direct product, metacyclic, supersoluble, monomial, Z-group, 5-hyperelementary
Aliases: C2×C41⋊C5, C82⋊C5, C41⋊2C10, SmallGroup(410,2)
Series: Derived ►Chief ►Lower central ►Upper central
| C41 — C2×C41⋊C5 |
Generators and relations for C2×C41⋊C5
G = < a,b,c | a2=b41=c5=1, ab=ba, ac=ca, cbc-1=b37 >
Character table of C2×C41⋊C5
| class | 1 | 2 | 5A | 5B | 5C | 5D | 10A | 10B | 10C | 10D | 41A | 41B | 41C | 41D | 41E | 41F | 41G | 41H | 82A | 82B | 82C | 82D | 82E | 82F | 82G | 82H | |
| size | 1 | 1 | 41 | 41 | 41 | 41 | 41 | 41 | 41 | 41 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | |
| 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 | ζ5 | ζ54 | ζ53 | ζ52 | ζ5 | ζ54 | ζ53 | ζ52 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 5 |
| ρ4 | 1 | 1 | ζ53 | ζ52 | ζ54 | ζ5 | ζ53 | ζ52 | ζ54 | ζ5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 5 |
| ρ5 | 1 | 1 | ζ54 | ζ5 | ζ52 | ζ53 | ζ54 | ζ5 | ζ52 | ζ53 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 5 |
| ρ6 | 1 | -1 | ζ52 | ζ53 | ζ5 | ζ54 | -ζ52 | -ζ53 | -ζ5 | -ζ54 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 10 |
| ρ7 | 1 | -1 | ζ5 | ζ54 | ζ53 | ζ52 | -ζ5 | -ζ54 | -ζ53 | -ζ52 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 10 |
| ρ8 | 1 | -1 | ζ53 | ζ52 | ζ54 | ζ5 | -ζ53 | -ζ52 | -ζ54 | -ζ5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 10 |
| ρ9 | 1 | 1 | ζ52 | ζ53 | ζ5 | ζ54 | ζ52 | ζ53 | ζ5 | ζ54 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | linear of order 5 |
| ρ10 | 1 | -1 | ζ54 | ζ5 | ζ52 | ζ53 | -ζ54 | -ζ5 | -ζ52 | -ζ53 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | -1 | linear of order 10 |
| ρ11 | 5 | -5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | -ζ4130-ζ4129-ζ4113-ζ417-ζ413 | -ζ4136-ζ4133-ζ4132-ζ4120-ζ412 | -ζ4140-ζ4131-ζ4125-ζ4123-ζ414 | -ζ4139-ζ4121-ζ419-ζ418-ζ415 | -ζ4126-ζ4119-ζ4117-ζ4114-ζ416 | -ζ4138-ζ4134-ζ4128-ζ4112-ζ4111 | -ζ4137-ζ4118-ζ4116-ζ4110-ζ41 | -ζ4135-ζ4127-ζ4124-ζ4122-ζ4115 | complex faithful |
| ρ12 | 5 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | complex lifted from C41⋊C5 |
| ρ13 | 5 | -5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | -ζ4135-ζ4127-ζ4124-ζ4122-ζ4115 | -ζ4137-ζ4118-ζ4116-ζ4110-ζ41 | -ζ4136-ζ4133-ζ4132-ζ4120-ζ412 | -ζ4140-ζ4131-ζ4125-ζ4123-ζ414 | -ζ4130-ζ4129-ζ4113-ζ417-ζ413 | -ζ4126-ζ4119-ζ4117-ζ4114-ζ416 | -ζ4139-ζ4121-ζ419-ζ418-ζ415 | -ζ4138-ζ4134-ζ4128-ζ4112-ζ4111 | complex faithful |
| ρ14 | 5 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | complex lifted from C41⋊C5 |
| ρ15 | 5 | -5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | -ζ4138-ζ4134-ζ4128-ζ4112-ζ4111 | -ζ4139-ζ4121-ζ419-ζ418-ζ415 | -ζ4137-ζ4118-ζ4116-ζ4110-ζ41 | -ζ4136-ζ4133-ζ4132-ζ4120-ζ412 | -ζ4135-ζ4127-ζ4124-ζ4122-ζ4115 | -ζ4130-ζ4129-ζ4113-ζ417-ζ413 | -ζ4140-ζ4131-ζ4125-ζ4123-ζ414 | -ζ4126-ζ4119-ζ4117-ζ4114-ζ416 | complex faithful |
| ρ16 | 5 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | complex lifted from C41⋊C5 |
