direct product, metacyclic, supersoluble, monomial, Z-group, 3-hyperelementary
Aliases: C2×C31⋊C3, C62⋊C3, C31⋊2C6, SmallGroup(186,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C31 — C2×C31⋊C3 |
Generators and relations for C2×C31⋊C3
G = < a,b,c | a2=b31=c3=1, ab=ba, ac=ca, cbc-1=b5 >
Character table of C2×C31⋊C3
| class | 1 | 2 | 3A | 3B | 6A | 6B | 31A | 31B | 31C | 31D | 31E | 31F | 31G | 31H | 31I | 31J | 62A | 62B | 62C | 62D | 62E | 62F | 62G | 62H | 62I | 62J | |
| size | 1 | 1 | 31 | 31 | 31 | 31 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | |
| ρ1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | trivial |
| ρ2 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 2 |
| ρ3 | 1 | 1 | ζ32 | ζ3 | ζ3 | ζ32 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ4 | 1 | -1 | ζ32 | ζ3 | ζ65 | ζ6 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 6 |
| ρ5 | 1 | -1 | ζ3 | ζ32 | ζ6 | ζ65 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 6 |
| ρ6 | 1 | 1 | ζ3 | ζ32 | ζ32 | ζ3 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 3 |
| ρ7 | 3 | 3 | 0 | 0 | 0 | 0 | ζ3123+ζ3122+ζ3117 | ζ3128+ζ3118+ζ3116 | ζ3114+ζ319+ζ318 | ζ3129+ζ3121+ζ3112 | ζ3125+ζ315+ζ31 | ζ3119+ζ3110+ζ312 | ζ3115+ζ3113+ζ313 | ζ3127+ζ3124+ζ3111 | ζ3120+ζ317+ζ314 | ζ3130+ζ3126+ζ316 | ζ3119+ζ3110+ζ312 | ζ3115+ζ3113+ζ313 | ζ3120+ζ317+ζ314 | ζ3130+ζ3126+ζ316 | ζ3128+ζ3118+ζ3116 | ζ3114+ζ319+ζ318 | ζ3129+ζ3121+ζ3112 | ζ3125+ζ315+ζ31 | ζ3127+ζ3124+ζ3111 | ζ3123+ζ3122+ζ3117 | complex lifted from C31⋊C3 |
| ρ8 | 3 | 3 | 0 | 0 | 0 | 0 | ζ3120+ζ317+ζ314 | ζ3123+ζ3122+ζ3117 | ζ3127+ζ3124+ζ3111 | ζ3125+ζ315+ζ31 | ζ3115+ζ3113+ζ313 | ζ3130+ζ3126+ζ316 | ζ3114+ζ319+ζ318 | ζ3119+ζ3110+ζ312 | ζ3129+ζ3121+ζ3112 | ζ3128+ζ3118+ζ3116 | ζ3130+ζ3126+ζ316 | ζ3114+ζ319+ζ318 | ζ3129+ζ3121+ζ3112 | ζ3128+ζ3118+ζ3116 | ζ3123+ζ3122+ζ3117 | ζ3127+ζ3124+ζ3111 | ζ3125+ζ315+ζ31 | ζ3115+ζ3113+ζ313 | ζ3119+ζ3110+ζ312 | ζ3120+ζ317+ζ314 | complex lifted from C31⋊C3 |
