(26,55),(27,56),(28,50),(29,40),(30,41),(31,42),(32,36),(33,37),(34,38),(35,39),(57,95),(58,96),(59,97),(60,98),(61,85),(62,86),(63,87),(64,88),(65,89),(66,90),(67,91),(68,92),(69,93),(70,94),(71,104),(72,105),(73,106),(74,107),(75,108),(76,109),(77,110),(78,111),(79,112),(80,99),(81,100),(82,101),(83,102),(84,103)], [(1,59),(2,67),(3,61),(4,69),(5,63),(6,57),(7,65),(8,62),(9,70),(10,64),(11,58),(12,66),(13,60),(14,68),(15,93),(16,87),(17,95),(18,89),(19,97),(20,91),(21,85),(22,79),(23,73),(24,81),(25,75),(26,83),(27,77),(28,71),(29,82),(30,76),(31,84),(32,78),(33,72),(34,80),(35,74),(36,111),(37,105),(38,99),(39,107),(40,101),(41,109),(42,103),(43,96),(44,90),(45,98),(46,92),(47,86),(48,94),(49,88),(50,104),(51,112),(52,106),(53,100),(54,108),(55,102),(56,110)], [(1,19),(2,20),(3,21),(4,15),(5,16),(6,17),(7,18),(8,47),(9,48),(10,49),(11,43),(12,44),(13,45),(14,46),(22,37),(23,38),(24,39),(25,40),(26,41),(27,42),(28,36),(29,54),(30,55),(31,56),(32,50),(33,51),(34,52),(35,53),(57,95),(58,96),(59,97),(60,98),(61,85),(62,86),(63,87),(64,88),(65,89),(66,90),(67,91),(68,92),(69,93),(70,94),(71,111),(72,112),(73,99),(74,100),(75,101),(76,102),(77,103),(78,104),(79,105),(80,106),(81,107),(82,108),(83,109),(84,110)], [(1,12),(2,13),(3,14),(4,8),(5,9),(6,10),(7,11),(15,47),(16,48),(17,49),(18,43),(19,44),(20,45),(21,46),(22,33),(23,34),(24,35),(25,29),(26,30),(27,31),(28,32),(36,50),(37,51),(38,52),(39,53),(40,54),(41,55),(42,56),(57,64),(58,65),(59,66),(60,67),(61,68),(62,69),(63,70),(71,78),(72,79),(73,80),(74,81),(75,82),(76,83),(77,84),(85,92),(86,93),(87,94),(88,95),(89,96),(90,97),(91,98),(99,106),(100,107),(101,108),(102,109),(103,110),(104,111),(105,112)], [(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)], [(1,25),(2,24),(3,23),(4,22),(5,28),(6,27),(7,26),(8,33),(9,32),(10,31),(11,30),(12,29),(13,35),(14,34),(15,37),(16,36),(17,42),(18,41),(19,40),(20,39),(21,38),(43,55),(44,54),(45,53),(46,52),(47,51),(48,50),(49,56),(57,110),(58,109),(59,108),(60,107),(61,106),(62,105),(63,104),(64,103),(65,102),(66,101),(67,100),(68,99),(69,112),(70,111),(71,94),(72,93),(73,92),(74,91),(75,90),(76,89),(77,88),(78,87),(79,86),(80,85),(81,98),(82,97),(83,96),(84,95)])
Matrix representation ►G ⊆ GL6(𝔽29)
| 28 | 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 | 13 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 28 | 0 | 0 | 0 | 0 | 0 |
| 1 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 7 | 0 | 0 |
| 0 | 0 | 0 | 28 | 0 | 0 |
| 0 | 0 | 16 | 27 | 28 | 6 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 28 | 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 | 0 |
| 0 | 0 | 0 | 0 | 0 | 28 |
| 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 |
| 6 | 0 | 0 | 0 | 0 | 0 |
| 14 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 8 | 28 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 7 | 0 | 10 | 28 |
| 24 | 19 | 0 | 0 | 0 | 0 |
| 14 | 5 | 0 | 0 | 0 | 0 |
| 0 | 0 | 19 | 0 | 23 | 0 |
| 0 | 0 | 7 | 0 | 10 | 28 |
| 0 | 0 | 2 | 0 | 10 | 0 |
| 0 | 0 | 8 | 28 | 0 | 0 |
G:=sub<GL(6,GF(29))| [28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,13,0,0,0,0,28,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[28,1,0,0,0,0,0,1,0,0,0,0,0,0,1,0,16,0,0,0,7,28,27,0,0,0,0,0,28,0,0,0,0,0,6,1],[28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28,0,0,0,0,0,0,28],[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],[6,14,0,0,0,0,0,5,0,0,0,0,0,0,1,8,0,7,0,0,0,28,0,0,0,0,0,0,1,10,0,0,0,0,0,28],[24,14,0,0,0,0,19,5,0,0,0,0,0,0,19,7,2,8,0,0,0,0,0,28,0,0,23,10,10,0,0,0,0,28,0,0] >;
82 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | ··· | 2I | 2J | 2K | 2L | 2M | 4A | 4B | 4C | ··· | 4H | 7A | 7B | 7C | 14A | ··· | 14U | 14V | ··· | 14AS | 28A | ··· | 28L |
| order | 1 | 2 | 2 | 2 | 2 | ··· | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | ··· | 4 | 7 | 7 | 7 | 14 | ··· | 14 | 14 | ··· | 14 | 28 | ··· | 28 |
| size | 1 | 1 | 1 | 1 | 2 | ··· | 2 | 4 | 4 | 28 | 28 | 4 | 4 | 28 | ··· | 28 | 2 | 2 | 2 | 2 | ··· | 2 | 4 | ··· | 4 | 4 | ··· | 4 |
82 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | ||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | D4 | D7 | D14 | D14 | D14 | C7⋊D4 | 2+ (1+4) | D4⋊6D14 |
| kernel | C24⋊7D14 | C23.23D14 | C23.18D14 | C23⋊D14 | Dic7⋊D4 | C2×C23.D7 | C24⋊D7 | C22×C7⋊D4 | D4×C2×C14 | C22×C14 | C22×D4 | C22×C4 | C2×D4 | C24 | C23 | C14 | C2 |
| # reps | 1 | 2 | 2 | 2 | 4 | 1 | 2 | 1 | 1 | 4 | 3 | 3 | 12 | 6 | 24 | 2 | 12 |
In GAP, Magma, Sage, TeX
C_2^4\rtimes_7D_{14} % in TeX
G:=Group("C2^4:7D14"); // GroupNames label
G:=SmallGroup(448,1257);
// by ID
G=gap.SmallGroup(448,1257);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-2,-7,758,675,570,18822]);
// 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,a*c=c*a,f*a*f=a*d=d*a,a*e=e*a,b*c=c*b,e*b*e^-1=b*d=d*b,f*b*f=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=e^-1>;
// generators/relations
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