Copied to
clipboard

G = C3×C20.46D4order 480 = 25·3·5

Direct product of C3 and C20.46D4

direct product, metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C3×C20.46D4, C60.217D4, C12.63D20, (C2×D20).7C6, C4.11(C3×D20), C20.46(C3×D4), C4.Dic52C6, (C6×D20).18C2, C158(C4.D4), (C3×M4(2))⋊7D5, M4(2)⋊3(C3×D5), (C5×M4(2))⋊7C6, C22.4(D5×C12), (C2×C12).211D10, (C22×D5).1C12, C12.114(C5⋊D4), C30.87(C22⋊C4), (C15×M4(2))⋊15C2, (C2×C60).276C22, C6.40(D10⋊C4), (D5×C2×C6).2C4, (C2×C4).1(C6×D5), C52(C3×C4.D4), (C2×C6).38(C4×D5), C4.21(C3×C5⋊D4), (C2×C20).12(C2×C6), (C2×C30).119(C2×C4), (C2×C10).22(C2×C12), C2.9(C3×D10⋊C4), C10.19(C3×C22⋊C4), (C3×C4.Dic5)⋊14C2, SmallGroup(480,101)

Series: Derived Chief Lower central Upper central

C1C2×C10 — C3×C20.46D4
C1C5C10C2×C10C2×C20C2×C60C6×D20 — C3×C20.46D4
C5C10C2×C10 — C3×C20.46D4
C1C6C2×C12C3×M4(2)

Generators and relations for C3×C20.46D4
 G = < a,b,c,d | a3=b20=d2=1, c4=b10, ab=ba, ac=ca, ad=da, cbc-1=dbd=b-1, dcd=b15c3 >

Subgroups: 416 in 92 conjugacy classes, 38 normal (34 characteristic)
C1, C2, C2 [×3], C3, C4 [×2], C22, C22 [×4], C5, C6, C6 [×3], C8 [×2], C2×C4, D4 [×2], C23 [×2], D5 [×2], C10, C10, C12 [×2], C2×C6, C2×C6 [×4], C15, M4(2), M4(2), C2×D4, C20 [×2], D10 [×4], C2×C10, C24 [×2], C2×C12, C3×D4 [×2], C22×C6 [×2], C3×D5 [×2], C30, C30, C4.D4, C52C8, C40, D20 [×2], C2×C20, C22×D5 [×2], C3×M4(2), C3×M4(2), C6×D4, C60 [×2], C6×D5 [×4], C2×C30, C4.Dic5, C5×M4(2), C2×D20, C3×C4.D4, C3×C52C8, C120, C3×D20 [×2], C2×C60, D5×C2×C6 [×2], C20.46D4, C3×C4.Dic5, C15×M4(2), C6×D20, C3×C20.46D4
Quotients: C1, C2 [×3], C3, C4 [×2], C22, C6 [×3], C2×C4, D4 [×2], D5, C12 [×2], C2×C6, C22⋊C4, D10, C2×C12, C3×D4 [×2], C3×D5, C4.D4, C4×D5, D20, C5⋊D4, C3×C22⋊C4, C6×D5, D10⋊C4, C3×C4.D4, D5×C12, C3×D20, C3×C5⋊D4, C20.46D4, C3×D10⋊C4, C3×C20.46D4

Smallest permutation representation of C3×C20.46D4
On 120 points
Generators in S120
(1 45 25)(2 46 26)(3 47 27)(4 48 28)(5 49 29)(6 50 30)(7 51 31)(8 52 32)(9 53 33)(10 54 34)(11 55 35)(12 56 36)(13 57 37)(14 58 38)(15 59 39)(16 60 40)(17 41 21)(18 42 22)(19 43 23)(20 44 24)(61 103 100)(62 104 81)(63 105 82)(64 106 83)(65 107 84)(66 108 85)(67 109 86)(68 110 87)(69 111 88)(70 112 89)(71 113 90)(72 114 91)(73 115 92)(74 116 93)(75 117 94)(76 118 95)(77 119 96)(78 120 97)(79 101 98)(80 102 99)
(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 67 16 72 11 77 6 62)(2 66 17 71 12 76 7 61)(3 65 18 70 13 75 8 80)(4 64 19 69 14 74 9 79)(5 63 20 68 15 73 10 78)(21 90 36 95 31 100 26 85)(22 89 37 94 32 99 27 84)(23 88 38 93 33 98 28 83)(24 87 39 92 34 97 29 82)(25 86 40 91 35 96 30 81)(41 113 56 118 51 103 46 108)(42 112 57 117 52 102 47 107)(43 111 58 116 53 101 48 106)(44 110 59 115 54 120 49 105)(45 109 60 114 55 119 50 104)
(2 20)(3 19)(4 18)(5 17)(6 16)(7 15)(8 14)(9 13)(10 12)(21 29)(22 28)(23 27)(24 26)(30 40)(31 39)(32 38)(33 37)(34 36)(41 49)(42 48)(43 47)(44 46)(50 60)(51 59)(52 58)(53 57)(54 56)(61 63)(64 80)(65 79)(66 78)(67 77)(68 76)(69 75)(70 74)(71 73)(82 100)(83 99)(84 98)(85 97)(86 96)(87 95)(88 94)(89 93)(90 92)(101 107)(102 106)(103 105)(108 120)(109 119)(110 118)(111 117)(112 116)(113 115)

