Finite Group Databasebeta

← Group #14301363

Character table — Group #14301363

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11222222244445588888888881010101010101012121616161616161616202020202020202020202020202020202020244040404040404048484848606060606060120120120
order122344666510121222266101520203030302446666241010303030306060444444441212121212121212121282661212121210204040244444888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11-1-1
χ311111111111111111111111111111111-1-111111111111111111111111111-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-111
χ5111111111111111-1-1-11111111111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1
χ6111111111111111-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-111
χ7111111111111111-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-1-1-1-1-1111
χ8111111111111111-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-111111-1-1
χ91111111111111-1-11111111111-1-1-1-1-1-1-11111111111ii−i−iii−i−i-1-1iiii−i−i−i−i1-1-1-1ii−i−i1111-1-1i−ii−i-1i−i
χ101111111111111-1-11111111111-1-1-1-1-1-1-11111111111−i−iii−i−iii-1-1−i−i−i−iiiii1-1-1-1−i−iii1111-1-1−ii−ii-1−ii
χ111111111111111-1-11111111111-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i-1-1iiii−i−i−i−i-1-1-1-1ii−i−i-1-1-1-111−ii−ii1−ii
χ121111111111111-1-11111111111-1-1-1-1-1-1-1-1-111111111−i−iii−i−iii-1-1−i−i−i−iiiii-1-1-1-1−i−iii-1-1-1-111i−ii−i1i−i
χ131111111111111-1-1-1-1-11111111-1-1-1-1-1-1-111-1-1-1-1-1-111ii−i−i−i−iii-1-1−i−i−i−iiiii-1111ii−i−i11-1-1-1-1i−ii−i1−ii
χ141111111111111-1-1-1-1-11111111-1-1-1-1-1-1-111-1-1-1-1-1-111−i−iiiii−i−i-1-1iiii−i−i−i−i-1111−i−iii11-1-1-1-1−ii−ii1i−i
χ151111111111111-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-1-1−i−i−i−iiiii1111ii−i−i-1-11111−ii−ii-1i−i
χ161111111111111-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-1-1iiii−i−i−i−i1111−i−iii-1-11111i−ii−i-1−ii
χ172222-2-222222-2-22200022-2-22222-2-2222200000000-2-22-22-20000-2-20000000000002-22-20000000000000
χ182222-2-222222-2-22200022-2-22222-2-2222200000000-2-2-22-220000-2-2000000000000-22-220000000000000
χ192222-2-222222-2-2-2-200022-2-2222-222-2-2-2-200000000-2-22i−2i−2i2i0000220000000000002i−2i−2i2i0000000000000
χ202222-2-222222-2-2-2-200022-2-2222-222-2-2-2-200000000-2-2−2i2i2i−2i000022000000000000−2i2i2i−2i0000000000000
χ21222-122-1-1-122-1-1222-1-12-122-1-1-1222-1-1-1-10022-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-102-1-1-1-1-1-10000000000000
χ22222-122-1-1-122-1-1222-1-12-122-1-1-1222-1-1-1-10022-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111102-1-111110000000000000
χ23222-122-1-1-122-1-122-2112-122-1-1-1222-1-1-1-100-2-21111-1-12222-2-2-2-2-1-1111111110-211-1-1-1-10000000000000
χ24222-122-1-1-122-1-122-2112-122-1-1-1222-1-1-1-100-2-21111-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-10-21111110000000000000
χ25222-122-1-1-122-1-1-2-22-1-12-122-1-1-1-2-2-211110022-1-1-1-1-1-12i2i−2i−2i2i2i−2i−2i11−i−i−i−iiiii0-211−i−iii0000000000000
χ26222-122-1-1-122-1-1-2-22-1-12-122-1-1-1-2-2-211110022-1-1-1-1-1-1−2i−2i2i2i−2i−2i2i2i11iiii−i−i−i−i0-211ii−i−i0000000000000
