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G = C11×D7order 154 = 2·7·11

Direct product of C11 and D7

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

Aliases: C11×D7, C7⋊C22, C773C2, SmallGroup(154,1)

Series: Derived Chief Lower central Upper central

C1C7 — C11×D7
C1C7C77 — C11×D7
C7 — C11×D7
C1C11

Generators and relations for C11×D7
 G = < a,b,c | a11=b7=c2=1, ab=ba, ac=ca, cbc=b-1 >

7C2
7C22

Smallest permutation representation of C11×D7
On 77 points
Generators in S77
(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)
(1 70 43 33 49 20 59)(2 71 44 23 50 21 60)(3 72 34 24 51 22 61)(4 73 35 25 52 12 62)(5 74 36 26 53 13 63)(6 75 37 27 54 14 64)(7 76 38 28 55 15 65)(8 77 39 29 45 16 66)(9 67 40 30 46 17 56)(10 68 41 31 47 18 57)(11 69 42 32 48 19 58)
(1 59)(2 60)(3 61)(4 62)(5 63)(6 64)(7 65)(8 66)(9 56)(10 57)(11 58)(12 73)(13 74)(14 75)(15 76)(16 77)(17 67)(18 68)(19 69)(20 70)(21 71)(22 72)(34 51)(35 52)(36 53)(37 54)(38 55)(39 45)(40 46)(41 47)(42 48)(43 49)(44 50)

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

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

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

55 conjugacy classes

class 1  2 7A7B7C11A···11J22A···22J77A···77AD
order1277711···1122···2277···77
size172221···17···72···2

55 irreducible representations

dim111122
type+++
imageC1C2C11C22D7C11×D7
kernelC11×D7C77D7C7C11C1
# reps111010330

Matrix representation of C11×D7 in GL2(𝔽463) generated by

2250
0225
,
3201
4620
,
01
10
G:=sub<GL(2,GF(463))| [225,0,0,225],[320,462,1,0],[0,1,1,0] >;

C11×D7 in GAP, Magma, Sage, TeX

C_{11}\times D_7
% in TeX

G:=Group("C11xD7");
// GroupNames label

G:=SmallGroup(154,1);
// by ID

G=gap.SmallGroup(154,1);
# by ID

G:=PCGroup([3,-2,-11,-7,1190]);
// Polycyclic

G:=Group<a,b,c|a^11=b^7=c^2=1,a*b=b*a,a*c=c*a,c*b*c=b^-1>;
// generators/relations

Export

Subgroup lattice of C11×D7 in TeX

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