G:=sub<Sym(120)| (1,45,25)(2,46,26)(3,47,27)(4,48,28)(5,49,29)(6,50,30)(7,51,31)(8,52,32)(9,53,33)(10,54,34)(11,55,35)(12,56,36)(13,57,37)(14,58,38)(15,59,39)(16,60,40)(17,41,21)(18,42,22)(19,43,23)(20,44,24)(61,103,100)(62,104,81)(63,105,82)(64,106,83)(65,107,84)(66,108,85)(67,109,86)(68,110,87)(69,111,88)(70,112,89)(71,113,90)(72,114,91)(73,115,92)(74,116,93)(75,117,94)(76,118,95)(77,119,96)(78,120,97)(79,101,98)(80,102,99), (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), (1,67,16,72,11,77,6,62)(2,66,17,71,12,76,7,61)(3,65,18,70,13,75,8,80)(4,64,19,69,14,74,9,79)(5,63,20,68,15,73,10,78)(21,90,36,95,31,100,26,85)(22,89,37,94,32,99,27,84)(23,88,38,93,33,98,28,83)(24,87,39,92,34,97,29,82)(25,86,40,91,35,96,30,81)(41,113,56,118,51,103,46,108)(42,112,57,117,52,102,47,107)(43,111,58,116,53,101,48,106)(44,110,59,115,54,120,49,105)(45,109,60,114,55,119,50,104), (2,20)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)(21,29)(22,28)(23,27)(24,26)(30,40)(31,39)(32,38)(33,37)(34,36)(41,49)(42,48)(43,47)(44,46)(50,60)(51,59)(52,58)(53,57)(54,56)(61,63)(64,80)(65,79)(66,78)(67,77)(68,76)(69,75)(70,74)(71,73)(82,100)(83,99)(84,98)(85,97)(86,96)(87,95)(88,94)(89,93)(90,92)(101,107)(102,106)(103,105)(108,120)(109,119)(110,118)(111,117)(112,116)(113,115)>;

G:=Group( (1,45,25)(2,46,26)(3,47,27)(4,48,28)(5,49,29)(6,50,30)(7,51,31)(8,52,32)(9,53,33)(10,54,34)(11,55,35)(12,56,36)(13,57,37)(14,58,38)(15,59,39)(16,60,40)(17,41,21)(18,42,22)(19,43,23)(20,44,24)(61,103,100)(62,104,81)(63,105,82)(64,106,83)(65,107,84)(66,108,85)(67,109,86)(68,110,87)(69,111,88)(70,112,89)(71,113,90)(72,114,91)(73,115,92)(74,116,93)(75,117,94)(76,118,95)(77,119,96)(78,120,97)(79,101,98)(80,102,99), (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), (1,67,16,72,11,77,6,62)(2,66,17,71,12,76,7,61)(3,65,18,70,13,75,8,80)(4,64,19,69,14,74,9,79)(5,63,20,68,15,73,10,78)(21,90,36,95,31,100,26,85)(22,89,37,94,32,99,27,84)(23,88,38,93,33,98,28,83)(24,87,39,92,34,97,29,82)(25,86,40,91,35,96,30,81)(41,113,56,118,51,103,46,108)(42,112,57,117,52,102,47,107)(43,111,58,116,53,101,48,106)(44,110,59,115,54,120,49,105)(45,109,60,114,55,119,50,104), (2,20)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)(21,29)(22,28)(23,27)(24,26)(30,40)(31,39)(32,38)(33,37)(34,36)(41,49)(42,48)(43,47)(44,46)(50,60)(51,59)(52,58)(53,57)(54,56)(61,63)(64,80)(65,79)(66,78)(67,77)(68,76)(69,75)(70,74)(71,73)(82,100)(83,99)(84,98)(85,97)(86,96)(87,95)(88,94)(89,93)(90,92)(101,107)(102,106)(103,105)(108,120)(109,119)(110,118)(111,117)(112,116)(113,115) );