| ρ17 | 5 | -5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | -ζ4139-ζ4121-ζ419-ζ418-ζ415 | -ζ4126-ζ4119-ζ4117-ζ4114-ζ416 | -ζ4138-ζ4134-ζ4128-ζ4112-ζ4111 | -ζ4135-ζ4127-ζ4124-ζ4122-ζ4115 | -ζ4137-ζ4118-ζ4116-ζ4110-ζ41 | -ζ4136-ζ4133-ζ4132-ζ4120-ζ412 | -ζ4130-ζ4129-ζ4113-ζ417-ζ413 | -ζ4140-ζ4131-ζ4125-ζ4123-ζ414 | complex faithful |
| ρ18 | 5 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | complex lifted from C41⋊C5 |
| ρ19 | 5 | -5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | -ζ4137-ζ4118-ζ4116-ζ4110-ζ41 | -ζ4138-ζ4134-ζ4128-ζ4112-ζ4111 | -ζ4135-ζ4127-ζ4124-ζ4122-ζ4115 | -ζ4130-ζ4129-ζ4113-ζ417-ζ413 | -ζ4136-ζ4133-ζ4132-ζ4120-ζ412 | -ζ4140-ζ4131-ζ4125-ζ4123-ζ414 | -ζ4126-ζ4119-ζ4117-ζ4114-ζ416 | -ζ4139-ζ4121-ζ419-ζ418-ζ415 | complex faithful |
| ρ20 | 5 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | complex lifted from C41⋊C5 |
| ρ21 | 5 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | complex lifted from C41⋊C5 |
| ρ22 | 5 | -5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | -ζ4126-ζ4119-ζ4117-ζ4114-ζ416 | -ζ4140-ζ4131-ζ4125-ζ4123-ζ414 | -ζ4139-ζ4121-ζ419-ζ418-ζ415 | -ζ4137-ζ4118-ζ4116-ζ4110-ζ41 | -ζ4138-ζ4134-ζ4128-ζ4112-ζ4111 | -ζ4135-ζ4127-ζ4124-ζ4122-ζ4115 | -ζ4136-ζ4133-ζ4132-ζ4120-ζ412 | -ζ4130-ζ4129-ζ4113-ζ417-ζ413 | complex faithful |
| ρ23 | 5 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | complex lifted from C41⋊C5 |
| ρ24 | 5 | -5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | -ζ4136-ζ4133-ζ4132-ζ4120-ζ412 | -ζ4135-ζ4127-ζ4124-ζ4122-ζ4115 | -ζ4130-ζ4129-ζ4113-ζ417-ζ413 | -ζ4126-ζ4119-ζ4117-ζ4114-ζ416 | -ζ4140-ζ4131-ζ4125-ζ4123-ζ414 | -ζ4139-ζ4121-ζ419-ζ418-ζ415 | -ζ4138-ζ4134-ζ4128-ζ4112-ζ4111 | -ζ4137-ζ4118-ζ4116-ζ4110-ζ41 | complex faithful |
| ρ25 | 5 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | complex lifted from C41⋊C5 |
| ρ26 | 5 | -5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ζ4137+ζ4118+ζ4116+ζ4110+ζ41 | ζ4140+ζ4131+ζ4125+ζ4123+ζ414 | ζ4130+ζ4129+ζ4113+ζ417+ζ413 | ζ4139+ζ4121+ζ419+ζ418+ζ415 | ζ4126+ζ4119+ζ4117+ζ4114+ζ416 | ζ4138+ζ4134+ζ4128+ζ4112+ζ4111 | ζ4135+ζ4127+ζ4124+ζ4122+ζ4115 | ζ4136+ζ4133+ζ4132+ζ4120+ζ412 | -ζ4140-ζ4131-ζ4125-ζ4123-ζ414 | -ζ4130-ζ4129-ζ4113-ζ417-ζ413 | -ζ4126-ζ4119-ζ4117-ζ4114-ζ416 | -ζ4138-ζ4134-ζ4128-ζ4112-ζ4111 | -ζ4139-ζ4121-ζ419-ζ418-ζ415 | -ζ4137-ζ4118-ζ4116-ζ4110-ζ41 | -ζ4135-ζ4127-ζ4124-ζ4122-ζ4115 | -ζ4136-ζ4133-ζ4132-ζ4120-ζ412 | complex faithful |
►On 82 points
Generators in S82
(1 42)(2 43)(3 44)(4 45)(5 46)(6 47)(7 48)(8 49)(9 50)(10 51)(11 52)(12 53)(13 54)(14 55)(15 56)(16 57)(17 58)(18 59)(19 60)(20 61)(21 62)(22 63)(23 64)(24 65)(25 66)(26 67)(27 68)(28 69)(29 70)(30 71)(31 72)(32 73)(33 74)(34 75)(35 76)(36 77)(37 78)(38 79)(39 80)(40 81)(41 82)
(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)
(2 11 19 17 38)(3 21 37 33 34)(4 31 14 8 30)(5 41 32 24 26)(6 10 9 40 22)(7 20 27 15 18)(12 29 35 13 39)(16 28 25 36 23)(43 52 60 58 79)(44 62 78 74 75)(45 72 55 49 71)(46 82 73 65 67)(47 51 50 81 63)(48 61 68 56 59)(53 70 76 54 80)(57 69 66 77 64)
