metabelian, supersoluble, monomial, 2-hyperelementary
Aliases: D60⋊8C22, Dic6⋊12D10, Dic10⋊12D6, C30.28C24, C60.52C23, D30.13C23, Dic15.15C23, D4⋊9(S3×D5), (C4×D5)⋊9D6, C5⋊D4⋊4D6, (C4×S3)⋊9D10, (C5×D4)⋊12D6, (D4×D15)⋊5C2, C3⋊D4⋊4D10, D15⋊Q8⋊5C2, C15⋊Q8⋊3C22, (C3×D4)⋊12D10, D4⋊2D5⋊6S3, D4⋊2S3⋊6D5, D15⋊2(C4○D4), C12.28D10⋊4C2, D10⋊D6⋊3C2, D60⋊C2⋊4C2, (S3×C20)⋊3C22, (C2×Dic5)⋊15D6, (D5×C12)⋊3C22, C3⋊D20⋊5C22, C15⋊7D4⋊4C22, C5⋊D12⋊5C22, (C2×C30).4C23, C6.28(C23×D5), (C2×Dic3)⋊15D10, Dic3.D10⋊4C2, Dic5.D6⋊4C2, (D4×C15)⋊10C22, C20.52(C22×S3), C10.28(S3×C23), (C5×Dic6)⋊8C22, (C6×D5).12C23, D6.13(C22×D5), C12.52(C22×D5), (S3×C10).13C23, D30.C2⋊12C22, (C6×Dic5)⋊13C22, (D5×Dic3)⋊12C22, (C3×Dic10)⋊8C22, (S3×Dic5)⋊12C22, D10.13(C22×S3), (C4×D15).18C22, (C10×Dic3)⋊13C22, Dic3.14(C22×D5), (C5×Dic3).15C23, Dic5.14(C22×S3), (C3×Dic5).13C23, (C22×D15).74C22, (C4×S3×D5)⋊4C2, C5⋊4(S3×C4○D4), C3⋊4(D5×C4○D4), C4.52(C2×S3×D5), C15⋊13(C2×C4○D4), C22.4(C2×S3×D5), (C3×D4⋊2D5)⋊6C2, (C5×D4⋊2S3)⋊6C2, C2.31(C22×S3×D5), (C3×C5⋊D4)⋊4C22, (C5×C3⋊D4)⋊4C22, (C2×S3×D5).10C22, (C2×C6).4(C22×D5), (C2×D30.C2)⋊21C2, (C2×C10).4(C22×S3), SmallGroup(480,1100)
Series: Derived ►Chief ►Lower central ►Upper central
Generators and relations for D30.C23
G = < a,b,c,d,e | a30=b2=c2=e2=1, d2=a15, bab=eae=a-1, cac=a11, ad=da, cbc=a25b, dbd-1=a15b, ebe=a28b, cd=dc, ce=ec, de=ed >
Subgroups: 1692 in 328 conjugacy classes, 110 normal (50 characteristic)
C1, C2, C2, C3, C4, C4, C22, C22, C5, S3, C6, C6, C2×C4, D4, D4, Q8, C23, D5, C10, C10, Dic3, Dic3, Dic3, C12, C12, D6, D6, C2×C6, C2×C6, C15, C22×C4, C2×D4, C2×Q8, C4○D4, Dic5, Dic5, Dic5, C20, C20, D10, D10, C2×C10, C2×C10, Dic6, Dic6, C4×S3, C4×S3, D12, C2×Dic3, C2×Dic3, C3⋊D4, C3⋊D4, C2×C12, C3×D4, C3×D4, C3×Q8, C22×S3, C5×S3, C3×D5, D15, D15, C30, C30, C2×C4○D4, Dic10, Dic10, C4×D5, C4×D5, D20, C2×Dic5, C2×Dic5, C5⋊D4, C5⋊D4, C2×C20, C5×D4, C5×D4, C5×Q8, C22×D5, S3×C2×C4, C4○D12, S3×D4, D4⋊2S3, D4⋊2S3, S3×Q8, Q8⋊3S3, C3×C4○D4, C5×Dic3, C5×Dic3, C3×Dic5, C3×Dic5, Dic15, C60, S3×D5, C6×D5, S3×C10, D30, D30, D30, C2×C30, C2×C4×D5, C4○D20, D4×D5, D4⋊2D5, D4⋊2D5, Q8×D5, Q8⋊2D5, C5×C4○D4, S3×C4○D4, D5×Dic3, S3×Dic5, D30.C2, D30.C2, C3⋊D20, C5⋊D12, C15⋊Q8, C3×Dic10, D5×C12, C6×Dic5, C3×C5⋊D4, C5×Dic6, S3×C20, C10×Dic3, C5×C3⋊D4, C4×D15, D60, C15⋊7D4, D4×C15, C2×S3×D5, C22×D15, D5×C4○D4, D60⋊C2, D15⋊Q8, C12.28D10, C4×S3×D5, Dic5.D6, Dic3.D10, C2×D30.C2, D10⋊D6, C3×D4⋊2D5, C5×D4⋊2S3, D4×D15, D30.C23
Quotients: C1, C2, C22, S3, C23, D5, D6, C4○D4, C24, D10, C22×S3, C2×C4○D4, C22×D5, S3×C23, S3×D5, C23×D5, S3×C4○D4, C2×S3×D5, D5×C4○D4, C22×S3×D5, D30.C23
►On 120 points
