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G = C7×D13order 182 = 2·7·13

Direct product of C7 and D13

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

Aliases: C7×D13, C13⋊C14, C912C2, SmallGroup(182,2)

Series: Derived Chief Lower central Upper central

C1C13 — C7×D13
C1C13C91 — C7×D13
C13 — C7×D13
C1C7

Generators and relations for C7×D13
 G = < a,b,c | a7=b13=c2=1, ab=ba, ac=ca, cbc=b-1 >

13C2
13C14

Smallest permutation representation of C7×D13
On 91 points
Generators in S91
(1 84 66 62 40 29 18)(2 85 67 63 41 30 19)(3 86 68 64 42 31 20)(4 87 69 65 43 32 21)(5 88 70 53 44 33 22)(6 89 71 54 45 34 23)(7 90 72 55 46 35 24)(8 91 73 56 47 36 25)(9 79 74 57 48 37 26)(10 80 75 58 49 38 14)(11 81 76 59 50 39 15)(12 82 77 60 51 27 16)(13 83 78 61 52 28 17)
(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 21)(15 20)(16 19)(17 18)(22 26)(23 25)(27 30)(28 29)(31 39)(32 38)(33 37)(34 36)(40 52)(41 51)(42 50)(43 49)(44 48)(45 47)(53 57)(54 56)(58 65)(59 64)(60 63)(61 62)(66 78)(67 77)(68 76)(69 75)(70 74)(71 73)(79 88)(80 87)(81 86)(82 85)(83 84)(89 91)

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

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

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

C7×D13 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+++
imageC1C2C7C14D13C7×D13
kernelC7×D13C91D13C13C7C1
# reps1166636

Matrix representation of C7×D13 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] >;

C7×D13 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 C7×D13 in TeX

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