metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: D95, C19⋊D5, C5⋊D19, C95⋊1C2, sometimes denoted D190 or Dih95 or Dih190, SmallGroup(190,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C95 — D95 |
Generators and relations for D95
G = < a,b | a95=b2=1, bab=a-1 >
Smallest permutation representation of D95
►On 95 points
Generators in S95
(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)
(1 95)(2 94)(3 93)(4 92)(5 91)(6 90)(7 89)(8 88)(9 87)(10 86)(11 85)(12 84)(13 83)(14 82)(15 81)(16 80)(17 79)(18 78)(19 77)(20 76)(21 75)(22 74)(23 73)(24 72)(25 71)(26 70)(27 69)(28 68)(29 67)(30 66)(31 65)(32 64)(33 63)(34 62)(35 61)(36 60)(37 59)(38 58)(39 57)(40 56)(41 55)(42 54)(43 53)(44 52)(45 51)(46 50)(47 49)
G:=sub<Sym(95)| (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), (1,95)(2,94)(3,93)(4,92)(5,91)(6,90)(7,89)(8,88)(9,87)(10,86)(11,85)(12,84)(13,83)(14,82)(15,81)(16,80)(17,79)(18,78)(19,77)(20,76)(21,75)(22,74)(23,73)(24,72)(25,71)(26,70)(27,69)(28,68)(29,67)(30,66)(31,65)(32,64)(33,63)(34,62)(35,61)(36,60)(37,59)(38,58)(39,57)(40,56)(41,55)(42,54)(43,53)(44,52)(45,51)(46,50)(47,49)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95), (1,95)(2,94)(3,93)(4,92)(5,91)(6,90)(7,89)(8,88)(9,87)(10,86)(11,85)(12,84)(13,83)(14,82)(15,81)(16,80)(17,79)(18,78)(19,77)(20,76)(21,75)(22,74)(23,73)(24,72)(25,71)(26,70)(27,69)(28,68)(29,67)(30,66)(31,65)(32,64)(33,63)(34,62)(35,61)(36,60)(37,59)(38,58)(39,57)(40,56)(41,55)(42,54)(43,53)(44,52)(45,51)(46,50)(47,49) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95)], [(1,95),(2,94),(3,93),(4,92),(5,91),(6,90),(7,89),(8,88),(9,87),(10,86),(11,85),(12,84),(13,83),(14,82),(15,81),(16,80),(17,79),(18,78),(19,77),(20,76),(21,75),(22,74),(23,73),(24,72),(25,71),(26,70),(27,69),(28,68),(29,67),(30,66),(31,65),(32,64),(33,63),(34,62),(35,61),(36,60),(37,59),(38,58),(39,57),(40,56),(41,55),(42,54),(43,53),(44,52),(45,51),(46,50),(47,49)]])
D95 is a maximal subgroup of
D5×D19
D95 is a maximal quotient of Dic95
49 conjugacy classes
| class | 1 | 2 | 5A | 5B | 19A | ··· | 19I | 95A | ··· | 95AJ |
| order | 1 | 2 | 5 | 5 | 19 | ··· | 19 | 95 | ··· | 95 |
| size | 1 | 95 | 2 | 2 | 2 | ··· | 2 | 2 | ··· | 2 |
49 irreducible representations
| dim | 1 | 1 | 2 | 2 | 2 |
| type | + | + | + | + | + |
| image | C1 | C2 | D5 | D19 | D95 |
| kernel | D95 | C95 | C19 | C5 | C1 |
| # reps | 1 | 1 | 2 | 9 | 36 |
Matrix representation of D95 ►in GL2(𝔽191) generated by
| 116 | 151 |
| 72 | 181 |
| 115 | 137 |
| 160 | 76 |
G:=sub<GL(2,GF(191))| [116,72,151,181],[115,160,137,76] >;
D95 in GAP, Magma, Sage, TeX
D_{95} % in TeX
G:=Group("D95"); // GroupNames label
G:=SmallGroup(190,3);
// by ID
G=gap.SmallGroup(190,3);
# by ID
G:=PCGroup([3,-2,-5,-19,49,1622]);
// Polycyclic
G:=Group<a,b|a^95=b^2=1,b*a*b=a^-1>;
// generators/relations
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