Finite Group Databasebeta

← Group #13030293

Character table — Group #13030293

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222244444444888888888888888810101010101010101010161616161616161616202020202020202020202020202020202020202020202040404040404040404040
order12224444444444510101024441010101020202020202020202244444444202020202020202020444444444444444444488882244888888
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−iiiiiii−i−i−i−i−i−iii−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−iiiiiii−i−iii-1-1-1-1−i−i−iiii
χ5111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-11-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-11-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1ii−i−iiiiiii−i−i−i−i−i−i−i−iii1111−i−i−iiii
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1−i−iii−i−i−i−i−i−iiiiiiiii−i−i1111iii−i−i−i
χ9111111-1-1-1-11-1-11111111-1-111111111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-11-1-1111111-1-1-1-111-1-1-1-11111-1-1111-1-11-1-1
χ10111111-1-1-1-11-1-11111111-1-111111111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-11-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-111-111
χ11111111-1-1-1-11-1-11111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-111ii−i−iii−i−i−i−i−i−iiiiiii−i−i11-1-1i−i−i−iii
χ12111111-1-1-1-11-1-11111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-111−i−iii−i−iiiiiii−i−i−i−i−i−iii11-1-1−iiii−i−i
χ13111111-1-1-1-11-1-111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-111-111
χ14111111-1-1-1-11-1-111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111111111-1-11-1-11-1-1
χ15111111-1-1-1-11-1-111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-111ii−i−iii−i−i−i−i−i−iiiii−i−iii-1-111−iiii−i−i
χ16111111-1-1-1-11-1-111111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-111−i−iii−i−iiiiiii−i−i−i−iii−i−i-1-111i−i−i−iii
χ171111-1-111-1-111-1-111111-11-1111111-1-111-1-11111-1-1-1-1111-1-1-1-111-1-1-11-11111-1-111-1-1-1-111-1-1-1-1-1-11-1-1111-111-1
χ181111-1-111-1-111-1-111111-11-1111111-1-111-1-11111-1-1-1-1111-1-1-1-111-1-1-11-1-1-1-1-111-1-11111-1-11111111-1-11-1-11-1-11
χ191111-1-111-1-111-1-111111-11-1111111-1-111-1-1-1-1-1-11111-1-11-1-1-1-111-1-11-11ii−i−i−i−iii−i−iii−i−iii−i−iii-111-1ii−i−i−ii
χ201111-1-111-1-111-1-111111-11-1111111-1-111-1-1-1-1-1-11111-1-11-1-1-1-111-1-11-11−i−iiiii−i−iii−i−iii−i−iii−i−i-111-1−i−iiii−i
χ211111-1-111-1-111-1-11111-11-11-1-1-1-111-1-111-1-11111-1-1-1-1111-111-1-1-111-11-11111-1-111-1-1-1-111-1-11111-111-1-1-11-1-11
χ221111-1-111-1-111-1-11111-11-11-1-1-1-111-1-111-1-11111-1-1-1-1111-111-1-1-111-11-1-1-1-1-111-1-11111-1-111-1-1-1-1-111-111-111-1
χ231111-1-111-1-111-1-11111-11-11-1-1-1-111-1-111-1-1-1-1-1-11111-1-11-111-1-1-1111-11ii−i−i−i−iii−i−iii−i−iiiii−i−i1-1-11−i−iiii−i
χ241111-1-111-1-111-1-11111-11-11-1-1-1-111-1-111-1-1-1-1-1-11111-1-11-111-1-1-1111-11−i−iiiii−i−iii−i−iii−i−i−i−iii1-1-11ii−i−i−ii
χ251111-1-1-1-1111-11-111111-1-11111111-1-1-1-11111-1-111-1-111-11-1-1-1-1-111-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-11-111-111-11
χ261111-1-1-1-1111-11-111111-1-11111111-1-1-1-11111-1-111-1-111-11-1-1-1-1-111-1-11-1-1-1-11111-1-11111-1-11111-11-11-11-1-11-1
χ271111-1-1-1-1111-11-111111-1-11111111-1-1-1-111-1-111-1-111-1-1-11-1-1-1-1-11111-1ii−i−i−i−i−i−iiiiiii−i−i−i−iii1-11-1i−ii−ii−i
χ281111-1-1-1-1111-11-111111-1-11111111-1-1-1-111-1-111-1-111-1-1-11-1-1-1-1-11111-1−i−iiiiiii−i−i−i−i−i−iiiii−i−i1-11-1−ii−ii−ii
χ291111-1-1-1-1111-11-11111-111-1-1-1-1-111-1-1-1-11111-1-111-1-111-1111-111-1-1-1-111111-1-1-1-111-1-1-1-11111111-11-1-11-1-11-1