| ρ9 | 3 | 3 | 0 | 0 | 0 | 0 | ζ3129+ζ3121+ζ3112 | ζ3120+ζ317+ζ314 | ζ3119+ζ3110+ζ312 | ζ3115+ζ3113+ζ313 | ζ3114+ζ319+ζ318 | ζ3128+ζ3118+ζ3116 | ζ3127+ζ3124+ζ3111 | ζ3130+ζ3126+ζ316 | ζ3125+ζ315+ζ31 | ζ3123+ζ3122+ζ3117 | ζ3128+ζ3118+ζ3116 | ζ3127+ζ3124+ζ3111 | ζ3125+ζ315+ζ31 | ζ3123+ζ3122+ζ3117 | ζ3120+ζ317+ζ314 | ζ3119+ζ3110+ζ312 | ζ3115+ζ3113+ζ313 | ζ3114+ζ319+ζ318 | ζ3130+ζ3126+ζ316 | ζ3129+ζ3121+ζ3112 | complex lifted from C31⋊C3 |
| ρ10 | 3 | 3 | 0 | 0 | 0 | 0 | ζ3128+ζ3118+ζ3116 | ζ3130+ζ3126+ζ316 | ζ3115+ζ3113+ζ313 | ζ3120+ζ317+ζ314 | ζ3129+ζ3121+ζ3112 | ζ3127+ζ3124+ζ3111 | ζ3125+ζ315+ζ31 | ζ3114+ζ319+ζ318 | ζ3123+ζ3122+ζ3117 | ζ3119+ζ3110+ζ312 | ζ3127+ζ3124+ζ3111 | ζ3125+ζ315+ζ31 | ζ3123+ζ3122+ζ3117 | ζ3119+ζ3110+ζ312 | ζ3130+ζ3126+ζ316 | ζ3115+ζ3113+ζ313 | ζ3120+ζ317+ζ314 | ζ3129+ζ3121+ζ3112 | ζ3114+ζ319+ζ318 | ζ3128+ζ3118+ζ3116 | complex lifted from C31⋊C3 |
| ρ11 | 3 | -3 | 0 | 0 | 0 | 0 | ζ3120+ζ317+ζ314 | ζ3123+ζ3122+ζ3117 | ζ3127+ζ3124+ζ3111 | ζ3125+ζ315+ζ31 | ζ3115+ζ3113+ζ313 | ζ3130+ζ3126+ζ316 | ζ3114+ζ319+ζ318 | ζ3119+ζ3110+ζ312 | ζ3129+ζ3121+ζ3112 | ζ3128+ζ3118+ζ3116 | -ζ3130-ζ3126-ζ316 | -ζ3114-ζ319-ζ318 | -ζ3129-ζ3121-ζ3112 | -ζ3128-ζ3118-ζ3116 | -ζ3123-ζ3122-ζ3117 | -ζ3127-ζ3124-ζ3111 | -ζ3125-ζ315-ζ31 | -ζ3115-ζ3113-ζ313 | -ζ3119-ζ3110-ζ312 | -ζ3120-ζ317-ζ314 | complex faithful |
| ρ12 | 3 | 3 | 0 | 0 | 0 | 0 | ζ3119+ζ3110+ζ312 | ζ3127+ζ3124+ζ3111 | ζ3129+ζ3121+ζ3112 | ζ3128+ζ3118+ζ3116 | ζ3123+ζ3122+ζ3117 | ζ3115+ζ3113+ζ313 | ζ3120+ζ317+ζ314 | ζ3125+ζ315+ζ31 | ζ3130+ζ3126+ζ316 | ζ3114+ζ319+ζ318 | ζ3115+ζ3113+ζ313 | ζ3120+ζ317+ζ314 | ζ3130+ζ3126+ζ316 | ζ3114+ζ319+ζ318 | ζ3127+ζ3124+ζ3111 | ζ3129+ζ3121+ζ3112 | ζ3128+ζ3118+ζ3116 | ζ3123+ζ3122+ζ3117 | ζ3125+ζ315+ζ31 | ζ3119+ζ3110+ζ312 | complex lifted from C31⋊C3 |
| ρ13 | 3 | -3 | 0 | 0 | 0 | 0 | ζ3125+ζ315+ζ31 | ζ3129+ζ3121+ζ3112 | ζ3130+ζ3126+ζ316 | ζ3114+ζ319+ζ318 | ζ3127+ζ3124+ζ3111 | ζ3123+ζ3122+ζ3117 | ζ3119+ζ3110+ζ312 | ζ3128+ζ3118+ζ3116 | ζ3115+ζ3113+ζ313 | ζ3120+ζ317+ζ314 | -ζ3123-ζ3122-ζ3117 | -ζ3119-ζ3110-ζ312 | -ζ3115-ζ3113-ζ313 | -ζ3120-ζ317-ζ314 | -ζ3129-ζ3121-ζ3112 | -ζ3130-ζ3126-ζ316 | -ζ3114-ζ319-ζ318 | -ζ3127-ζ3124-ζ3111 | -ζ3128-ζ3118-ζ3116 | -ζ3125-ζ315-ζ31 | complex faithful |
