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G = C4014D6order 480 = 25·3·5

14th semidirect product of C40 and D6 acting via D6/C3=C22

metabelian, supersoluble, monomial, 2-hyperelementary

Aliases: C4014D6, C2414D10, D20.1D6, D151SD16, Dic61D10, Dic101D6, D30.20D4, D12.1D10, C12020C22, C60.139C23, Dic15.25D4, C814(S3×D5), C32(D5×SD16), C52(S3×SD16), C40⋊C25S3, C24⋊C25D5, D15⋊Q88C2, C6.28(D4×D5), C30.9(C2×D4), C153(C2×SD16), (C8×D15)⋊10C2, C10.28(S3×D4), C20⋊D6.2C2, C30.D49C2, C20.D69C2, C153C835C22, C2.6(C20⋊D6), C20.68(C22×S3), C12.68(C22×D5), (C5×Dic6)⋊14C22, (C3×D20).25C22, (C4×D15).53C22, (C5×D12).25C22, (C3×Dic10)⋊14C22, C4.112(C2×S3×D5), (C5×C24⋊C2)⋊7C2, (C3×C40⋊C2)⋊9C2, SmallGroup(480,331)

Series: Derived Chief Lower central Upper central

C1C60 — C4014D6
C1C5C15C30C60C3×D20C20⋊D6 — C4014D6
C15C30C60 — C4014D6
C1C2C4C8

Generators and relations for C4014D6
 G = < a,b,c | a40=b6=c2=1, bab-1=a19, cac=a9, cbc=b-1 >

Subgroups: 908 in 136 conjugacy classes, 40 normal (38 characteristic)
C1, C2, C2, C3, C4, C4, C22, C5, S3, C6, C6, C8, C8, C2×C4, D4, Q8, C23, D5, C10, C10, Dic3, C12, C12, D6, C2×C6, C15, C2×C8, SD16, C2×D4, C2×Q8, Dic5, C20, C20, D10, C2×C10, C3⋊C8, C24, Dic6, Dic6, C4×S3, D12, C3⋊D4, C3×D4, C3×Q8, C22×S3, C5×S3, C3×D5, D15, C30, C2×SD16, C52C8, C40, Dic10, Dic10, C4×D5, D20, C5⋊D4, C5×D4, C5×Q8, C22×D5, S3×C8, C24⋊C2, D4.S3, Q82S3, C3×SD16, S3×D4, S3×Q8, C5×Dic3, C3×Dic5, Dic15, C60, S3×D5, C6×D5, S3×C10, D30, C8×D5, C40⋊C2, D4.D5, Q8⋊D5, C5×SD16, D4×D5, Q8×D5, S3×SD16, C153C8, C120, D30.C2, C15⋊D4, C15⋊Q8, C3×Dic10, C3×D20, C5×Dic6, C5×D12, C4×D15, C2×S3×D5, D5×SD16, C30.D4, C20.D6, C3×C40⋊C2, C5×C24⋊C2, C8×D15, D15⋊Q8, C20⋊D6, C4014D6
Quotients: C1, C2, C22, S3, D4, C23, D5, D6, SD16, C2×D4, D10, C22×S3, C2×SD16, C22×D5, S3×D4, S3×D5, D4×D5, S3×SD16, C2×S3×D5, D5×SD16, C20⋊D6, C4014D6

Smallest permutation representation of C4014D6
On 120 points
Generators in S120
(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)
(1 101 59)(2 120 60 20 102 78)(3 99 61 39 103 57)(4 118 62 18 104 76)(5 97 63 37 105 55)(6 116 64 16 106 74)(7 95 65 35 107 53)(8 114 66 14 108 72)(9 93 67 33 109 51)(10 112 68 12 110 70)(11 91 69 31 111 49)(13 89 71 29 113 47)(15 87 73 27 115 45)(17 85 75 25 117 43)(19 83 77 23 119 41)(21 81 79)(22 100 80 40 82 58)(24 98 42 38 84 56)(26 96 44 36 86 54)(28 94 46 34 88 52)(30 92 48 32 90 50)
(1 79)(2 48)(3 57)(4 66)(5 75)(6 44)(7 53)(8 62)(9 71)(10 80)(11 49)(12 58)(13 67)(14 76)(15 45)(16 54)(17 63)(18 72)(19 41)(20 50)(21 59)(22 68)(23 77)(24 46)(25 55)(26 64)(27 73)(28 42)(29 51)(30 60)(31 69)(32 78)(33 47)(34 56)(35 65)(36 74)(37 43)(38 52)(39 61)(40 70)(81 101)(82 110)(83 119)(84 88)(85 97)(86 106)(87 115)(89 93)(90 102)(91 111)(92 120)(94 98)(95 107)(96 116)(99 103)(100 112)(104 108)(105 117)(109 113)(114 118)

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

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

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

51 conjugacy classes

class 1 2A2B2C2D2E 3 4A4B4C4D5A5B6A6B8A8B8C8D10A10B10C10D12A12B15A15B20A20B20C20D24A24B30A30B40A40B40C40D60A60B60C60D120A···120H
order1222223444455668888101010101212151520202020242430304040404060606060120···120
size11121515202212203022240223030222424440444424244444444444444···4

51 irreducible representations

dim111111112222222222244444444
type++++++++++++++++++++++
imageC1C2C2C2C2C2C2C2S3D4D4D5D6D6D6SD16D10D10D10S3×D4S3×D5D4×D5S3×SD16C2×S3×D5D5×SD16C20⋊D6C4014D6
kernelC4014D6C30.D4C20.D6C3×C40⋊C2C5×C24⋊C2C8×D15D15⋊Q8C20⋊D6C40⋊C2Dic15D30C24⋊C2C40Dic10D20D15C24Dic6D12C10C8C6C5C4C3C2C1
# reps111111111112111422212222448

Matrix representation of C4014D6 in GL6(𝔽241)

192220000
19190000
0015200
0018918900
00002400
00000240
,
100000
02400000
001000
0018924000
0000240240
000010
,
24000000
02400000
001000
0018924000
0000240240
000001

G:=sub<GL(6,GF(241))| [19,19,0,0,0,0,222,19,0,0,0,0,0,0,1,189,0,0,0,0,52,189,0,0,0,0,0,0,240,0,0,0,0,0,0,240],[1,0,0,0,0,0,0,240,0,0,0,0,0,0,1,189,0,0,0,0,0,240,0,0,0,0,0,0,240,1,0,0,0,0,240,0],[240,0,0,0,0,0,0,240,0,0,0,0,0,0,1,189,0,0,0,0,0,240,0,0,0,0,0,0,240,0,0,0,0,0,240,1] >;

C4014D6 in GAP, Magma, Sage, TeX

C_{40}\rtimes_{14}D_6
% in TeX

G:=Group("C40:14D6");
// GroupNames label

G:=SmallGroup(480,331);
// by ID

G=gap.SmallGroup(480,331);
# by ID

G:=PCGroup([7,-2,-2,-2,-2,-2,-3,-5,254,135,58,675,346,80,1356,18822]);
// Polycyclic

G:=Group<a,b,c|a^40=b^6=c^2=1,b*a*b^-1=a^19,c*a*c=a^9,c*b*c=b^-1>;
// generators/relations

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