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G = C91⋊C3order 273 = 3·7·13

3rd semidirect product of C91 and C3 acting faithfully

metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary

Aliases: C913C3, C71(C13⋊C3), C131(C7⋊C3), SmallGroup(273,3)

Series: Derived Chief Lower central Upper central

C1C91 — C91⋊C3
C1C13C91 — C91⋊C3
C91 — C91⋊C3
C1

Generators and relations for C91⋊C3
 G = < a,b | a91=b3=1, bab-1=a74 >

91C3
13C7⋊C3
7C13⋊C3

Smallest permutation representation of C91⋊C3
On 91 points
Generators in S91
(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)
(2 17 75)(3 33 58)(4 49 41)(5 65 24)(6 81 7)(8 22 64)(9 38 47)(10 54 30)(11 70 13)(12 86 87)(14 27 53)(15 43 36)(16 59 19)(18 91 76)(20 32 42)(21 48 25)(23 80 82)(26 37 31)(28 69 88)(29 85 71)(34 74 77)(35 90 60)(39 63 83)(40 79 66)(44 52 89)(45 68 72)(46 84 55)(50 57 78)(51 73 61)(56 62 67)

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

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

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

33 conjugacy classes

class 1 3A3B7A7B13A13B13C13D91A···91X
order133771313131391···91
size191913333333···3

33 irreducible representations

dim11333
type+
imageC1C3C7⋊C3C13⋊C3C91⋊C3
kernelC91⋊C3C91C13C7C1
# reps122424

Matrix representation of C91⋊C3 in GL3(𝔽547) generated by

376104235
235544464
464448219
,
100
82252464
72465294
G:=sub<GL(3,GF(547))| [376,235,464,104,544,448,235,464,219],[1,82,72,0,252,465,0,464,294] >;

C91⋊C3 in GAP, Magma, Sage, TeX

C_{91}\rtimes C_3
% in TeX

G:=Group("C91:C3");
// GroupNames label

G:=SmallGroup(273,3);
// by ID

G=gap.SmallGroup(273,3);
# by ID

G:=PCGroup([3,-3,-7,-13,37,569]);
// Polycyclic

G:=Group<a,b|a^91=b^3=1,b*a*b^-1=a^74>;
// generators/relations

Export

Subgroup lattice of C91⋊C3 in TeX

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