G:=sub<Sym(82)| (1,42)(2,43)(3,44)(4,45)(5,46)(6,47)(7,48)(8,49)(9,50)(10,51)(11,52)(12,53)(13,54)(14,55)(15,56)(16,57)(17,58)(18,59)(19,60)(20,61)(21,62)(22,63)(23,64)(24,65)(25,66)(26,67)(27,68)(28,69)(29,70)(30,71)(31,72)(32,73)(33,74)(34,75)(35,76)(36,77)(37,78)(38,79)(39,80)(40,81)(41,82), (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), (2,11,19,17,38)(3,21,37,33,34)(4,31,14,8,30)(5,41,32,24,26)(6,10,9,40,22)(7,20,27,15,18)(12,29,35,13,39)(16,28,25,36,23)(43,52,60,58,79)(44,62,78,74,75)(45,72,55,49,71)(46,82,73,65,67)(47,51,50,81,63)(48,61,68,56,59)(53,70,76,54,80)(57,69,66,77,64)>;
G:=Group( (1,42)(2,43)(3,44)(4,45)(5,46)(6,47)(7,48)(8,49)(9,50)(10,51)(11,52)(12,53)(13,54)(14,55)(15,56)(16,57)(17,58)(18,59)(19,60)(20,61)(21,62)(22,63)(23,64)(24,65)(25,66)(26,67)(27,68)(28,69)(29,70)(30,71)(31,72)(32,73)(33,74)(34,75)(35,76)(36,77)(37,78)(38,79)(39,80)(40,81)(41,82), (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), (2,11,19,17,38)(3,21,37,33,34)(4,31,14,8,30)(5,41,32,24,26)(6,10,9,40,22)(7,20,27,15,18)(12,29,35,13,39)(16,28,25,36,23)(43,52,60,58,79)(44,62,78,74,75)(45,72,55,49,71)(46,82,73,65,67)(47,51,50,81,63)(48,61,68,56,59)(53,70,76,54,80)(57,69,66,77,64) );
G=PermutationGroup([[(1,42),(2,43),(3,44),(4,45),(5,46),(6,47),(7,48),(8,49),(9,50),(10,51),(11,52),(12,53),(13,54),(14,55),(15,56),(16,57),(17,58),(18,59),(19,60),(20,61),(21,62),(22,63),(23,64),(24,65),(25,66),(26,67),(27,68),(28,69),(29,70),(30,71),(31,72),(32,73),(33,74),(34,75),(35,76),(36,77),(37,78),(38,79),(39,80),(40,81),(41,82)], [(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)], [(2,11,19,17,38),(3,21,37,33,34),(4,31,14,8,30),(5,41,32,24,26),(6,10,9,40,22),(7,20,27,15,18),(12,29,35,13,39),(16,28,25,36,23),(43,52,60,58,79),(44,62,78,74,75),(45,72,55,49,71),(46,82,73,65,67),(47,51,50,81,63),(48,61,68,56,59),(53,70,76,54,80),(57,69,66,77,64)]])
Matrix representation of C2×C41⋊C5 ►in GL5(𝔽821)
| 820 | 0 | 0 | 0 | 0 |
| 0 | 820 | 0 | 0 | 0 |
| 0 | 0 | 820 | 0 | 0 |
| 0 | 0 | 0 | 820 | 0 |
| 0 | 0 | 0 | 0 | 820 |
| 690 | 315 | 631 | 328 | 1 |
| 1 | 0 | 0 | 0 | 0 |
| 0 | 1 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 0 |
| 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 0 |
| 496 | 287 | 718 | 396 | 8 |
| 650 | 720 | 626 | 241 | 739 |
| 277 | 771 | 596 | 656 | 683 |
| 506 | 399 | 231 | 621 | 72 |
G:=sub<GL(5,GF(821))| [820,0,0,0,0,0,820,0,0,0,0,0,820,0,0,0,0,0,820,0,0,0,0,0,820],[690,1,0,0,0,315,0,1,0,0,631,0,0,1,0,328,0,0,0,1,1,0,0,0,0],[1,496,650,277,506,0,287,720,771,399,0,718,626,596,231,0,396,241,656,621,0,8,739,683,72] >;
C2×C41⋊C5 in GAP, Magma, Sage, TeX
C_2\times C_{41}\rtimes C_5 % in TeX
G:=Group("C2xC41:C5"); // GroupNames label
G:=SmallGroup(410,2);
// by ID
G=gap.SmallGroup(410,2);
# by ID
G:=PCGroup([3,-2,-5,-41,455]);
// Polycyclic
G:=Group<a,b,c|a^2=b^41=c^5=1,a*b=b*a,a*c=c*a,c*b*c^-1=b^37>;
// generators/relations
Export
Subgroup lattice of C2×C41⋊C5 in TeX
Character table of C2×C41⋊C5 in TeX