| ρ14 | 3 | 3 | 0 | 0 | 0 | 0 | ζ3127+ζ3124+ζ3111 | ζ3114+ζ319+ζ318 | ζ3120+ζ317+ζ314 | ζ3130+ζ3126+ζ316 | ζ3128+ζ3118+ζ3116 | ζ3125+ζ315+ζ31 | ζ3123+ζ3122+ζ3117 | ζ3129+ζ3121+ζ3112 | ζ3119+ζ3110+ζ312 | ζ3115+ζ3113+ζ313 | ζ3125+ζ315+ζ31 | ζ3123+ζ3122+ζ3117 | ζ3119+ζ3110+ζ312 | ζ3115+ζ3113+ζ313 | ζ3114+ζ319+ζ318 | ζ3120+ζ317+ζ314 | ζ3130+ζ3126+ζ316 | ζ3128+ζ3118+ζ3116 | ζ3129+ζ3121+ζ3112 | ζ3127+ζ3124+ζ3111 | complex lifted from C31⋊C3 |
| ρ15 | 3 | -3 | 0 | 0 | 0 | 0 | ζ3129+ζ3121+ζ3112 | ζ3120+ζ317+ζ314 | ζ3119+ζ3110+ζ312 | ζ3115+ζ3113+ζ313 | ζ3114+ζ319+ζ318 | ζ3128+ζ3118+ζ3116 | ζ3127+ζ3124+ζ3111 | ζ3130+ζ3126+ζ316 | ζ3125+ζ315+ζ31 | ζ3123+ζ3122+ζ3117 | -ζ3128-ζ3118-ζ3116 | -ζ3127-ζ3124-ζ3111 | -ζ3125-ζ315-ζ31 | -ζ3123-ζ3122-ζ3117 | -ζ3120-ζ317-ζ314 | -ζ3119-ζ3110-ζ312 | -ζ3115-ζ3113-ζ313 | -ζ3114-ζ319-ζ318 | -ζ3130-ζ3126-ζ316 | -ζ3129-ζ3121-ζ3112 | complex faithful |
| ρ16 | 3 | 3 | 0 | 0 | 0 | 0 | ζ3114+ζ319+ζ318 | ζ3115+ζ3113+ζ313 | ζ3123+ζ3122+ζ3117 | ζ3119+ζ3110+ζ312 | ζ3130+ζ3126+ζ316 | ζ3129+ζ3121+ζ3112 | ζ3128+ζ3118+ζ3116 | ζ3120+ζ317+ζ314 | ζ3127+ζ3124+ζ3111 | ζ3125+ζ315+ζ31 | ζ3129+ζ3121+ζ3112 | ζ3128+ζ3118+ζ3116 | ζ3127+ζ3124+ζ3111 | ζ3125+ζ315+ζ31 | ζ3115+ζ3113+ζ313 | ζ3123+ζ3122+ζ3117 | ζ3119+ζ3110+ζ312 | ζ3130+ζ3126+ζ316 | ζ3120+ζ317+ζ314 | ζ3114+ζ319+ζ318 | complex lifted from C31⋊C3 |
| ρ17 | 3 | 3 | 0 | 0 | 0 | 0 | ζ3130+ζ3126+ζ316 | ζ3119+ζ3110+ζ312 | ζ3125+ζ315+ζ31 | ζ3123+ζ3122+ζ3117 | ζ3120+ζ317+ζ314 | ζ3114+ζ319+ζ318 | ζ3129+ζ3121+ζ3112 | ζ3115+ζ3113+ζ313 | ζ3128+ζ3118+ζ3116 | ζ3127+ζ3124+ζ3111 | ζ3114+ζ319+ζ318 | ζ3129+ζ3121+ζ3112 | ζ3128+ζ3118+ζ3116 | ζ3127+ζ3124+ζ3111 | ζ3119+ζ3110+ζ312 | ζ3125+ζ315+ζ31 | ζ3123+ζ3122+ζ3117 | ζ3120+ζ317+ζ314 | ζ3115+ζ3113+ζ313 | ζ3130+ζ3126+ζ316 | complex lifted from C31⋊C3 |
| ρ18 | 3 | -3 | 0 | 0 | 0 | 0 | ζ3123+ζ3122+ζ3117 | ζ3128+ζ3118+ζ3116 | ζ3114+ζ319+ζ318 | ζ3129+ζ3121+ζ3112 | ζ3125+ζ315+ζ31 | ζ3119+ζ3110+ζ312 | ζ3115+ζ3113+ζ313 | ζ3127+ζ3124+ζ3111 | ζ3120+ζ317+ζ314 | ζ3130+ζ3126+ζ316 | -ζ3119-ζ3110-ζ312 | -ζ3115-ζ3113-ζ313 | -ζ3120-ζ317-ζ314 | -ζ3130-ζ3126-ζ316 | -ζ3128-ζ3118-ζ3116 | -ζ3114-ζ319-ζ318 | -ζ3129-ζ3121-ζ3112 | -ζ3125-ζ315-ζ31 | -ζ3127-ζ3124-ζ3111 | -ζ3123-ζ3122-ζ3117 | complex faithful |
