Copied to
clipboard

G = C7xD13order 182 = 2·7·13

Direct product of C7 and D13

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

Aliases: C7xD13, C13:C14, C91:2C2, SmallGroup(182,2)

Series: Derived Chief Lower central Upper central

C1C13 — C7xD13
C1C13C91 — C7xD13
C13 — C7xD13
C1C7

Generators and relations for C7xD13
 G = < a,b,c | a7=b13=c2=1, ab=ba, ac=ca, cbc=b-1 >

Subgroups: 32 in 8 conjugacy classes, 6 normal (all characteristic)
Quotients: C1, C2, C7, C14, D13, C7xD13
13C2
13C14

Smallest permutation representation of C7xD13
On 91 points
Generators in S91
(1 84 74 64 44 32 23)(2 85 75 65 45 33 24)(3 86 76 53 46 34 25)(4 87 77 54 47 35 26)(5 88 78 55 48 36 14)(6 89 66 56 49 37 15)(7 90 67 57 50 38 16)(8 91 68 58 51 39 17)(9 79 69 59 52 27 18)(10 80 70 60 40 28 19)(11 81 71 61 41 29 20)(12 82 72 62 42 30 21)(13 83 73 63 43 31 22)
(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)
(1 13)(2 12)(3 11)(4 10)(5 9)(6 8)(14 18)(15 17)(19 26)(20 25)(21 24)(22 23)(27 36)(28 35)(29 34)(30 33)(31 32)(37 39)(40 47)(41 46)(42 45)(43 44)(48 52)(49 51)(53 61)(54 60)(55 59)(56 58)(62 65)(63 64)(66 68)(69 78)(70 77)(71 76)(72 75)(73 74)(79 88)(80 87)(81 86)(82 85)(83 84)(89 91)

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

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

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

C7xD13 is a maximal subgroup of   C91:C4

56 conjugacy classes

class 1  2 7A···7F13A···13F14A···14F91A···91AJ
order127···713···1314···1491···91
size1131···12···213···132···2

56 irreducible representations

dim111122
type+++
imageC1C2C7C14D13C7xD13
kernelC7xD13C91D13C13C7C1
# reps1166636

Matrix representation of C7xD13 in GL2(F547) generated by

5200
0520
,
3661
334388
,
388546
118159
G:=sub<GL(2,GF(547))| [520,0,0,520],[366,334,1,388],[388,118,546,159] >;

C7xD13 in GAP, Magma, Sage, TeX

C_7\times D_{13}
% in TeX

G:=Group("C7xD13");
// GroupNames label

G:=SmallGroup(182,2);
// by ID

G=gap.SmallGroup(182,2);
# by ID

G:=PCGroup([3,-2,-7,-13,1514]);
// Polycyclic

G:=Group<a,b,c|a^7=b^13=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C7xD13 in TeX

׿
x
:
Z
F
o
wr
Q
<