direct product, abelian, monomial, 7-elementary
Aliases: C7xC14, SmallGroup(98,5)
Series: Derived ►Chief ►Lower central ►Upper central
| C1 — C7xC14 |
| C1 — C7xC14 |
| C1 — C7xC14 |
Generators and relations for C7xC14
G = < a,b | a7=b14=1, ab=ba >
Quotients: C1, C2, C7, C14, C72, C7xC14
Smallest permutation representation of C7xC14
►Regular action on 98 points
Generators in S98
(1 35 77 23 59 90 54)(2 36 78 24 60 91 55)(3 37 79 25 61 92 56)(4 38 80 26 62 93 43)(5 39 81 27 63 94 44)(6 40 82 28 64 95 45)(7 41 83 15 65 96 46)(8 42 84 16 66 97 47)(9 29 71 17 67 98 48)(10 30 72 18 68 85 49)(11 31 73 19 69 86 50)(12 32 74 20 70 87 51)(13 33 75 21 57 88 52)(14 34 76 22 58 89 53)
(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)
G:=sub<Sym(98)| (1,35,77,23,59,90,54)(2,36,78,24,60,91,55)(3,37,79,25,61,92,56)(4,38,80,26,62,93,43)(5,39,81,27,63,94,44)(6,40,82,28,64,95,45)(7,41,83,15,65,96,46)(8,42,84,16,66,97,47)(9,29,71,17,67,98,48)(10,30,72,18,68,85,49)(11,31,73,19,69,86,50)(12,32,74,20,70,87,51)(13,33,75,21,57,88,52)(14,34,76,22,58,89,53), (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)>;
G:=Group( (1,35,77,23,59,90,54)(2,36,78,24,60,91,55)(3,37,79,25,61,92,56)(4,38,80,26,62,93,43)(5,39,81,27,63,94,44)(6,40,82,28,64,95,45)(7,41,83,15,65,96,46)(8,42,84,16,66,97,47)(9,29,71,17,67,98,48)(10,30,72,18,68,85,49)(11,31,73,19,69,86,50)(12,32,74,20,70,87,51)(13,33,75,21,57,88,52)(14,34,76,22,58,89,53), (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) );
G=PermutationGroup([[(1,35,77,23,59,90,54),(2,36,78,24,60,91,55),(3,37,79,25,61,92,56),(4,38,80,26,62,93,43),(5,39,81,27,63,94,44),(6,40,82,28,64,95,45),(7,41,83,15,65,96,46),(8,42,84,16,66,97,47),(9,29,71,17,67,98,48),(10,30,72,18,68,85,49),(11,31,73,19,69,86,50),(12,32,74,20,70,87,51),(13,33,75,21,57,88,52),(14,34,76,22,58,89,53)], [(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)]])
C7xC14 is a maximal subgroup of
C7:Dic7
98 conjugacy classes
| class | 1 | 2 | 7A | ··· | 7AV | 14A | ··· | 14AV |
| order | 1 | 2 | 7 | ··· | 7 | 14 | ··· | 14 |
| size | 1 | 1 | 1 | ··· | 1 | 1 | ··· | 1 |
98 irreducible representations
| dim | 1 | 1 | 1 | 1 |
| type | + | + | ||
| image | C1 | C2 | C7 | C14 |
| kernel | C7xC14 | C72 | C14 | C7 |
| # reps | 1 | 1 | 48 | 48 |
Matrix representation of C7xC14 ►in GL2(F29) generated by
| 1 | 0 |
| 0 | 25 |
| 9 | 0 |
| 0 | 9 |
G:=sub<GL(2,GF(29))| [1,0,0,25],[9,0,0,9] >;
C7xC14 in GAP, Magma, Sage, TeX
C_7\times C_{14} % in TeX
G:=Group("C7xC14"); // GroupNames label
G:=SmallGroup(98,5);
// by ID
G=gap.SmallGroup(98,5);
# by ID
G:=PCGroup([3,-2,-7,-7]);
// Polycyclic
G:=Group<a,b|a^7=b^14=1,a*b=b*a>;
// generators/relations
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