| ρ19 | 3 | -3 | 0 | 0 | 0 | 0 | ζ3119+ζ3110+ζ312 | ζ3127+ζ3124+ζ3111 | ζ3129+ζ3121+ζ3112 | ζ3128+ζ3118+ζ3116 | ζ3123+ζ3122+ζ3117 | ζ3115+ζ3113+ζ313 | ζ3120+ζ317+ζ314 | ζ3125+ζ315+ζ31 | ζ3130+ζ3126+ζ316 | ζ3114+ζ319+ζ318 | -ζ3115-ζ3113-ζ313 | -ζ3120-ζ317-ζ314 | -ζ3130-ζ3126-ζ316 | -ζ3114-ζ319-ζ318 | -ζ3127-ζ3124-ζ3111 | -ζ3129-ζ3121-ζ3112 | -ζ3128-ζ3118-ζ3116 | -ζ3123-ζ3122-ζ3117 | -ζ3125-ζ315-ζ31 | -ζ3119-ζ3110-ζ312 | complex faithful |
| ρ20 | 3 | -3 | 0 | 0 | 0 | 0 | ζ3115+ζ3113+ζ313 | ζ3125+ζ315+ζ31 | ζ3128+ζ3118+ζ3116 | ζ3127+ζ3124+ζ3111 | ζ3119+ζ3110+ζ312 | ζ3120+ζ317+ζ314 | ζ3130+ζ3126+ζ316 | ζ3123+ζ3122+ζ3117 | ζ3114+ζ319+ζ318 | ζ3129+ζ3121+ζ3112 | -ζ3120-ζ317-ζ314 | -ζ3130-ζ3126-ζ316 | -ζ3114-ζ319-ζ318 | -ζ3129-ζ3121-ζ3112 | -ζ3125-ζ315-ζ31 | -ζ3128-ζ3118-ζ3116 | -ζ3127-ζ3124-ζ3111 | -ζ3119-ζ3110-ζ312 | -ζ3123-ζ3122-ζ3117 | -ζ3115-ζ3113-ζ313 | complex faithful |
| ρ21 | 3 | -3 | 0 | 0 | 0 | 0 | ζ3130+ζ3126+ζ316 | ζ3119+ζ3110+ζ312 | ζ3125+ζ315+ζ31 | ζ3123+ζ3122+ζ3117 | ζ3120+ζ317+ζ314 | ζ3114+ζ319+ζ318 | ζ3129+ζ3121+ζ3112 | ζ3115+ζ3113+ζ313 | ζ3128+ζ3118+ζ3116 | ζ3127+ζ3124+ζ3111 | -ζ3114-ζ319-ζ318 | -ζ3129-ζ3121-ζ3112 | -ζ3128-ζ3118-ζ3116 | -ζ3127-ζ3124-ζ3111 | -ζ3119-ζ3110-ζ312 | -ζ3125-ζ315-ζ31 | -ζ3123-ζ3122-ζ3117 | -ζ3120-ζ317-ζ314 | -ζ3115-ζ3113-ζ313 | -ζ3130-ζ3126-ζ316 | complex faithful |
| ρ22 | 3 | -3 | 0 | 0 | 0 | 0 | ζ3127+ζ3124+ζ3111 | ζ3114+ζ319+ζ318 | ζ3120+ζ317+ζ314 | ζ3130+ζ3126+ζ316 | ζ3128+ζ3118+ζ3116 | ζ3125+ζ315+ζ31 | ζ3123+ζ3122+ζ3117 | ζ3129+ζ3121+ζ3112 | ζ3119+ζ3110+ζ312 | ζ3115+ζ3113+ζ313 | -ζ3125-ζ315-ζ31 | -ζ3123-ζ3122-ζ3117 | -ζ3119-ζ3110-ζ312 | -ζ3115-ζ3113-ζ313 | -ζ3114-ζ319-ζ318 | -ζ3120-ζ317-ζ314 | -ζ3130-ζ3126-ζ316 | -ζ3128-ζ3118-ζ3116 | -ζ3129-ζ3121-ζ3112 | -ζ3127-ζ3124-ζ3111 | complex faithful |
| ρ23 | 3 | -3 | 0 | 0 | 0 | 0 | ζ3128+ζ3118+ζ3116 | ζ3130+ζ3126+ζ316 | ζ3115+ζ3113+ζ313 | ζ3120+ζ317+ζ314 | ζ3129+ζ3121+ζ3112 | ζ3127+ζ3124+ζ3111 | ζ3125+ζ315+ζ31 | ζ3114+ζ319+ζ318 | ζ3123+ζ3122+ζ3117 | ζ3119+ζ3110+ζ312 | -ζ3127-ζ3124-ζ3111 | -ζ3125-ζ315-ζ31 | -ζ3123-ζ3122-ζ3117 | -ζ3119-ζ3110-ζ312 | -ζ3130-ζ3126-ζ316 | -ζ3115-ζ3113-ζ313 | -ζ3120-ζ317-ζ314 | -ζ3129-ζ3121-ζ3112 | -ζ3114-ζ319-ζ318 | -ζ3128-ζ3118-ζ3116 | complex faithful |
