Copied to
clipboard

G = C3×C31⋊C5order 465 = 3·5·31

Direct product of C3 and C31⋊C5

direct product, metacyclic, supersoluble, monomial, Z-group, 5-hyperelementary

Aliases: C3×C31⋊C5, C93⋊C5, C312C15, SmallGroup(465,2)

Series: Derived Chief Lower central Upper central

C1C31 — C3×C31⋊C5
C1C31C31⋊C5 — C3×C31⋊C5
C31 — C3×C31⋊C5
C1C3

Generators and relations for C3×C31⋊C5
 G = < a,b,c | a3=b31=c5=1, ab=ba, ac=ca, cbc-1=b2 >

31C5
31C15

Smallest permutation representation of C3×C31⋊C5
On 93 points
Generators in S93
(1 63 32)(2 64 33)(3 65 34)(4 66 35)(5 67 36)(6 68 37)(7 69 38)(8 70 39)(9 71 40)(10 72 41)(11 73 42)(12 74 43)(13 75 44)(14 76 45)(15 77 46)(16 78 47)(17 79 48)(18 80 49)(19 81 50)(20 82 51)(21 83 52)(22 84 53)(23 85 54)(24 86 55)(25 87 56)(26 88 57)(27 89 58)(28 90 59)(29 91 60)(30 92 61)(31 93 62)
(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)
(2 17 9 5 3)(4 18 25 13 7)(6 19 10 21 11)(8 20 26 29 15)(12 22 27 14 23)(16 24 28 30 31)(33 48 40 36 34)(35 49 56 44 38)(37 50 41 52 42)(39 51 57 60 46)(43 53 58 45 54)(47 55 59 61 62)(64 79 71 67 65)(66 80 87 75 69)(68 81 72 83 73)(70 82 88 91 77)(74 84 89 76 85)(78 86 90 92 93)

G:=sub<Sym(93)| (1,63,32)(2,64,33)(3,65,34)(4,66,35)(5,67,36)(6,68,37)(7,69,38)(8,70,39)(9,71,40)(10,72,41)(11,73,42)(12,74,43)(13,75,44)(14,76,45)(15,77,46)(16,78,47)(17,79,48)(18,80,49)(19,81,50)(20,82,51)(21,83,52)(22,84,53)(23,85,54)(24,86,55)(25,87,56)(26,88,57)(27,89,58)(28,90,59)(29,91,60)(30,92,61)(31,93,62), (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), (2,17,9,5,3)(4,18,25,13,7)(6,19,10,21,11)(8,20,26,29,15)(12,22,27,14,23)(16,24,28,30,31)(33,48,40,36,34)(35,49,56,44,38)(37,50,41,52,42)(39,51,57,60,46)(43,53,58,45,54)(47,55,59,61,62)(64,79,71,67,65)(66,80,87,75,69)(68,81,72,83,73)(70,82,88,91,77)(74,84,89,76,85)(78,86,90,92,93)>;

G:=Group( (1,63,32)(2,64,33)(3,65,34)(4,66,35)(5,67,36)(6,68,37)(7,69,38)(8,70,39)(9,71,40)(10,72,41)(11,73,42)(12,74,43)(13,75,44)(14,76,45)(15,77,46)(16,78,47)(17,79,48)(18,80,49)(19,81,50)(20,82,51)(21,83,52)(22,84,53)(23,85,54)(24,86,55)(25,87,56)(26,88,57)(27,89,58)(28,90,59)(29,91,60)(30,92,61)(31,93,62), (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), (2,17,9,5,3)(4,18,25,13,7)(6,19,10,21,11)(8,20,26,29,15)(12,22,27,14,23)(16,24,28,30,31)(33,48,40,36,34)(35,49,56,44,38)(37,50,41,52,42)(39,51,57,60,46)(43,53,58,45,54)(47,55,59,61,62)(64,79,71,67,65)(66,80,87,75,69)(68,81,72,83,73)(70,82,88,91,77)(74,84,89,76,85)(78,86,90,92,93) );

G=PermutationGroup([(1,63,32),(2,64,33),(3,65,34),(4,66,35),(5,67,36),(6,68,37),(7,69,38),(8,70,39),(9,71,40),(10,72,41),(11,73,42),(12,74,43),(13,75,44),(14,76,45),(15,77,46),(16,78,47),(17,79,48),(18,80,49),(19,81,50),(20,82,51),(21,83,52),(22,84,53),(23,85,54),(24,86,55),(25,87,56),(26,88,57),(27,89,58),(28,90,59),(29,91,60),(30,92,61),(31,93,62)], [(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)], [(2,17,9,5,3),(4,18,25,13,7),(6,19,10,21,11),(8,20,26,29,15),(12,22,27,14,23),(16,24,28,30,31),(33,48,40,36,34),(35,49,56,44,38),(37,50,41,52,42),(39,51,57,60,46),(43,53,58,45,54),(47,55,59,61,62),(64,79,71,67,65),(66,80,87,75,69),(68,81,72,83,73),(70,82,88,91,77),(74,84,89,76,85),(78,86,90,92,93)])

33 conjugacy classes

class 1 3A3B5A5B5C5D15A···15H31A···31F93A···93L
order133555515···1531···3193···93
size1113131313131···315···55···5

33 irreducible representations

dim111155
type+
imageC1C3C5C15C31⋊C5C3×C31⋊C5
kernelC3×C31⋊C5C31⋊C5C93C31C3C1
# reps1248612

Matrix representation of C3×C31⋊C5 in GL5(𝔽1861)

4540000
0454000
0045400
0004540
0000454
,
159163516127081
10000
01000
00100
00010
,
10000
00100
00001
115352413491729904
207211769930131

G:=sub<GL(5,GF(1861))| [454,0,0,0,0,0,454,0,0,0,0,0,454,0,0,0,0,0,454,0,0,0,0,0,454],[1591,1,0,0,0,635,0,1,0,0,1612,0,0,1,0,708,0,0,0,1,1,0,0,0,0],[1,0,0,1153,20,0,0,0,524,721,0,1,0,1349,1769,0,0,0,1729,930,0,0,1,904,131] >;

C3×C31⋊C5 in GAP, Magma, Sage, TeX

C_3\times C_{31}\rtimes C_5
% in TeX

G:=Group("C3xC31:C5");
// GroupNames label

G:=SmallGroup(465,2);
// by ID

G=gap.SmallGroup(465,2);
# by ID

G:=PCGroup([3,-3,-5,-31,725]);
// Polycyclic

G:=Group<a,b,c|a^3=b^31=c^5=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^2>;
// generators/relations

Export

Subgroup lattice of C3×C31⋊C5 in TeX

׿
×
𝔽