(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120)
(1 50)(2 49)(3 48)(4 47)(5 46)(6 45)(7 44)(8 43)(9 42)(10 41)(11 40)(12 39)(13 38)(14 37)(15 36)(16 35)(17 34)(18 33)(19 32)(20 31)(21 60)(22 59)(23 58)(24 57)(25 56)(26 55)(27 54)(28 53)(29 52)(30 51)(61 120)(62 119)(63 118)(64 117)(65 116)(66 115)(67 114)(68 113)(69 112)(70 111)(71 110)(72 109)(73 108)(74 107)(75 106)(76 105)(77 104)(78 103)(79 102)(80 101)(81 100)(82 99)(83 98)(84 97)(85 96)(86 95)(87 94)(88 93)(89 92)(90 91)
(2 12)(3 23)(5 15)(6 26)(8 18)(9 29)(11 21)(14 24)(17 27)(20 30)(31 56)(32 37)(33 48)(34 59)(35 40)(36 51)(38 43)(39 54)(41 46)(42 57)(44 49)(45 60)(47 52)(50 55)(53 58)(61 71)(62 82)(64 74)(65 85)(67 77)(68 88)(70 80)(73 83)(76 86)(79 89)(91 96)(92 107)(93 118)(94 99)(95 110)(97 102)(98 113)(100 105)(101 116)(103 108)(104 119)(106 111)(109 114)(112 117)(115 120)
(1 66 16 81)(2 67 17 82)(3 68 18 83)(4 69 19 84)(5 70 20 85)(6 71 21 86)(7 72 22 87)(8 73 23 88)(9 74 24 89)(10 75 25 90)(11 76 26 61)(12 77 27 62)(13 78 28 63)(14 79 29 64)(15 80 30 65)(31 111 46 96)(32 112 47 97)(33 113 48 98)(34 114 49 99)(35 115 50 100)(36 116 51 101)(37 117 52 102)(38 118 53 103)(39 119 54 104)(40 120 55 105)(41 91 56 106)(42 92 57 107)(43 93 58 108)(44 94 59 109)(45 95 60 110)
(1 16)(2 15)(3 14)(4 13)(5 12)(6 11)(7 10)(8 9)(17 30)(18 29)(19 28)(20 27)(21 26)(22 25)(23 24)(31 56)(32 55)(33 54)(34 53)(35 52)(36 51)(37 50)(38 49)(39 48)(40 47)(41 46)(42 45)(43 44)(57 60)(58 59)(61 86)(62 85)(63 84)(64 83)(65 82)(66 81)(67 80)(68 79)(69 78)(70 77)(71 76)(72 75)(73 74)(87 90)(88 89)(91 96)(92 95)(93 94)(97 120)(98 119)(99 118)(100 117)(101 116)(102 115)(103 114)(104 113)(105 112)(106 111)(107 110)(108 109)
G:=sub<Sym(120)| (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)(91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120), (1,50)(2,49)(3,48)(4,47)(5,46)(6,45)(7,44)(8,43)(9,42)(10,41)(11,40)(12,39)(13,38)(14,37)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,60)(22,59)(23,58)(24,57)(25,56)(26,55)(27,54)(28,53)(29,52)(30,51)(61,120)(62,119)(63,118)(64,117)(65,116)(66,115)(67,114)(68,113)(69,112)(70,111)(71,110)(72,109)(73,108)(74,107)(75,106)(76,105)(77,104)(78,103)(79,102)(80,101)(81,100)(82,99)(83,98)(84,97)(85,96)(86,95)(87,94)(88,93)(89,92)(90,91), (2,12)(3,23)(5,15)(6,26)(8,18)(9,29)(11,21)(14,24)(17,27)(20,30)(31,56)(32,37)(33,48)(34,59)(35,40)(36,51)(38,43)(39,54)(41,46)(42,57)(44,49)(45,60)(47,52)(50,55)(53,58)(61,71)(62,82)(64,74)(65,85)(67,77)(68,88)(70,80)(73,83)(76,86)(79,89)(91,96)(92,107)(93,118)(94,99)(95,110)(97,102)(98,113)(100,105)(101,116)(103,108)(104,119)(106,111)(109,114)(112,117)(115,120