χ301111-1-1-1-1111-11-11111-111-1-1-1-1-111-1-1-1-11111-1-111-1-111-1111-111-1-1-1-11-1-1-1-11111-1-11111-1-1-1-1-1-11-11-11-111-11
χ311111-1-1-1-1111-11-11111-111-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1111-111-1-111-1ii−i−i−i−i−i−iiiiiii−i−iii−i−i-11-11−ii−ii−ii
χ321111-1-1-1-1111-11-11111-111-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1111-111-1-111-1−i−iiiiiii−i−i−i−i−i−iii−i−iii-11-11i−ii−ii−i
χ332222222222-2-2-2-2222200000000-2-222222222-2-2-2-2-2-2-2-2-2-200-20000222000000000000000000000000000000
χ342222222222-2-2-2-2222200000000-2-2222222-2-222222222-2-200-20000-2-2-2000000000000000000000000000000
χ35222222-2-2-2-2-222-2222200000000-2-222-2-2-2-2222222-2-2-2-22200-200002-2-2000000000000000000000000000000
χ36222222-2-2-2-2-222-2222200000000-2-222-2-2-2-2-2-2-2-2-2-222222200-20000-222000000000000000000000000000000
χ372222-2-222-2-2-2-222222200000000-2-2-2-222-2-222-2-22222-2-2-220020000-22-2000000000000000000000000000000
χ382222-2-222-2-2-2-222222200000000-2-2-2-222-2-2-2-222-2-2-2-222-2200200002-22000000000000000000000000000000
χ392222-2-2-2-222-22-22222200000000-2-2-2-2-2-2222222-2-222-2-22-20020000-2-22000000000000000000000000000000
χ402222-2-2-2-222-22-22222200000000-2-2-2-2-2-222-2-2-2-222-2-2222-2002000022-2000000000000000000000000000000
χ412-22-22-22i−2i2i−2i00002-22-200000000002-22i−2i2i−2i002-22-22i−2i2i−2i0000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000
χ422-22-22-22i−2i2i−2i00002-22-200000000002-22i−2i2i−2i002-22-22i−2i2i−2i000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000
χ432-22-22-22i−2i2i−2i00002-22-200000000002-22i−2i2i−2i00-22-22−2i2i−2i2i0000000000001−i−1+i1+i−1−i1−i−1+i−1−i1+i−1−i1+i1+i−1−i−1+i1−i−1+i1−i00000000000000
χ442-22-22-22i−2i2i−2i00002-22-200000000002-22i−2i2i−2i00-22-22−2i2i−2i2i000000000000−1+i1−i−1−i1+i−1+i1−i1+i−1−i1+i−1−i−1−i1+i1−i−1+i1−i−1+i00000000000000
χ452-22-22-2−2i2i−2i2i00002-22-200000000002-2−2i2i−2i2i002-22-2−2i2i−2i2i0000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000
χ462-22-22-2−2i2i−2i2i00002-22-200000000002-2−2i2i−2i2i002-22-2−2i2i−2i2i000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000
χ472-22-22-2−2i2i−2i2i00002-22-200000000002-2−2i2i−2i2i00-22-222i−2i2i−2i0000000000001+i−1−i1−i−1+i1+i−1−i−1+i1−i−1+i1−i1−i−1+i−1−i1+i−1−i1+i00000000000000
χ482-22-22-2−2i2i−2i2i00002-22-200000000002-2−2i2i−2i2i00-22-222i−2i2i−2i000000000000−1−i1+i−1+i1−i−1−i1+i1−i−1+i1−i−1+i−1+i1−i1+i−1−i1+i−1−i00000000000000
χ492-22-2-222i−2i−2i2i00002-22-20000000000-222i−2i−2i2i002-2-22−2i2i2i−2i0000000000001+i−1−i1−i−1+i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i−1−i1+i00000000000000
χ502-22-2-222i−2i−2i2i00002-22-20000000000-222i−2i−2i2i002-2-22−2i2i2i−2i000000000000−1−i1+i−1+i1−i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i1+i−1−i00000000000000
χ512-22-2-222i−2i−2i2i00002-22-20000000000-222i−2i−2i2i00-222-22i−2i−2i2i0000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000000000
χ522-22-2-222i−2i−2i2i00002-22-20000000000-222i−2i−2i2i00-222-22i−2i−2i2i000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000000000
χ532-22-2-22−2i2i2i−2i00002-22-20000000000-22−2i2i2i−2i002-2-222i−2i−2i2i0000000000001−i−1+i1+i−1−i−1+i1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i−1+i1−i00000000000000
χ542-22-2-22−2i2i2i−2i00002-22-20000000000-22−2i2i2i−2i002-2-222i−2i−2i2i000000000000−1+i1−i−1−i1+i1−i−1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i1−i−1+i00000000000000
χ552-22-2-22−2i2i2i−2i00002-22-20000000000-22−2i2i2i−2i00-222-2−2i2i2i−2i0000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000000000
