metacyclic, supersoluble, monomial, Z-group, 2-hyperelementary
Aliases: C29⋊C4, D29.C2, SmallGroup(116,3)
Series: Derived ►Chief ►Lower central ►Upper central
| C29 — C29⋊C4 |
Generators and relations for C29⋊C4
G = < a,b | a29=b4=1, bab-1=a17 >
Character table of C29⋊C4
| class | 1 | 2 | 4A | 4B | 29A | 29B | 29C | 29D | 29E | 29F | 29G | |
| size | 1 | 29 | 29 | 29 | 4 | 4 | 4 | 4 | 4 | 4 | 4 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 2 |
| ρ3 | 1 | -1 | i | -i | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 4 |
| ρ4 | 1 | -1 | -i | i | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 4 |
| ρ5 | 4 | 0 | 0 | 0 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | orthogonal faithful |
| ρ6 | 4 | 0 | 0 | 0 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2921+ζ2920+ζ299+ζ298 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | orthogonal faithful |
| ρ7 | 4 | 0 | 0 | 0 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2926+ζ2922+ζ297+ζ293 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | orthogonal faithful |
| ρ8 | 4 | 0 | 0 | 0 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | orthogonal faithful |
| ρ9 | 4 | 0 | 0 | 0 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2926+ζ2922+ζ297+ζ293 | ζ2927+ζ2924+ζ295+ζ292 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2923+ζ2915+ζ2914+ζ296 | orthogonal faithful |
| ρ10 | 4 | 0 | 0 | 0 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2921+ζ2920+ζ299+ζ298 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2927+ζ2924+ζ295+ζ292 | ζ2918+ζ2916+ζ2913+ζ2911 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | orthogonal faithful |
| ρ11 | 4 | 0 | 0 | 0 | ζ2927+ζ2924+ζ295+ζ292 | ζ2926+ζ2922+ζ297+ζ293 | ζ2925+ζ2919+ζ2910+ζ294 | ζ2921+ζ2920+ζ299+ζ298 | ζ2923+ζ2915+ζ2914+ζ296 | ζ2928+ζ2917+ζ2912+ζ29 | ζ2918+ζ2916+ζ2913+ζ2911 | orthogonal faithful |
►On 29 points: primitive - transitive group 29T3
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 13 29 18)(3 25 28 6)(4 8 27 23)(5 20 26 11)(7 15 24 16)(9 10 22 21)(12 17 19 14)
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), (2,13,29,18)(3,25,28,6)(4,8,27,23)(5,20,26,11)(7,15,24,16)(9,10,22,21)(12,17,19,14)>;
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), (2,13,29,18)(3,25,28,6)(4,8,27,23)(5,20,26,11)(7,15,24,16)(9,10,22,21)(12,17,19,14) );
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)], [(2,13,29,18),(3,25,28,6),(4,8,27,23),(5,20,26,11),(7,15,24,16),(9,10,22,21),(12,17,19,14)]])
G:=TransitiveGroup(29,3);
C29⋊C4 is a maximal subgroup of
C87⋊C4
C29⋊C4 is a maximal quotient of C29⋊C8 C87⋊C4
Matrix representation of C29⋊C4 ►in GL4(𝔽233) generated by
| 232 | 1 | 0 | 0 |
| 232 | 0 | 1 | 0 |
| 232 | 0 | 0 | 1 |
| 216 | 212 | 21 | 16 |
| 61 | 25 | 47 | 222 |
| 217 | 212 | 21 | 16 |
| 57 | 166 | 56 | 137 |
| 14 | 209 | 189 | 137 |
G:=sub<GL(4,GF(233))| [232,232,232,216,1,0,0,212,0,1,0,21,0,0,1,16],[61,217,57,14,25,212,166,209,47,21,56,189,222,16,137,137] >;
C29⋊C4 in GAP, Magma, Sage, TeX
C_{29}\rtimes C_4 % in TeX
G:=Group("C29:C4"); // GroupNames label
G:=SmallGroup(116,3);
// by ID
G=gap.SmallGroup(116,3);
# by ID
G:=PCGroup([3,-2,-2,-29,6,434,509]);
// Polycyclic
G:=Group<a,b|a^29=b^4=1,b*a*b^-1=a^17>;
// generators/relations
Export
Subgroup lattice of C29⋊C4 in TeX
Character table of C29⋊C4 in TeX