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G = C2×C7⋊D7order 196 = 22·72

Direct product of C2 and C7⋊D7

direct product, metabelian, supersoluble, monomial, A-group

Aliases: C2×C7⋊D7, C14⋊D7, C72D14, C723C22, (C7×C14)⋊2C2, SmallGroup(196,11)

Series: Derived Chief Lower central Upper central

C1C72 — C2×C7⋊D7
C1C7C72C7⋊D7 — C2×C7⋊D7
C72 — C2×C7⋊D7
C1C2

Generators and relations for C2×C7⋊D7
 G = < a,b,c,d | a2=b7=c7=d2=1, ab=ba, ac=ca, ad=da, bc=cb, dbd=b-1, dcd=c-1 >

49C2
49C2
49C22
7D7
7D7
7D7
7D7
7D7
7D7
7D7
7D7
7D7
7D7
7D7
7D7
7D7
7D7
7D7
7D7
7D14
7D14
7D14
7D14
7D14
7D14
7D14
7D14

Smallest permutation representation of C2×C7⋊D7
On 98 points
Generators in S98
(1 16)(2 17)(3 18)(4 19)(5 20)(6 21)(7 15)(8 56)(9 50)(10 51)(11 52)(12 53)(13 54)(14 55)(22 70)(23 64)(24 65)(25 66)(26 67)(27 68)(28 69)(29 77)(30 71)(31 72)(32 73)(33 74)(34 75)(35 76)(36 84)(37 78)(38 79)(39 80)(40 81)(41 82)(42 83)(43 91)(44 85)(45 86)(46 87)(47 88)(48 89)(49 90)(57 94)(58 95)(59 96)(60 97)(61 98)(62 92)(63 93)
(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)
(1 61 83 68 53 87 72)(2 62 84 69 54 88 73)(3 63 78 70 55 89 74)(4 57 79 64 56 90 75)(5 58 80 65 50 91 76)(6 59 81 66 51 85 77)(7 60 82 67 52 86 71)(8 49 34 19 94 38 23)(9 43 35 20 95 39 24)(10 44 29 21 96 40 25)(11 45 30 15 97 41 26)(12 46 31 16 98 42 27)(13 47 32 17 92 36 28)(14 48 33 18 93 37 22)
(1 72)(2 71)(3 77)(4 76)(5 75)(6 74)(7 73)(8 39)(9 38)(10 37)(11 36)(12 42)(13 41)(14 40)(15 32)(16 31)(17 30)(18 29)(19 35)(20 34)(21 33)(22 25)(23 24)(26 28)(43 94)(44 93)(45 92)(46 98)(47 97)(48 96)(49 95)(50 79)(51 78)(52 84)(53 83)(54 82)(55 81)(56 80)(57 91)(58 90)(59 89)(60 88)(61 87)(62 86)(63 85)(64 65)(66 70)(67 69)

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

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

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

C2×C7⋊D7 is a maximal subgroup of   Dic72D7  C7⋊D28  C28⋊D7  C727D4  C2×D72
C2×C7⋊D7 is a maximal quotient of   C724Q8  C28⋊D7  C727D4

52 conjugacy classes

class 1 2A2B2C7A···7X14A···14X
order12227···714···14
size1149492···22···2

52 irreducible representations

dim11122
type+++++
imageC1C2C2D7D14
kernelC2×C7⋊D7C7⋊D7C7×C14C14C7
# reps1212424

Matrix representation of C2×C7⋊D7 in GL4(𝔽29) generated by

28000
02800
0010
0001
,
1000
0100
002219
001010
,
0100
281800
0001
00287
,
0100
1000
001919
00710
G:=sub<GL(4,GF(29))| [28,0,0,0,0,28,0,0,0,0,1,0,0,0,0,1],[1,0,0,0,0,1,0,0,0,0,22,10,0,0,19,10],[0,28,0,0,1,18,0,0,0,0,0,28,0,0,1,7],[0,1,0,0,1,0,0,0,0,0,19,7,0,0,19,10] >;

C2×C7⋊D7 in GAP, Magma, Sage, TeX

C_2\times C_7\rtimes D_7
% in TeX

G:=Group("C2xC7:D7");
// GroupNames label

G:=SmallGroup(196,11);
// by ID

G=gap.SmallGroup(196,11);
# by ID

G:=PCGroup([4,-2,-2,-7,-7,290,2691]);
// Polycyclic

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

Export

Subgroup lattice of C2×C7⋊D7 in TeX

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