), (1,66,16,81)(2,67,17,82)(3,68,18,83)(4,69,19,84)(5,70,20,85)(6,71,21,86)(7,72,22,87)(8,73,23,88)(9,74,24,89)(10,75,25,90)(11,76,26,61)(12,77,27,62)(13,78,28,63)(14,79,29,64)(15,80,30,65)(31,111,46,96)(32,112,47,97)(33,113,48,98)(34,114,49,99)(35,115,50,100)(36,116,51,101)(37,117,52,102)(38,118,53,103)(39,119,54,104)(40,120,55,105)(41,91,56,106)(42,92,57,107)(43,93,58,108)(44,94,59,109)(45,95,60,110), (1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(31,56)(32,55)(33,54)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)(57,60)(58,59)(61,86)(62,85)(63,84)(64,83)(65,82)(66,81)(67,80)(68,79)(69,78)(70,77)(71,76)(72,75)(73,74)(87,90)(88,89)(91,96)(92,95)(93,94)(97,120)(98,119)(99,118)(100,117)(101,116)(102,115)(103,114)(104,113)(105,112)(106,111)(107,110)(108,109)>;
G:=Group( (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)(91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120), (1,50)(2,49)(3,48)(4,47)(5,46)(6,45)(7,44)(8,43)(9,42)(10,41)(11,40)(12,39)(13,38)(14,37)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,60)(22,59)(23,58)(24,57)(25,56)(26,55)(27,54)(28,53)(29,52)(30,51)(61,120)(62,119)(63,118)(64,117)(65,116)(66,115)(67,114)(68,113)(69,112)(70,111)(71,110)(72,109)(73,108)(74,107)(75,106)(76,105)(77,104)(78,103)(79,102)(80,101)(81,100)(82,99)(83,98)(84,97)(85,96)(86,95)(87,94)(88,93)(89,92)(90,91), (2,12)(3,23)(5,15)(6,26)(8,18)(9,29)(11,21)(14,24)(17,27)(20,30)(31,56)(32,37)(33,48)(34,59)(35,40)(36,51)(38,43)(39,54)(41,46)(42,57)(44,49)(45,60)(47,52)(50,55)(53,58)(61,71)(62,82)(64,74)(65,85)(67,77)(68,88)(70,80)(73,83)(76,86)(79,89)(91,96)(92,107)(93,118)(94,99)(95,110)(97,102)(98,113)(100,105)(101,116)(103,108)(104,119)(106,111)(109,114)(112,117)(115,120), (1,66,16,81)(2,67,17,82)(3,68,18,83)(4,69,19,84)(5,70,20,85)(6,71,21,86)(7,72,22,87)(8,73,23,88)(9,74,24,89)(10,75,25,90)(11,76,26,61)(12,77,27,62)(13,78,28,63)(14,79,29,64)(15,80,30,65)(31,111,46,96)(32,112,47,97)(33,113,48,98)(34,114,49,99)(35,115,50,100)(36,116,51,101)(37,117,52,102)(38,118,53,103)(39,119,54,104)(40,120,55,105)(41,91,56,106)(42,92,57,107)(43,93,58,108)(44,94,59,109)(45,95,60,110), (1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(31,56)(32,55)(33,54)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)(57,60)(58,59)(61,86)(62,85)(63,84)(64,83)(65,82)(66,81)(67,80)(68,79)(69,78)(70,77)(71,76)(72,75)(73,74)(87,90)(88,89)(91,96)(92,95)(93,94)(97,120)(98,119)(99,118)(100,117)(101,116)(102,115)(103,114)(104,113)(105,112)(106,111)(107,110)(108,109) );
