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G = C43⋊C7order 301 = 7·43

The semidirect product of C43 and C7 acting faithfully

metacyclic, supersoluble, monomial, Z-group, 7-hyperelementary

Aliases: C43⋊C7, SmallGroup(301,1)

Series: Derived Chief Lower central Upper central

C1C43 — C43⋊C7
C1C43 — C43⋊C7
C43 — C43⋊C7
C1

Generators and relations for C43⋊C7
 G = < a,b | a43=b7=1, bab-1=a21 >

43C7

Character table of C43⋊C7

 class 17A7B7C7D7E7F43A43B43C43D43E43F
 size 1434343434343777777
ρ11111111111111    trivial
ρ21ζ75ζ74ζ76ζ7ζ73ζ72111111    linear of order 7
ρ31ζ76ζ72ζ73ζ74ζ75ζ7111111    linear of order 7
ρ41ζ7ζ75ζ74ζ73ζ72ζ76111111    linear of order 7
ρ51ζ73ζ7ζ75ζ72ζ76ζ74111111    linear of order 7
ρ61ζ72ζ73ζ7ζ76ζ74ζ75111111    linear of order 7
ρ71ζ74ζ76ζ72ζ75ζ7ζ73111111    linear of order 7
ρ87000000ζ433443304329432843264318437ζ433643254317431543144313439ζ4341433543214316431143443ζ43424339433243274322438432ζ434043384331432443234310436ζ43374333432043194312435433    complex faithful
ρ97000000ζ43374333432043194312435433ζ434043384331432443234310436ζ433643254317431543144313439ζ433443304329432843264318437ζ4341433543214316431143443ζ43424339433243274322438432    complex faithful
ρ107000000ζ433643254317431543144313439ζ433443304329432843264318437ζ43424339433243274322438432ζ4341433543214316431143443ζ43374333432043194312435433ζ434043384331432443234310436    complex faithful
ρ117000000ζ43424339433243274322438432ζ4341433543214316431143443ζ434043384331432443234310436ζ43374333432043194312435433ζ433643254317431543144313439ζ433443304329432843264318437    complex faithful
ρ127000000ζ4341433543214316431143443ζ43424339433243274322438432ζ43374333432043194312435433ζ434043384331432443234310436ζ433443304329432843264318437ζ433643254317431543144313439    complex faithful
ρ137000000ζ434043384331432443234310436ζ43374333432043194312435433ζ433443304329432843264318437ζ433643254317431543144313439ζ43424339433243274322438432ζ4341433543214316431143443    complex faithful

Smallest permutation representation of C43⋊C7
On 43 points: primitive
Generators in S43
(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)
(2 42 5 36 17 12 22)(3 40 9 28 33 23 43)(4 38 13 20 6 34 21)(7 32 25 39 11 24 41)(8 30 29 31 27 35 19)(10 26 37 15 16 14 18)

G:=sub<Sym(43)| (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), (2,42,5,36,17,12,22)(3,40,9,28,33,23,43)(4,38,13,20,6,34,21)(7,32,25,39,11,24,41)(8,30,29,31,27,35,19)(10,26,37,15,16,14,18)>;

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), (2,42,5,36,17,12,22)(3,40,9,28,33,23,43)(4,38,13,20,6,34,21)(7,32,25,39,11,24,41)(8,30,29,31,27,35,19)(10,26,37,15,16,14,18) );

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)], [(2,42,5,36,17,12,22),(3,40,9,28,33,23,43),(4,38,13,20,6,34,21),(7,32,25,39,11,24,41),(8,30,29,31,27,35,19),(10,26,37,15,16,14,18)])

Matrix representation of C43⋊C7 in GL7(𝔽3011)

0100000
0010000
0001000
0000100
0000010
0000001
11951916107319419171072
,
1000000
27713002247937227327961647
2816109519382817109419391
1626163619571668219329922771
2988219412822792239012822816
721292633929042335571626
6571853728302083732988

G:=sub<GL(7,GF(3011))| [0,0,0,0,0,0,1,1,0,0,0,0,0,195,0,1,0,0,0,0,1916,0,0,1,0,0,0,1073,0,0,0,1,0,0,194,0,0,0,0,1,0,1917,0,0,0,0,0,1,1072],[1,2771,2816,1626,2988,721,657,0,3002,1095,1636,2194,2926,185,0,2479,1938,1957,1282,339,372,0,372,2817,1668,2792,2904,830,0,273,1094,2193,2390,2335,208,0,2796,1939,2992,1282,57,373,0,1647,1,2771,2816,1626,2988] >;

C43⋊C7 in GAP, Magma, Sage, TeX

C_{43}\rtimes C_7
% in TeX

G:=Group("C43:C7");
// GroupNames label

G:=SmallGroup(301,1);
// by ID

G=gap.SmallGroup(301,1);
# by ID

G:=PCGroup([2,-7,-43,1149]);
// Polycyclic

G:=Group<a,b|a^43=b^7=1,b*a*b^-1=a^21>;
// generators/relations

Export

Subgroup lattice of C43⋊C7 in TeX
Character table of C43⋊C7 in TeX

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