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G = C11⋊C40  order 440 = 23·5·11

The semidirect product of C11 and C40 acting via C40/C4=C10

metacyclic, supersoluble, monomial, Z-group

Aliases: C11⋊C40, C22.C20, C4.2F11, C44.2C10, C11⋊C8⋊C5, C11⋊C5⋊C8, C2.(C11⋊C20), (C2×C11⋊C5).C4, (C4×C11⋊C5).2C2, SmallGroup(440,1)

Series: Derived ►Chief ►Lower central ►Upper central

Derived series
C1 — C11 — C11⋊C40
Chief series
C1 — C11 — C22 — C44 — C4×C11⋊C5 — C11⋊C40
Lower central
C11 — C11⋊C40
Upper central
C1 — C4

Generators and relations for C11⋊C40
 G = < a,b | a11=b40=1, bab-1=a8 >

C1
C2
11C5
C11
C4
11C10
C22
C11⋊C5
11C8
11C20
C44
C2×C11⋊C5
11C40
C11⋊C8
C4×C11⋊C5
C11⋊C40

Smallest permutation representation of C11⋊C40
►On 88 points
Generators in S88
(1 24 69 48 40 16 53 77 85 32 61)(2 86 17 70 62 78 41 25 33 54 9)(3 34 79 18 10 26 63 87 55 42 71)(4 56 27 80 72 88 11 35 43 64 19)(5 44 49 28 20 36 73 57 65 12 81)(6 66 37 50 82 58 21 45 13 74 29)(7 14 59 38 30 46 83 67 75 22 51)(8 76 47 60 52 68 31 15 23 84 39)

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

44 conjugacy classes

class 1  2 4A4B5A5B5C5D8A8B8C8D10A10B10C10D 11 20A···20H 22 40A···40P44A44B
order124455558888101010101120···202240···404444
size11111111111111111111111111111011···111011···111010

44 irreducible representations

dim11111111101010
type+++-
imageC1C2C4C5C8C10C20C40F11C11⋊C20C11⋊C40
kernelC11⋊C40C4×C11⋊C5C2×C11⋊C5C11⋊C8C11⋊C5C44C22C11C4C2C1
# reps112444816112

Matrix representation of C11⋊C40 ►in GL10(𝔽881)

880100000000
880010000000
880001000000
880000100000
880000010000
880000001000
880000000100
880000000010
880000000001
880000000000
,
0560321321321560081400
3210032125456005600560
3218140321056056003210
3215600032100560321814
0032132100814560321560
3215603212540056056000
2545603210056000321560
0560032132105600254560
3210321032181456000560
0025403215605605603210

G:=sub<GL(10,GF(881))| [880,880,880,880,880,880,880,880,880,880,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,0],[0,321,321,321,0,321,254,0,321,0,560,0,814,560,0,560,560,560,0,0,321,0,0,0,321,321,321,0,321,254,321,321,321,0,321,254,0,321,0,0,321,254,0,321,0,0,0,321,321,321,560,560,560,0,0,0,560,0,814,560,0,0,560,0,814,560,0,560,560,560,814,560,0,560,560,560,0,0,0,560,0,0,321,321,321,0,321,254,0,321,0,560,0,814,560,0,560,560,560,0] >;
 

C11⋊C40 in GAP, Magma, Sage, TeX 

C_{11}\rtimes C_{40}
 
% in TeX
 
G:=Group("C11:C40");
 
// GroupNames label
 
G:=SmallGroup(440,1);
 
// by ID
 
G=gap.SmallGroup(440,1);
 
# by ID
 
G:=PCGroup([5,-2,-5,-2,-2,-11,50,42,10004,4509]);
 
// Polycyclic
 
G:=Group<a,b|a^11=b^40=1,b*a*b^-1=a^8>;
 
// generators/relations
 

Export

Subgroup lattice of C11⋊C40 in TeX

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