G=PermutationGroup([[(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),(91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120)], [(1,50),(2,49),(3,48),(4,47),(5,46),(6,45),(7,44),(8,43),(9,42),(10,41),(11,40),(12,39),(13,38),(14,37),(15,36),(16,35),(17,34),(18,33),(19,32),(20,31),(21,60),(22,59),(23,58),(24,57),(25,56),(26,55),(27,54),(28,53),(29,52),(30,51),(61,120),(62,119),(63,118),(64,117),(65,116),(66,115),(67,114),(68,113),(69,112),(70,111),(71,110),(72,109),(73,108),(74,107),(75,106),(76,105),(77,104),(78,103),(79,102),(80,101),(81,100),(82,99),(83,98),(84,97),(85,96),(86,95),(87,94),(88,93),(89,92),(90,91)], [(2,12),(3,23),(5,15),(6,26),(8,18),(9,29),(11,21),(14,24),(17,27),(20,30),(31,56),(32,37),(33,48),(34,59),(35,40),(36,51),(38,43),(39,54),(41,46),(42,57),(44,49),(45,60),(47,52),(50,55),(53,58),(61,71),(62,82),(64,74),(65,85),(67,77),(68,88),(70,80),(73,83),(76,86),(79,89),(91,96),(92,107),(93,118),(94,99),(95,110),(97,102),(98,113),(100,105),(101,116),(103,108),(104,119),(106,111),(109,114),(112,117),(115,120)], [(1,66,16,81),(2,67,17,82),(3,68,18,83),(4,69,19,84),(5,70,20,85),(6,71,21,86),(7,72,22,87),(8,73,23,88),(9,74,24,89),(10,75,25,90),(11,76,26,61),(12,77,27,62),(13,78,28,63),(14,79,29,64),(15,80,30,65),(31,111,46,96),(32,112,47,97),(33,113,48,98),(34,114,49,99),(35,115,50,100),(36,116,51,101),(37,117,52,102),(38,118,53,103),(39,119,54,104),(40,120,55,105),(41,91,56,106),(42,92,57,107),(43,93,58,108),(44,94,59,109),(45,95,60,110)], [(1,16),(2,15),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9),(17,30),(18,29),(19,28),(20,27),(21,26),(22,25),(23,24),(31,56),(32,55),(33,54),(34,53),(35,52),(36,51),(37,50),(38,49),(39,48),(40,47),(41,46),(42,45),(43,44),(57,60),(58,59),(61,86),(62,85),(63,84),(64,83),(65,82),(66,81),(67,80),(68,79),(69,78),(70,77),(71,76),(72,75),(73,74),(87,90),(88,89),(91,96),(92,95),(93,94),(97,120),(98,119),(99,118),(100,117),(101,116),(102,115),(103,114),(104,113),(105,112),(106,111),(107,110),(108,109)]])
60 conjugacy classes
| class | 1 | 2A | 2B | 2C | 2D | 2E | 2F | 2G | 2H | 2I | 3 | 4A | 4B | 4C | 4D | 4E | 4F | 4G | 4H | 4I | 4J | 5A | 5B | 6A | 6B | 6C | 6D | 10A | 10B | 10C | 10D | 10E | 10F | 10G | 10H | 12A | 12B | 12C | 12D | 12E | 15A | 15B | 20A | 20B | 20C | 20D | 20E | 20F | 20G | 20H | 20I | 20J | 30A | 30B | 30C | 30D | 30E | 30F | 60A | 60B |
| order | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 3 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | 5 | 5 | 6 | 6 | 6 | 6 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 12 | 12 | 12 | 12 | 12 | 15 | 15 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 20 | 30 | 30 | 30 | 30 | 30 | 30 | 60 | 60 |