χ562-22-2-22−2i2i2i−2i00002-22-20000000000-22−2i2i2i−2i00-222-2−2i2i2i−2i000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000000000
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
χ5844444444444444-1-1-1-1-4-4-4-41111-1-1-1-1-1-1-1-10000000000-1-111-11111000000000000000000000000000000000
χ594444444444-4-4-4-4-1-1-1-1000055−5−511-1-1-1-1-1-10000000000115−515−55−5000000000000000000000000000000000
χ604444444444-4-4-4-4-1-1-1-10000−5−55511-1-1-1-1-1-1000000000011−551−55−55000000000000000000000000000000000
χ61444444-4-4-4-44-4-44-1-1-1-144-4-4-1-1-1-1-1-1-1-11111000000000011-1-1-11111000000000000000000000000000000000
χ62444444-4-4-4-44-4-44-1-1-1-1-4-4441111-1-1-1-1111100000000001111-1-1-1-1-1000000000000000000000000000000000
χ63444444-4-4-4-4-444-4-1-1-1-1000055−5−511-1-111110000000000-1-15−51−55−55000000000000000000000000000000000
χ64444444-4-4-4-4-444-4-1-1-1-10000−5−55511-1-111110000000000-1-1−5515−55−5000000000000000000000000000000000
χ654444-4-444-4-444-4-4-1-1-1-14-44-4-1-1-1-1-1-111-1-1110000000000-11111-1-111000000000000000000000000000000000
χ664444-4-444-4-444-4-4-1-1-1-1-44-441111-1-111-1-1110000000000-11-1-1111-1-1000000000000000000000000000000000
χ674444-4-444-4-4-4-444-1-1-1-1000055−5−51111-1-11100000000001-1−55-15−5−55000000000000000000000000000000000
χ684444-4-444-4-4-4-444-1-1-1-10000−5−5551111-1-11100000000001-15−5-1−555−5000000000000000000000000000000000
χ694444-4-4-4-4444-44-4-1-1-1-14-4-44-1-1-1-1-1-11111-1-100000000001-111111-1-1000000000000000000000000000000000
χ704444-4-4-4-4444-44-4-1-1-1-1-444-41111-1-11111-1-100000000001-1-1-11-1-111000000000000000000000000000000000
χ714444-4-4-4-444-44-44-1-1-1-1000055−5−5111111-1-10000000000-11−55-1−555−5000000000000000000000000000000000
χ724444-4-4-4-444-44-44-1-1-1-10000−5−555111111-1-10000000000-115−5-15−5−55000000000000000000000000000000000
χ734-4-4400000000004-4-4400000000000000004-40000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ744-4-4400000000004-4-4400000000000000004-4000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ754-4-4400000000004-4-440000000000000000-4400000000000000000000000000000000000022−22−22220000000000
χ764-4-4400000000004-4-440000000000000000-44000000000000000000000000000000000000−222222−220000000000
χ7788-8-8000000000088-8-800000000000000000000000000000000000000000000000000000000000000000000
χ7888-8-80000000000-2-2220000−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ3625−250000000000000000000000000000000000000000000000000000000000
χ7988-8-80000000000-2-2220000−2ζ4−2ζ12+2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ362ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ36−25250000000000000000000000000000000000000000000000000000000000
χ8088-8-80000000000-2-22200002ζ4−2ζ12+2ζ28−2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ3625−250000000000000000000000000000000000000000000000000000000000
χ8188-8-80000000000-2-22200002ζ4+2ζ12−2ζ28−2ζ36−2ζ4−2ζ12+2ζ28+2ζ36−2ζ4+2ζ12−2ζ28+2ζ362ζ4−2ζ12+2ζ28−2ζ36−25250000000000000000000000000000000000000000000000000000000000
χ828-88-88-88i−8i8i−8i0000-22-220000000000-22−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ838-88-88-8−8i8i−8i8i0000-22-220000000000-222i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ848-88-8-888i−8i−8i8i0000-22-2200000000002-2−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ858-88-8-88−8i8i8i−8i0000-22-2200000000002-22i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ8616-16-16160000000000-444-400000000000000000000000000000000000000000000000000000000000000000000

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