Finite Group Databasebeta

← Group #13030647

Character table — Group #13030647

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244444444888888888888888810101010101010101010161616161616161616202020202020202020202020202020202020202020202040404040404040404040
order12222244442444510101024441010202020202020202020202222444444101010202020202020244444488888888888888882444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1ii−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1iii−i−i−i
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1−i−iii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1−i−i−iiii
χ5111111111111111111-1-1-1-111111111-1-1-1-111111111111-1-11-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ6111111111111111111-1-1-1-111111111-1-1-1-111111111111-1-11-1-11-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ7111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11-1-1-1-1-1ii−i−i−i−i−i−i−i−i−i−iiiiiiiii1111iii−i−i−i
χ8111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11-1-1-1-1-1−i−iiiiiiiiiii−i−i−i−i−i−i−i−i1111−i−i−iiii
χ9111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-111-1111-1-1-1-1111111111-1-1-1-11111-1-1-1-111-1-11-1-11-1-1
χ10111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-111-1111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-111-111
χ11111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1111-1-111-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-111i−i−i−iii
χ12111111-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1111-1-111-1−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-111−iiii−i−i
χ13111111-1-1-1-1-1-1111111-1-11111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1111-1-111111-1-1-1-11111-1-1-1-11111-1-1111-1-11-1-1
χ14111111-1-1-1-1-1-1111111-1-11111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-111-111
χ15111111-1-1-1-1-1-1111111-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1i−i−i−iii
χ16111111-1-1-1-1-1-1111111-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1−i−iiiiiii−i−i−i−i−i−i−i−iiiii11-1-1−iiii−i−i
χ171111-1-111-1-11-11-111111-11-1-1-1-1-11111111111-1-1-1-111-1-1111-1-1-1-1-1-1-111ii−i−iii−i−iii−i−iii−i−iii−i−i1-11-1−ii−iii−i
χ181111-1-111-1-11-11-111111-11-1-1-1-1-11111111111-1-1-1-111-1-1111-1-1-1-1-1-1-111−i−iii−i−iii−i−iii−i−iii−i−iii1-11-1i−ii−i−ii
χ191111-1-111-1-11-11-111111-11-1-1-1-1-111111111-1-11111-1-111111-1-1-1-1-1-11-1-1111111-1-111-1-1-1-111-1-111-11-11-11-1-1-11
χ201111-1-111-1-11-11-111111-11-1-1-1-1-111111111-1-11111-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-11-111-1111-1
χ211111-1-111-1-11-11-11111-11-11-1-1-1-11111-1-1-1-111-1-1-1-111-1-11-1-1-111-111-111ii−i−i−i−iii−i−iii−i−iii−i−iii-11-11−ii−iii−i
χ221111-1-111-1-11-11-11111-11-11-1-1-1-11111-1-1-1-111-1-1-1-111-1-11-1-1-111-111-111−i−iiiii−i−iii−i−iii−i−iii−i−i-11-11i−ii−i−ii
χ231111-1-111-1-11-11-11111-11-11-1-1-1-11111-1-1-1-1-1-11111-1-1111-1-1-111-1111-1-11111-1-111-1-11111-1-111-1-11-11-1-11-1-1-11
χ241111-1-111-1-11-11-11111-11-11-1-1-1-11111-1-1-1-1-1-11111-1-1111-1-1-111-1111-1-1-1-1-1-111-1-111-1-1-1-111-1-1111-11-11-1111-1
χ251111-1-1-1-111-111-111111-1-11-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1111-1-1-1111-11ii−i−iii−i−i−i−iiiii−i−i−i−iii1-1-11−i−iii−ii
χ261111-1-1-1-111-111-111111-1-11-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1111-1-1-1111-11−i−iii−i−iiiii−i−i−i−iiiii−i−i1-1-11ii−i−ii−i
χ271111-1-1-1-111-111-111111-1-11-1-11111-1-1-1-1-1-1-1-111-1-11111-1111-1-1-111-11-1111111-1-1-1-111-1-11111-1-1-111-1-1-11-11-1