| size | 1 | 1 | 2 | 2 | 6 | 10 | 15 | 15 | 30 | 30 | 2 | 2 | 3 | 3 | 5 | 5 | 6 | 6 | 10 | 10 | 30 | 2 | 2 | 2 | 4 | 4 | 20 | 2 | 2 | 4 | 4 | 4 | 4 | 12 | 12 | 4 | 10 | 10 | 20 | 20 | 4 | 4 | 4 | 4 | 6 | 6 | 6 | 6 | 12 | 12 | 12 | 12 | 4 | 4 | 8 | 8 | 8 | 8 | 8 | 8 |
60 irreducible representations
| dim | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 4 | 4 | 4 | 4 | 4 | 8 |
| type | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | + | |||
| image | C1 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | C2 | S3 | D5 | D6 | D6 | D6 | D6 | D6 | C4○D4 | D10 | D10 | D10 | D10 | D10 | S3×D5 | S3×C4○D4 | C2×S3×D5 | C2×S3×D5 | D5×C4○D4 | D30.C23 |
| kernel | D30.C23 | D60⋊C2 | D15⋊Q8 | C12.28D10 | C4×S3×D5 | Dic5.D6 | Dic3.D10 | C2×D30.C2 | D10⋊D6 | C3×D4⋊2D5 | C5×D4⋊2S3 | D4×D15 | D4⋊2D5 | D4⋊2S3 | Dic10 | C4×D5 | C2×Dic5 | C5⋊D4 | C5×D4 | D15 | Dic6 | C4×S3 | C2×Dic3 | C3⋊D4 | C3×D4 | D4 | C5 | C4 | C22 | C3 | C1 |
| # reps | 1 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 2 | 1 | 1 | 2 | 2 | 1 | 4 | 2 | 2 | 4 | 4 | 2 | 2 | 2 | 2 | 4 | 4 | 2 |
Matrix representation of D30.C23 ►in GL6(𝔽61)
| 60 | 0 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 43 | 60 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 1 |
| 0 | 0 | 0 | 0 | 60 | 0 |
| 60 | 46 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 43 | 60 | 0 | 0 |
| 0 | 0 | 18 | 18 | 0 | 0 |
| 0 | 0 | 0 | 0 | 60 | 0 |
| 0 | 0 | 0 | 0 | 60 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 |
| 8 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 50 | 0 | 0 | 0 | 0 | 0 |
| 34 | 11 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 60 | 0 | 0 | 0 | 0 | 0 |
| 0 | 60 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 43 | 60 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 |
| 0 | 0 | 0 | 0 | 1 | 0 |
G:=sub<GL(6,GF(61))| [60,0,0,0,0,0,0,60,0,0,0,0,0,0,43,1,0,0,0,0,60,0,0,0,0,0,0,0,60,60,0,0,0,0,1,0],[60,0,0,0,0,0,46,1,0,0,0,0,0,0,43,18,0,0,0,0,60,18,0,0,0,0,0,0,60,60,0,0,0,0,0,1],[1,8,0,0,0,0,0,60,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,1,0],[50,34,0,0,0,0,0,11,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,1],[60,0,0,0,0,0,0,60,0,0,0,0,0,0,1,43,0,0,0,0,0,60,0,0,0,0,0,0,0,1,0,0,0,0,1,0] >;
D30.C23 in GAP, Magma, Sage, TeX
D_{30}.C_2^3 % in TeX
G:=Group("D30.C2^3"); // GroupNames label
G:=SmallGroup(480,1100);
// by ID
G=gap.SmallGroup(480,1100);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,100,675,346,185,1356,18822]);
// Polycyclic
G:=Group<a,b,c,d,e|a^30=b^2=c^2=e^2=1,d^2=a^15,b*a*b=e*a*e=a^-1,c*a*c=a^11,a*d=d*a,c*b*c=a^25*b,d*b*d^-1=a^15*b,e*b*e=a^28*b,c*d=d*c,c*e=e*c,d*e=e*d>;
// generators/relations