Copied to
clipboard

G = C4×D31order 248 = 23·31

Direct product of C4 and D31

direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary

Aliases: C4×D31, D62.C2, C1242C2, C2.1D62, Dic312C2, C62.2C22, C311(C2×C4), SmallGroup(248,4)

Series: Derived Chief Lower central Upper central

C1C31 — C4×D31
C1C31C62D62 — C4×D31
C31 — C4×D31
C1C4

Generators and relations for C4×D31
 G = < a,b,c | a4=b31=c2=1, ab=ba, ac=ca, cbc=b-1 >

31C2
31C2
31C22
31C4
31C2×C4

Smallest permutation representation of C4×D31
On 124 points
Generators in S124
(1 120 34 93)(2 121 35 63)(3 122 36 64)(4 123 37 65)(5 124 38 66)(6 94 39 67)(7 95 40 68)(8 96 41 69)(9 97 42 70)(10 98 43 71)(11 99 44 72)(12 100 45 73)(13 101 46 74)(14 102 47 75)(15 103 48 76)(16 104 49 77)(17 105 50 78)(18 106 51 79)(19 107 52 80)(20 108 53 81)(21 109 54 82)(22 110 55 83)(23 111 56 84)(24 112 57 85)(25 113 58 86)(26 114 59 87)(27 115 60 88)(28 116 61 89)(29 117 62 90)(30 118 32 91)(31 119 33 92)
(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124)
(1 31)(2 30)(3 29)(4 28)(5 27)(6 26)(7 25)(8 24)(9 23)(10 22)(11 21)(12 20)(13 19)(14 18)(15 17)(32 35)(33 34)(36 62)(37 61)(38 60)(39 59)(40 58)(41 57)(42 56)(43 55)(44 54)(45 53)(46 52)(47 51)(48 50)(63 91)(64 90)(65 89)(66 88)(67 87)(68 86)(69 85)(70 84)(71 83)(72 82)(73 81)(74 80)(75 79)(76 78)(92 93)(94 114)(95 113)(96 112)(97 111)(98 110)(99 109)(100 108)(101 107)(102 106)(103 105)(115 124)(116 123)(117 122)(118 121)(119 120)

G:=sub<Sym(124)| (1,120,34,93)(2,121,35,63)(3,122,36,64)(4,123,37,65)(5,124,38,66)(6,94,39,67)(7,95,40,68)(8,96,41,69)(9,97,42,70)(10,98,43,71)(11,99,44,72)(12,100,45,73)(13,101,46,74)(14,102,47,75)(15,103,48,76)(16,104,49,77)(17,105,50,78)(18,106,51,79)(19,107,52,80)(20,108,53,81)(21,109,54,82)(22,110,55,83)(23,111,56,84)(24,112,57,85)(25,113,58,86)(26,114,59,87)(27,115,60,88)(28,116,61,89)(29,117,62,90)(30,118,32,91)(31,119,33,92), (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)(94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124), (1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)(32,35)(33,34)(36,62)(37,61)(38,60)(39,59)(40,58)(41,57)(42,56)(43,55)(44,54)(45,53)(46,52)(47,51)(48,50)(63,91)(64,90)(65,89)(66,88)(67,87)(68,86)(69,85)(70,84)(71,83)(72,82)(73,81)(74,80)(75,79)(76,78)(92,93)(94,114)(95,113)(96,112)(97,111)(98,110)(99,109)(100,108)(101,107)(102,106)(103,105)(115,124)(116,123)(117,122)(118,121)(119,120)>;

G:=Group( (1,120,34,93)(2,121,35,63)(3,122,36,64)(4,123,37,65)(5,124,38,66)(6,94,39,67)(7,95,40,68)(8,96,41,69)(9,97,42,70)(10,98,43,71)(11,99,44,72)(12,100,45,73)(13,101,46,74)(14,102,47,75)(15,103,48,76)(16,104,49,77)(17,105,50,78)(18,106,51,79)(19,107,52,80)(20,108,53,81)(21,109,54,82)(22,110,55,83)(23,111,56,84)(24,112,57,85)(25,113,58,86)(26,114,59,87)(27,115,60,88)(28,116,61,89)(29,117,62,90)(30,118,32,91)(31,119,33,92), (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)(94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124), (1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)(32,35)(33,34)(36,62)(37,61)(38,60)(39,59)(40,58)(41,57)(42,56)(43,55)(44,54)(45,53)(46,52)(47,51)(48,50)(63,91)(64,90)(65,89)(66,88)(67,87)(68,86)(69,85)(70,84)(71,83)(72,82)(73,81)(74,80)(75,79)(76,78)(92,93)(94,114)(95,113)(96,112)(97,111)(98,110)(99,109)(100,108)(101,107)(102,106)(103,105)(115,124)(116,123)(117,122)(118,121)(119,120) );

G=PermutationGroup([(1,120,34,93),(2,121,35,63),(3,122,36,64),(4,123,37,65),(5,124,38,66),(6,94,39,67),(7,95,40,68),(8,96,41,69),(9,97,42,70),(10,98,43,71),(11,99,44,72),(12,100,45,73),(13,101,46,74),(14,102,47,75),(15,103,48,76),(16,104,49,77),(17,105,50,78),(18,106,51,79),(19,107,52,80),(20,108,53,81),(21,109,54,82),(22,110,55,83),(23,111,56,84),(24,112,57,85),(25,113,58,86),(26,114,59,87),(27,115,60,88),(28,116,61,89),(29,117,62,90),(30,118,32,91),(31,119,33,92)], [(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),(94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124)], [(1,31),(2,30),(3,29),(4,28),(5,27),(6,26),(7,25),(8,24),(9,23),(10,22),(11,21),(12,20),(13,19),(14,18),(15,17),(32,35),(33,34),(36,62),(37,61),(38,60),(39,59),(40,58),(41,57),(42,56),(43,55),(44,54),(45,53),(46,52),(47,51),(48,50),(63,91),(64,90),(65,89),(66,88),(67,87),(68,86),(69,85),(70,84),(71,83),(72,82),(73,81),(74,80),(75,79),(76,78),(92,93),(94,114),(95,113),(96,112),(97,111),(98,110),(99,109),(100,108),(101,107),(102,106),(103,105),(115,124),(116,123),(117,122),(118,121),(119,120)])

C4×D31 is a maximal subgroup of   C8⋊D31  D1245C2  D42D31  Q82D31
C4×D31 is a maximal quotient of   C8⋊D31  Dic31⋊C4  D62⋊C4

68 conjugacy classes

class 1 2A2B2C4A4B4C4D31A···31O62A···62O124A···124AD
order1222444431···3162···62124···124
size1131311131312···22···22···2

68 irreducible representations

dim11111222
type++++++
imageC1C2C2C2C4D31D62C4×D31
kernelC4×D31Dic31C124D62D31C4C2C1
# reps11114151530

Matrix representation of C4×D31 in GL3(𝔽373) generated by

10400
03720
00372
,
100
001
0372194
,
37200
001
010
G:=sub<GL(3,GF(373))| [104,0,0,0,372,0,0,0,372],[1,0,0,0,0,372,0,1,194],[372,0,0,0,0,1,0,1,0] >;

C4×D31 in GAP, Magma, Sage, TeX

C_4\times D_{31}
% in TeX

G:=Group("C4xD31");
// GroupNames label

G:=SmallGroup(248,4);
// by ID

G=gap.SmallGroup(248,4);
# by ID

G:=PCGroup([4,-2,-2,-2,-31,21,3843]);
// Polycyclic

G:=Group<a,b,c|a^4=b^31=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C4×D31 in TeX

׿
×
𝔽