χ281111-1-1-1-111-111-111111-1-11-1-11111-1-1-1-1-1-1-1-111-1-11111-1111-1-1-111-11-1-1-1-1-1-1-11111-1-111-1-1-1-111-111-111-11-11
χ291111-1-1-1-111-111-11111-111-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1111-1-1-11-11ii−i−i−i−iiiii−i−i−i−iiiii−i−i-111-1−i−iii−ii
χ301111-1-1-1-111-111-11111-111-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1111-1-1-11-11−i−iiiii−i−i−i−iiiii−i−i−i−iii-111-1ii−i−ii−i
χ311111-1-1-1-111-111-11111-111-1-1-11111-1-11111-1-111-1-11111-1-1-1111-1-1-1-11-11111-1-11111-1-111-1-1-1-1111-1-11-1-11-11-1
χ321111-1-1-1-111-111-11111-111-1-1-11111-1-11111-1-111-1-11111-1-1-1111-1-1-1-11-1-1-1-1-111-1-1-1-111-1-11111-1-11-1-1111-11-11
χ332222222222-2-2-2-2222200002222-2-222000022222222-2-2-200-200-200-2-2-2000000000000000000000000000000
χ342222222222-2-2-2-2222200002222-2-2220000-2-2-2-2-2-2-2-222-200-200-200222000000000000000000000000000000
χ35222222-2-2-2-222-2-22222000022-2-2-2-2-2-200002222-2-2-2-2-2-2200200-20022-2000000000000000000000000000000
χ36222222-2-2-2-222-2-22222000022-2-2-2-2-2-20000-2-2-2-2222222200200-200-2-22000000000000000000000000000000
χ372222-2-222-2-2-22-2222220000-2-2-2-2-2-222000022-2-2-2-22222-2002002002-2-2000000000000000000000000000000
χ382222-2-222-2-2-22-2222220000-2-2-2-2-2-2220000-2-22222-2-2-2-2-200200200-222000000000000000000000000000000
χ392222-2-2-2-2222-2-2222220000-2-222-2-2-2-2000022-2-222-2-222200-200200-22-2000000000000000000000000000000
χ402222-2-2-2-2222-2-2222220000-2-222-2-2-2-20000-2-222-2-222-2-2200-2002002-22000000000000000000000000000000
χ4122-2-22-22i−2i2i−2i00002-22-200002-22i−2i002i−2i00002-22-22i−2i2i−2i0000000000000000002−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000000
χ4222-2-22-22i−2i2i−2i00002-22-200002-22i−2i002i−2i00002-22-22i−2i2i−2i000000000000000000−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000000
χ4322-2-22-22i−2i2i−2i00002-22-200002-22i−2i002i−2i0000-22-22−2i2i−2i2i000000000000000000i2−i2i2−i2−22−22−i2i2−i2i22−22−20000000000
χ4422-2-22-22i−2i2i−2i00002-22-200002-22i−2i002i−2i0000-22-22−2i2i−2i2i000000000000000000−i2i2−i2i22−22−2i2−i2i2−i2−22−220000000000
χ4522-2-22-2−2i2i−2i2i00002-22-200002-2−2i2i00−2i2i00002-22-2−2i2i−2i2i0000000000000000002−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000000
χ4622-2-22-2−2i2i−2i2i00002-22-200002-2−2i2i00−2i2i00002-22-2−2i2i−2i2i000000000000000000−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000000
χ4722-2-22-2−2i2i−2i2i00002-22-200002-2−2i2i00−2i2i0000-22-222i−2i2i−2i000000000000000000i2−i2i2−i22−22−2−i2i2−i2i2−22−220000000000
χ4822-2-22-2−2i2i−2i2i00002-22-200002-2−2i2i00−2i2i0000-22-222i−2i2i−2i000000000000000000−i2i2−i2i2−22−22i2−i2i2−i22−22−20000000000
χ4922-2-2-222i−2i−2i2i00002-22-20000-22−2i2i002i−2i00002-2-22−2i2i2i−2i000000000000000000i2−i2−i2i2−222−2i2−i2−i2i2−222−20000000000
χ5022-2-2-222i−2i−2i2i00002-22-20000-22−2i2i002i−2i00002-2-22−2i2i2i−2i000000000000000000−i2i2i2−i22−2−22−i2i2i2−i22−2−220000000000
χ5122-2-2-222i−2i−2i2i00002-22-20000-22−2i2i002i−2i0000-222-22i−2i−2i2i0000000000000000002−2−22i2−i2−i2i2−222−2−i2i2i2−i20000000000
χ5222-2-2-222i−2i−2i2i00002-22-20000-22−2i2i002i−2i0000-222-22i−2i−2i2i000000000000000000−222−2−i2i2i2−i22−2−22i2−i2−i2i20000000000
χ5322-2-2-22−2i2i2i−2i00002-22-20000-222i−2i00−2i2i00002-2-222i−2i−2i2i000000000000000000i2−i2−i2i22−2−22i2−i2−i2i22−2−220000000000
χ5422-2-2-22−2i2i2i−2i00002-22-20000-222i−2i00−2i2i00002-2-222i−2i−2i2i000000000000000000−i2i2i2−i2−222−2−i2i2i2−i2−222−20000000000
χ5522-2-2-22−2i2i2i−2i00002-22-20000-222i−2i00−2i2i0000-222-2−2i2i2i−2i0000000000000000002−2−22−i2i2i2−i2−222−2i2−i2−i2i20000000000
