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G = C8×C11⋊C5order 440 = 23·5·11

Direct product of C8 and C11⋊C5

direct product, metacyclic, supersoluble, monomial, Z-group, 5-hyperelementary

Aliases: C8×C11⋊C5, C88⋊C5, C112C40, C44.4C10, C22.2C20, C2.(C4×C11⋊C5), C4.2(C2×C11⋊C5), (C4×C11⋊C5).4C2, (C2×C11⋊C5).2C4, SmallGroup(440,2)

Series: Derived Chief Lower central Upper central

C1C11 — C8×C11⋊C5
C1C11C22C44C4×C11⋊C5 — C8×C11⋊C5
C11 — C8×C11⋊C5
C1C8

Generators and relations for C8×C11⋊C5
 G = < a,b,c | a8=b11=c5=1, ab=ba, ac=ca, cbc-1=b3 >

11C5
11C10
11C20
11C40

Smallest permutation representation of C8×C11⋊C5
On 88 points
Generators in S88
(1 78 34 56 12 67 23 45)(2 79 35 57 13 68 24 46)(3 80 36 58 14 69 25 47)(4 81 37 59 15 70 26 48)(5 82 38 60 16 71 27 49)(6 83 39 61 17 72 28 50)(7 84 40 62 18 73 29 51)(8 85 41 63 19 74 30 52)(9 86 42 64 20 75 31 53)(10 87 43 65 21 76 32 54)(11 88 44 66 22 77 33 55)
(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)
(2 5 6 10 4)(3 9 11 8 7)(13 16 17 21 15)(14 20 22 19 18)(24 27 28 32 26)(25 31 33 30 29)(35 38 39 43 37)(36 42 44 41 40)(46 49 50 54 48)(47 53 55 52 51)(57 60 61 65 59)(58 64 66 63 62)(68 71 72 76 70)(69 75 77 74 73)(79 82 83 87 81)(80 86 88 85 84)

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

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

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

56 conjugacy classes

class 1  2 4A4B5A5B5C5D8A8B8C8D10A10B10C10D11A11B20A···20H22A22B40A···40P44A44B44C44D88A···88H
order12445555888810101010111120···20222240···404444444488···88
size1111111111111111111111115511···115511···1155555···5

56 irreducible representations

dim111111115555
type++
imageC1C2C4C5C8C10C20C40C11⋊C5C2×C11⋊C5C4×C11⋊C5C8×C11⋊C5
kernelC8×C11⋊C5C4×C11⋊C5C2×C11⋊C5C88C11⋊C5C44C22C11C8C4C2C1
# reps1124448162248

Matrix representation of C8×C11⋊C5 in GL5(𝔽881)

2190000
0219000
0021900
0002190
0000219
,
00001
1000171
0100880
00101
0001170
,
10201
001701171
007100880
0017201
011690170

G:=sub<GL(5,GF(881))| [219,0,0,0,0,0,219,0,0,0,0,0,219,0,0,0,0,0,219,0,0,0,0,0,219],[0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1,1,171,880,1,170],[1,0,0,0,0,0,0,0,0,1,2,170,710,172,169,0,1,0,0,0,1,171,880,1,170] >;

C8×C11⋊C5 in GAP, Magma, Sage, TeX

C_8\times C_{11}\rtimes C_5
% in TeX

G:=Group("C8xC11:C5");
// GroupNames label

G:=SmallGroup(440,2);
// by ID

G=gap.SmallGroup(440,2);
# by ID

G:=PCGroup([5,-2,-5,-2,-2,-11,50,42,2009]);
// Polycyclic

G:=Group<a,b,c|a^8=b^11=c^5=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^3>;
// generators/relations

Export

Subgroup lattice of C8×C11⋊C5 in TeX

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