direct product, metacyclic, supersoluble, monomial, A-group, 2-hyperelementary
Aliases: D94, C2×D47, C94⋊C2, C47⋊C22, sometimes denoted D188 or Dih94 or Dih188, SmallGroup(188,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C47 — D94 |
Generators and relations for D94
G = < a,b | a94=b2=1, bab=a-1 >
Smallest permutation representation of D94
►On 94 points
Generators in S94
(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)
(1 94)(2 93)(3 92)(4 91)(5 90)(6 89)(7 88)(8 87)(9 86)(10 85)(11 84)(12 83)(13 82)(14 81)(15 80)(16 79)(17 78)(18 77)(19 76)(20 75)(21 74)(22 73)(23 72)(24 71)(25 70)(26 69)(27 68)(28 67)(29 66)(30 65)(31 64)(32 63)(33 62)(34 61)(35 60)(36 59)(37 58)(38 57)(39 56)(40 55)(41 54)(42 53)(43 52)(44 51)(45 50)(46 49)(47 48)
G:=sub<Sym(94)| (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), (1,94)(2,93)(3,92)(4,91)(5,90)(6,89)(7,88)(8,87)(9,86)(10,85)(11,84)(12,83)(13,82)(14,81)(15,80)(16,79)(17,78)(18,77)(19,76)(20,75)(21,74)(22,73)(23,72)(24,71)(25,70)(26,69)(27,68)(28,67)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60)(36,59)(37,58)(38,57)(39,56)(40,55)(41,54)(42,53)(43,52)(44,51)(45,50)(46,49)(47,48)>;
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), (1,94)(2,93)(3,92)(4,91)(5,90)(6,89)(7,88)(8,87)(9,86)(10,85)(11,84)(12,83)(13,82)(14,81)(15,80)(16,79)(17,78)(18,77)(19,76)(20,75)(21,74)(22,73)(23,72)(24,71)(25,70)(26,69)(27,68)(28,67)(29,66)(30,65)(31,64)(32,63)(33,62)(34,61)(35,60)(36,59)(37,58)(38,57)(39,56)(40,55)(41,54)(42,53)(43,52)(44,51)(45,50)(46,49)(47,48) );
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)], [(1,94),(2,93),(3,92),(4,91),(5,90),(6,89),(7,88),(8,87),(9,86),(10,85),(11,84),(12,83),(13,82),(14,81),(15,80),(16,79),(17,78),(18,77),(19,76),(20,75),(21,74),(22,73),(23,72),(24,71),(25,70),(26,69),(27,68),(28,67),(29,66),(30,65),(31,64),(32,63),(33,62),(34,61),(35,60),(36,59),(37,58),(38,57),(39,56),(40,55),(41,54),(42,53),(43,52),(44,51),(45,50),(46,49),(47,48)]])
D94 is a maximal subgroup of
D188 C47⋊D4
D94 is a maximal quotient of Dic94 D188 C47⋊D4
50 conjugacy classes
| class | 1 | 2A | 2B | 2C | 47A | ··· | 47W | 94A | ··· | 94W |
| order | 1 | 2 | 2 | 2 | 47 | ··· | 47 | 94 | ··· | 94 |
| size | 1 | 1 | 47 | 47 | 2 | ··· | 2 | 2 | ··· | 2 |
50 irreducible representations
| dim | 1 | 1 | 1 | 2 | 2 |
| type | + | + | + | + | + |
| image | C1 | C2 | C2 | D47 | D94 |
| kernel | D94 | D47 | C94 | C2 | C1 |
| # reps | 1 | 2 | 1 | 23 | 23 |
Matrix representation of D94 ►in GL2(𝔽283) generated by
| 260 | 99 |
| 273 | 43 |
| 222 | 83 |
| 245 | 61 |
G:=sub<GL(2,GF(283))| [260,273,99,43],[222,245,83,61] >;
D94 in GAP, Magma, Sage, TeX
D_{94} % in TeX
G:=Group("D94"); // GroupNames label
G:=SmallGroup(188,3);
// by ID
G=gap.SmallGroup(188,3);
# by ID
G:=PCGroup([3,-2,-2,-47,1658]);
// Polycyclic
G:=Group<a,b|a^94=b^2=1,b*a*b=a^-1>;
// generators/relations
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