χ5622-2-2-22−2i2i2i−2i00002-22-20000-222i−2i00−2i2i0000-222-2−2i2i2i−2i000000000000000000−222−2i2−i2−i2i22−2−22−i2i2i2−i20000000000
χ5744444444444444-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-10000000000-1-1-1-1-1-1-1-1-1000000000000000000000000000000000
χ5844444444444444-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-111110000000000-111-111-111000000000000000000000000000000000
χ594444444444-4-4-4-4-1-1-1-10000-1-1-1-111-1-155−5−5000000000015−515−515−5000000000000000000000000000000000
χ604444444444-4-4-4-4-1-1-1-10000-1-1-1-111-1-1−5−55500000000001−551−551−55000000000000000000000000000000000
χ61444444-4-4-4-444-4-4-1-1-1-10000-1-111111155−5−50000000000-1−55-1−5515−5000000000000000000000000000000000
χ62444444-4-4-4-444-4-4-1-1-1-10000-1-1111111−5−5550000000000-15−5-15−51−55000000000000000000000000000000000
χ63444444-4-4-4-4-4-444-1-1-1-144-4-4-1-111-1-111111100000000001-1-11-1-1-111000000000000000000000000000000000
χ64444444-4-4-4-4-4-444-1-1-1-1-4-444-1-111-1-111-1-1-1-10000000000111111-1-1-1000000000000000000000000000000000
χ654444-4-444-4-44-44-4-1-1-1-14-44-41111-1-1-1-1-1-1-1-10000000000-1-1-1111111000000000000000000000000000000000
χ664444-4-444-4-44-44-4-1-1-1-1-44-441111-1-1-1-111110000000000-1111-1-11-1-1000000000000000000000000000000000
χ674444-4-444-4-4-44-44-1-1-1-10000111111-1-155−5−5000000000015−5-1−55-1−55000000000000000000000000000000000
χ684444-4-444-4-4-44-44-1-1-1-10000111111-1-1−5−55500000000001−55-15−5-15−5000000000000000000000000000000000
χ694444-4-4-4-4444-4-44-1-1-1-1000011-1-1111155−5−50000000000-1−5515−5-1−55000000000000000000000000000000000
χ704444-4-4-4-4444-4-44-1-1-1-1000011-1-11111−5−5550000000000-15−51−55-15−5000000000000000000000000000000000
χ714444-4-4-4-444-444-4-1-1-1-14-4-4411-1-1-1-111111100000000001-1-1-1111-1-1000000000000000000000000000000000
χ724444-4-4-4-444-444-4-1-1-1-1-444-411-1-1-1-111-1-1-1-10000000000111-1-1-1111000000000000000000000000000000000
χ734-4-44000000000044-4-40000000000000000000000004i−4i0000000000002+2i−2−2i2−2i−2+2i00000000000000000000000000
χ744-4-44000000000044-4-40000000000000000000000004i−4i000000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000
χ754-4-44000000000044-4-4000000000000000000000000−4i4i0000000000002−2i−2+2i2+2i−2−2i00000000000000000000000000
χ764-4-44000000000044-4-4000000000000000000000000−4i4i000000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000
χ7788-8-88-88i−8i8i−8i0000-22-220000-22−2i2i00−2i2i00000000000000000000000000000000000000000000000000000000
χ7888-8-88-8−8i8i−8i8i0000-22-220000-222i−2i002i−2i00000000000000000000000000000000000000000000000000000000
χ7988-8-8-888i−8i−8i8i0000-22-2200002-22i−2i00−2i2i00000000000000000000000000000000000000000000000000000000
χ8088-8-8-88−8i8i8i−8i0000-22-2200002-2−2i2i002i−2i00000000000000000000000000000000000000000000000000000000
χ818-88-800000000008-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ828-88-80000000000-222-20000000025−2500−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ360000000000000000000000000000000000000000000000000000
χ838-88-80000000000-222-20000000025−25002ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ360000000000000000000000000000000000000000000000000000
χ848-88-80000000000-222-200000000−252500−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ360000000000000000000000000000000000000000000000000000
χ858-88-80000000000-222-200000000−2525002ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ360000000000000000000000000000000000000000000000000000
χ8616-16-16160000000000-4-44400000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.