| ρ24 | 3 | 3 | 0 | 0 | 0 | 0 | ζ3115+ζ3113+ζ313 | ζ3125+ζ315+ζ31 | ζ3128+ζ3118+ζ3116 | ζ3127+ζ3124+ζ3111 | ζ3119+ζ3110+ζ312 | ζ3120+ζ317+ζ314 | ζ3130+ζ3126+ζ316 | ζ3123+ζ3122+ζ3117 | ζ3114+ζ319+ζ318 | ζ3129+ζ3121+ζ3112 | ζ3120+ζ317+ζ314 | ζ3130+ζ3126+ζ316 | ζ3114+ζ319+ζ318 | ζ3129+ζ3121+ζ3112 | ζ3125+ζ315+ζ31 | ζ3128+ζ3118+ζ3116 | ζ3127+ζ3124+ζ3111 | ζ3119+ζ3110+ζ312 | ζ3123+ζ3122+ζ3117 | ζ3115+ζ3113+ζ313 | complex lifted from C31⋊C3 |
| ρ25 | 3 | 3 | 0 | 0 | 0 | 0 | ζ3125+ζ315+ζ31 | ζ3129+ζ3121+ζ3112 | ζ3130+ζ3126+ζ316 | ζ3114+ζ319+ζ318 | ζ3127+ζ3124+ζ3111 | ζ3123+ζ3122+ζ3117 | ζ3119+ζ3110+ζ312 | ζ3128+ζ3118+ζ3116 | ζ3115+ζ3113+ζ313 | ζ3120+ζ317+ζ314 | ζ3123+ζ3122+ζ3117 | ζ3119+ζ3110+ζ312 | ζ3115+ζ3113+ζ313 | ζ3120+ζ317+ζ314 | ζ3129+ζ3121+ζ3112 | ζ3130+ζ3126+ζ316 | ζ3114+ζ319+ζ318 | ζ3127+ζ3124+ζ3111 | ζ3128+ζ3118+ζ3116 | ζ3125+ζ315+ζ31 | complex lifted from C31⋊C3 |
| ρ26 | 3 | -3 | 0 | 0 | 0 | 0 | ζ3114+ζ319+ζ318 | ζ3115+ζ3113+ζ313 | ζ3123+ζ3122+ζ3117 | ζ3119+ζ3110+ζ312 | ζ3130+ζ3126+ζ316 | ζ3129+ζ3121+ζ3112 | ζ3128+ζ3118+ζ3116 | ζ3120+ζ317+ζ314 | ζ3127+ζ3124+ζ3111 | ζ3125+ζ315+ζ31 | -ζ3129-ζ3121-ζ3112 | -ζ3128-ζ3118-ζ3116 | -ζ3127-ζ3124-ζ3111 | -ζ3125-ζ315-ζ31 | -ζ3115-ζ3113-ζ313 | -ζ3123-ζ3122-ζ3117 | -ζ3119-ζ3110-ζ312 | -ζ3130-ζ3126-ζ316 | -ζ3120-ζ317-ζ314 | -ζ3114-ζ319-ζ318 | complex faithful |
►On 62 points
Generators in S62
(1 32)(2 33)(3 34)(4 35)(5 36)(6 37)(7 38)(8 39)(9 40)(10 41)(11 42)(12 43)(13 44)(14 45)(15 46)(16 47)(17 48)(18 49)(19 50)(20 51)(21 52)(22 53)(23 54)(24 55)(25 56)(26 57)(27 58)(28 59)(29 60)(30 61)(31 62)
(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)
(2 26 6)(3 20 11)(4 14 16)(5 8 21)(7 27 31)(9 15 10)(12 28 25)(13 22 30)(17 29 19)(18 23 24)(33 57 37)(34 51 42)(35 45 47)(36 39 52)(38 58 62)(40 46 41)(43 59 56)(44 53 61)(48 60 50)(49 54 55)
