metacyclic, supersoluble, monomial, Z-group, 7-hyperelementary
Aliases: C29⋊C7, SmallGroup(203,1)
Series: Derived ►Chief ►Lower central ►Upper central
| C29 — C29⋊C7 |
Generators and relations for C29⋊C7
G = < a,b | a29=b7=1, bab-1=a20 >
Character table of C29⋊C7
| class | 1 | 7A | 7B | 7C | 7D | 7E | 7F | 29A | 29B | 29C | 29D | |
| size | 1 | 29 | 29 | 29 | 29 | 29 | 29 | 7 | 7 | 7 | 7 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | ζ7 | ζ75 | ζ74 | ζ73 | ζ72 | ζ76 | 1 | 1 | 1 | 1 | linear of order 7 |
| ρ3 | 1 | ζ72 | ζ73 | ζ7 | ζ76 | ζ74 | ζ75 | 1 | 1 | 1 | 1 | linear of order 7 |
| ρ4 | 1 | ζ74 | ζ76 | ζ72 | ζ75 | ζ7 | ζ73 | 1 | 1 | 1 | 1 | linear of order 7 |
| ρ5 | 1 | ζ76 | ζ72 | ζ73 | ζ74 | ζ75 | ζ7 | 1 | 1 | 1 | 1 | linear of order 7 |
| ρ6 | 1 | ζ73 | ζ7 | ζ75 | ζ72 | ζ76 | ζ74 | 1 | 1 | 1 | 1 | linear of order 7 |
| ρ7 | 1 | ζ75 | ζ74 | ζ76 | ζ7 | ζ73 | ζ72 | 1 | 1 | 1 | 1 | linear of order 7 |
| ρ8 | 7 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2927+ζ2926+ζ2918+ζ2915+ζ2912+ζ2910+ζ298 | ζ2925+ζ2924+ζ2923+ζ2920+ζ2916+ζ297+ζ29 | ζ2921+ζ2919+ζ2917+ζ2914+ζ2911+ζ293+ζ292 | ζ2928+ζ2922+ζ2913+ζ299+ζ296+ζ295+ζ294 | complex faithful |
| ρ9 | 7 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2928+ζ2922+ζ2913+ζ299+ζ296+ζ295+ζ294 | ζ2927+ζ2926+ζ2918+ζ2915+ζ2912+ζ2910+ζ298 | ζ2925+ζ2924+ζ2923+ζ2920+ζ2916+ζ297+ζ29 | ζ2921+ζ2919+ζ2917+ζ2914+ζ2911+ζ293+ζ292 | complex faithful |
| ρ10 | 7 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2925+ζ2924+ζ2923+ζ2920+ζ2916+ζ297+ζ29 | ζ2921+ζ2919+ζ2917+ζ2914+ζ2911+ζ293+ζ292 | ζ2928+ζ2922+ζ2913+ζ299+ζ296+ζ295+ζ294 | ζ2927+ζ2926+ζ2918+ζ2915+ζ2912+ζ2910+ζ298 | complex faithful |
| ρ11 | 7 | 0 | 0 | 0 | 0 | 0 | 0 | ζ2921+ζ2919+ζ2917+ζ2914+ζ2911+ζ293+ζ292 | ζ2928+ζ2922+ζ2913+ζ299+ζ296+ζ295+ζ294 | ζ2927+ζ2926+ζ2918+ζ2915+ζ2912+ζ2910+ζ298 | ζ2925+ζ2924+ζ2923+ζ2920+ζ2916+ζ297+ζ29 | complex faithful |
►On 29 points: primitive - transitive group 29T4
Generators in S29
(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)
(2 17 25 8 26 24 21)(3 4 20 15 22 18 12)(5 7 10 29 14 6 23)(9 13 19 28 27 11 16)
G:=sub<Sym(29)| (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), (2,17,25,8,26,24,21)(3,4,20,15,22,18,12)(5,7,10,29,14,6,23)(9,13,19,28,27,11,16)>;
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), (2,17,25,8,26,24,21)(3,4,20,15,22,18,12)(5,7,10,29,14,6,23)(9,13,19,28,27,11,16) );
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)], [(2,17,25,8,26,24,21),(3,4,20,15,22,18,12),(5,7,10,29,14,6,23),(9,13,19,28,27,11,16)]])
G:=TransitiveGroup(29,4);
C29⋊C7 is a maximal subgroup of
C29⋊C14
Matrix representation of C29⋊C7 ►in GL7(𝔽2437)
| 0 | 1 | 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 1 | 1689 | 2174 | 481 | 1905 | 749 | 262 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2356 | 1874 | 867 | 1348 | 1842 | 706 | 148 |
| 1234 | 2283 | 2360 | 2299 | 715 | 1652 | 1764 |
| 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 490 | 1615 | 1608 | 1243 | 1461 | 2056 | 2248 |
| 790 | 598 | 1991 | 1199 | 1652 | 1615 | 932 |
| 0 | 0 | 0 | 0 | 1 | 0 | 0 |
G:=sub<GL(7,GF(2437))| [0,0,0,0,0,0,1,1,0,0,0,0,0,1689,0,1,0,0,0,0,2174,0,0,1,0,0,0,481,0,0,0,1,0,0,1905,0,0,0,0,1,0,749,0,0,0,0,0,1,262],[1,2356,1234,0,490,790,0,0,1874,2283,0,1615,598,0,0,867,2360,1,1608,1991,0,0,1348,2299,0,1243,1199,0,0,1842,715,0,1461,1652,1,0,706,1652,0,2056,1615,0,0,148,1764,0,2248,932,0] >;
C29⋊C7 in GAP, Magma, Sage, TeX
C_{29}\rtimes C_7 % in TeX
G:=Group("C29:C7"); // GroupNames label
G:=SmallGroup(203,1);
// by ID
G=gap.SmallGroup(203,1);
# by ID
G:=PCGroup([2,-7,-29,449]);
// Polycyclic
G:=Group<a,b|a^29=b^7=1,b*a*b^-1=a^20>;
// generators/relations
Export
Subgroup lattice of C29⋊C7 in TeX
Character table of C29⋊C7 in TeX