G=PermutationGroup([(1,45,25),(2,46,26),(3,47,27),(4,48,28),(5,49,29),(6,50,30),(7,51,31),(8,52,32),(9,53,33),(10,54,34),(11,55,35),(12,56,36),(13,57,37),(14,58,38),(15,59,39),(16,60,40),(17,41,21),(18,42,22),(19,43,23),(20,44,24),(61,103,100),(62,104,81),(63,105,82),(64,106,83),(65,107,84),(66,108,85),(67,109,86),(68,110,87),(69,111,88),(70,112,89),(71,113,90),(72,114,91),(73,115,92),(74,116,93),(75,117,94),(76,118,95),(77,119,96),(78,120,97),(79,101,98),(80,102,99)], [(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)], [(1,67,16,72,11,77,6,62),(2,66,17,71,12,76,7,61),(3,65,18,70,13,75,8,80),(4,64,19,69,14,74,9,79),(5,63,20,68,15,73,10,78),(21,90,36,95,31,100,26,85),(22,89,37,94,32,99,27,84),(23,88,38,93,33,98,28,83),(24,87,39,92,34,97,29,82),(25,86,40,91,35,96,30,81),(41,113,56,118,51,103,46,108),(42,112,57,117,52,102,47,107),(43,111,58,116,53,101,48,106),(44,110,59,115,54,120,49,105),(45,109,60,114,55,119,50,104)], [(2,20),(3,19),(4,18),(5,17),(6,16),(7,15),(8,14),(9,13),(10,12),(21,29),(22,28),(23,27),(24,26),(30,40),(31,39),(32,38),(33,37),(34,36),(41,49),(42,48),(43,47),(44,46),(50,60),(51,59),(52,58),(53,57),(54,56),(61,63),(64,80),(65,79),(66,78),(67,77),(68,76),(69,75),(70,74),(71,73),(82,100),(83,99),(84,98),(85,97),(86,96),(87,95),(88,94),(89,93),(90,92),(101,107),(102,106),(103,105),(108,120),(109,119),(110,118),(111,117),(112,116),(113,115)])

93 conjugacy classes

class 1 2A2B2C2D3A3B4A4B5A5B6A6B6C6D6E6F6G6H8A8B8C8D10A10B10C10D12A12B12C12D15A15B15C15D20A20B20C20D20E20F24A24B24C24D24E24F24G24H30A30B30C30D30E30F30G30H40A···40H60A···60H60I60J60K60L120A···120P
order122223344556666666688881010101012121212151515152020202020202424242424242424303030303030303040···4060···6060606060120···120
size1122020112222112220202020442020224422222222222244444420202020222244444···42···244444···4

93 irreducible representations

dim11111111112222222222224444
type++++++++++
imageC1C2C2C2C3C4C6C6C6C12D4D5D10C3×D4C3×D5D20C5⋊D4C4×D5C6×D5C3×D20C3×C5⋊D4D5×C12C4.D4C3×C4.D4C20.46D4C3×C20.46D4
kernelC3×C20.46D4C3×C4.Dic5C15×M4(2)C6×D20C20.46D4D5×C2×C6C4.Dic5C5×M4(2)C2×D20C22×D5C60C3×M4(2)C2×C12C20M4(2)C12C12C2×C6C2×C4C4C4C22C15C5C3C1
# reps11112422282224444448881248

Matrix representation of C3×C20.46D4 in GL4(𝔽241) generated by

225000
022500
002250
000225
,
854100
20012200
008541
00200122
,
002400
00521
20015600
1194100
,
240000
52100
002400
00521
G:=sub<GL(4,GF(241))| [225,0,0,0,0,225,0,0,0,0,225,0,0,0,0,225],[85,200,0,0,41,122,0,0,0,0,85,200,0,0,41,122],[0,0,200,119,0,0,156,41,240,52,0,0,0,1,0,0],[240,52,0,0,0,1,0,0,0,0,240,52,0,0,0,1] >;

C3×C20.46D4 in GAP, Magma, Sage, TeX

C_3\times C_{20}._{46}D_4
% in TeX

G:=Group("C3xC20.46D4");
// GroupNames label

G:=SmallGroup(480,101);
// by ID

G=gap.SmallGroup(480,101);
# by ID

G:=PCGroup([7,-2,-2,-3,-2,-2,-2,-5,365,92,1683,136,1271,18822]);
// Polycyclic

G:=Group<a,b,c,d|a^3=b^20=d^2=1,c^4=b^10,a*b=b*a,a*c=c*a,a*d=d*a,c*b*c^-1=d*b*d=b^-1,d*c*d=b^15*c^3>;
// generators/relations

׿
×
𝔽