G:=sub<Sym(62)| (1,32)(2,33)(3,34)(4,35)(5,36)(6,37)(7,38)(8,39)(9,40)(10,41)(11,42)(12,43)(13,44)(14,45)(15,46)(16,47)(17,48)(18,49)(19,50)(20,51)(21,52)(22,53)(23,54)(24,55)(25,56)(26,57)(27,58)(28,59)(29,60)(30,61)(31,62), (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), (2,26,6)(3,20,11)(4,14,16)(5,8,21)(7,27,31)(9,15,10)(12,28,25)(13,22,30)(17,29,19)(18,23,24)(33,57,37)(34,51,42)(35,45,47)(36,39,52)(38,58,62)(40,46,41)(43,59,56)(44,53,61)(48,60,50)(49,54,55)>;
G:=Group( (1,32)(2,33)(3,34)(4,35)(5,36)(6,37)(7,38)(8,39)(9,40)(10,41)(11,42)(12,43)(13,44)(14,45)(15,46)(16,47)(17,48)(18,49)(19,50)(20,51)(21,52)(22,53)(23,54)(24,55)(25,56)(26,57)(27,58)(28,59)(29,60)(30,61)(31,62), (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), (2,26,6)(3,20,11)(4,14,16)(5,8,21)(7,27,31)(9,15,10)(12,28,25)(13,22,30)(17,29,19)(18,23,24)(33,57,37)(34,51,42)(35,45,47)(36,39,52)(38,58,62)(40,46,41)(43,59,56)(44,53,61)(48,60,50)(49,54,55) );
G=PermutationGroup([[(1,32),(2,33),(3,34),(4,35),(5,36),(6,37),(7,38),(8,39),(9,40),(10,41),(11,42),(12,43),(13,44),(14,45),(15,46),(16,47),(17,48),(18,49),(19,50),(20,51),(21,52),(22,53),(23,54),(24,55),(25,56),(26,57),(27,58),(28,59),(29,60),(30,61),(31,62)], [(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)], [(2,26,6),(3,20,11),(4,14,16),(5,8,21),(7,27,31),(9,15,10),(12,28,25),(13,22,30),(17,29,19),(18,23,24),(33,57,37),(34,51,42),(35,45,47),(36,39,52),(38,58,62),(40,46,41),(43,59,56),(44,53,61),(48,60,50),(49,54,55)]])
C2×C31⋊C3 is a maximal subgroup of
C31⋊C12
Matrix representation of C2×C31⋊C3 ►in GL3(𝔽5) generated by
| 4 | 0 | 0 |
| 0 | 4 | 0 |
| 0 | 0 | 4 |
| 1 | 3 | 2 |
| 1 | 2 | 4 |
| 0 | 1 | 2 |
| 1 | 4 | 1 |
| 0 | 0 | 1 |
| 0 | 4 | 4 |
G:=sub<GL(3,GF(5))| [4,0,0,0,4,0,0,0,4],[1,1,0,3,2,1,2,4,2],[1,0,0,4,0,4,1,1,4] >;
C2×C31⋊C3 in GAP, Magma, Sage, TeX
C_2\times C_{31}\rtimes C_3 % in TeX
G:=Group("C2xC31:C3"); // GroupNames label
G:=SmallGroup(186,2);
// by ID
G=gap.SmallGroup(186,2);
# by ID
G:=PCGroup([3,-2,-3,-31,680]);
// Polycyclic
G:=Group<a,b,c|a^2=b^31=c^3=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^5>;
// generators/relations
Export
Subgroup lattice of C2×C31⋊C3 in TeX
Character table of C2×C31⋊C3 in TeX