Copied to
clipboard

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 [×4], C3, C4, C4 [×3], C22 [×5], C5, S3 [×3], C6, C6, C8, C8, C2×C4 [×2], D4 [×3], Q8 [×3], C23, D5 [×3], C10, C10, Dic3 [×2], C12, C12, D6 [×4], C2×C6, C15, C2×C8, SD16 [×4], C2×D4, C2×Q8, Dic5 [×2], C20, C20, D10 [×4], C2×C10, C3⋊C8, C24, Dic6, Dic6, C4×S3 [×2], D12, C3⋊D4, C3×D4, C3×Q8, C22×S3, C5×S3, C3×D5, D15 [×2], C30, C2×SD16, C52C8, C40, Dic10, Dic10, C4×D5 [×2], 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 [×2], 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 [×7], C22 [×7], S3, D4 [×2], C23, D5, D6 [×3], SD16 [×2], C2×D4, D10 [×3], 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)
(1 102 56)(2 81 57 20 103 75)(3 100 58 39 104 54)(4 119 59 18 105 73)(5 98 60 37 106 52)(6 117 61 16 107 71)(7 96 62 35 108 50)(8 115 63 14 109 69)(9 94 64 33 110 48)(10 113 65 12 111 67)(11 92 66 31 112 46)(13 90 68 29 114 44)(15 88 70 27 116 42)(17 86 72 25 118 80)(19 84 74 23 120 78)(21 82 76)(22 101 77 40 83 55)(24 99 79 38 85 53)(26 97 41 36 87 51)(28 95 43 34 89 49)(30 93 45 32 91 47)
(1 76)(2 45)(3 54)(4 63)(5 72)(6 41)(7 50)(8 59)(9 68)(10 77)(11 46)(12 55)(13 64)(14 73)(15 42)(16 51)(17 60)(18 69)(19 78)(20 47)(21 56)(22 65)(23 74)(24 43)(25 52)(26 61)(27 70)(28 79)(29 48)(30 57)(31 66)(32 75)(33 44)(34 53)(35 62)(36 71)(37 80)(38 49)(39 58)(40 67)(81 93)(82 102)(83 111)(84 120)(85 89)(86 98)(87 107)(88 116)(90 94)(91 103)(92 112)(95 99)(96 108)(97 117)(100 104)(101 113)(105 109)(106 118)(110 114)(115 119)

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

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

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

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

׿
×
𝔽