χ27222-122-1-1-122-1-1-2-2-2112-122-1-1-1-2-2-2111100-2-21111-1-12i2i−2i−2i−2i−2i2i2i11iiii−i−i−i−i02-1-1−i−iii0000000000000
χ28222-122-1-1-122-1-1-2-2-2112-122-1-1-1-2-2-2111100-2-21111-1-1−2i−2i2i2i2i2i−2i−2i11−i−i−i−iiiii02-1-1ii−i−i0000000000000
χ29222-1-2-2-1-1-12211220−i3i32-1-2-2-1-1-12-2-2-1-1-1-10000−i3−i3i3i3112-22-2000011−i3−i3i3i3−i3−i3i3i300−i3i3-11-110000000000000
χ30222-1-2-2-1-1-12211220−i3i32-1-2-2-1-1-12-2-2-1-1-1-10000−i3−i3i3i311-22-22000011i3i3−i3−i3i3i3−i3−i300−i3i31-11-10000000000000
χ31222-1-2-2-1-1-12211220i3−i32-1-2-2-1-1-12-2-2-1-1-1-10000i3i3−i3−i3112-22-2000011i3i3−i3−i3i3i3−i3−i300i3−i3-11-110000000000000
χ32222-1-2-2-1-1-12211220i3−i32-1-2-2-1-1-12-2-2-1-1-1-10000i3i3−i3−i311-22-22000011−i3−i3i3i3−i3−i3i3i300i3−i31-11-10000000000000
χ33222-1-2-2-1-1-12211-2-20−i3i32-1-2-2-1-1-1-22211110000−i3−i3i3i3112i−2i−2i2i0000-1-133−3−3−3−33300i3−i3−iii−i0000000000000
χ34222-1-2-2-1-1-12211-2-20−i3i32-1-2-2-1-1-1-22211110000−i3−i3i3i311−2i2i2i−2i0000-1-1−3−33333−3−300i3−i3i−i−ii0000000000000
χ35222-1-2-2-1-1-12211-2-20i3−i32-1-2-2-1-1-1-22211110000i3i3−i3−i3112i−2i−2i2i0000-1-1−3−33333−3−300−i3i3−iii−i0000000000000
χ36222-1-2-2-1-1-12211-2-20i3−i32-1-2-2-1-1-1-22211110000i3i3−i3−i311−2i2i2i−2i0000-1-133−3−3−3−33300−i3i3i−i−ii0000000000000
χ3722-222-2-2-22222-222000-222-2-2-22-2-222-2-22000000002-2000000002-2000000000000000000000022-2-2000
χ3822-222-2-2-22222-222000-222-2-2-22-2-222-2-22000000002-2000000002-20000000000000000000000-2-222000
χ3922-222-2-2-22222-2-2-2000-222-2-2-2222-2-222-2000000002-200000000-2200000000000000000000002i−2i−2i2i000
χ4022-222-2-2-22222-2-2-2000-222-2-2-2222-2-222-2000000002-200000000-220000000000000000000000−2i2i2i−2i000
χ4122-22-22-2-2222-2222000-22-22-2-22-22-22-2-222-2000000-2200000000-2200000000000000002-2002-20000000
χ4222-22-22-2-2222-2222000-22-22-2-22-22-22-2-22-22000000-2200000000-220000000000000000-2200-220000000
χ4322-22-22-2-2222-22-2-2000-22-22-2-222-22-222-22-2000000-22000000002-200000000000000002-200-220000000
χ4422-22-22-2-2222-22-2-2000-22-22-2-222-22-222-2-22000000-22000000002-20000000000000000-22002-20000000
χ45444444444-1-14400444-1-1-1-1-1-1-1000000044-1-1-1-1-1-1-1-100000000000000000040000000-1-1-1-1000000000
χ46444444444-1-14400444-1-1-1-1-1-1-10000000-4-4-1-1-1-1-1-1-1-1000000000000000000-400000001111000000000
χ47444444444-1-14400-4-4-4-1-1-1-1-1-1-1000000044111111-1-1000000000000000000-40000000-1-111000000000
χ48444444444-1-14400-4-4-4-1-1-1-1-1-1-10000000-4-4111111-1-10000000000000000004000000011-1-1000000000
χ4944-44-44-4-44-1-1-44000001-11-111-100000004-4−55−55−551-100000000000000000000000000-11−55000000000
χ5044-44-44-4-44-1-1-44000001-11-111-100000004-45−55−55−51-100000000000000000000000000-115−5000000000
χ5144-44-44-4-44-1-1-44000001-11-111-10000000-44−55−55−551-1000000000000000000000000001-15−5000000000
χ5244-44-44-4-44-1-1-44000001-11-111-10000000-445−55−55−51-1000000000000000000000000001-1−55000000000
χ5344-4-24-422-244-2244000-4-24-422-2-4-44-222-200000000-2200000000-2200000000000000000000000000000
χ5444-4-24-422-244-22-4-4000-4-24-422-244-42-2-2200000000-22000000002-200000000000000000000000000000
χ5544-4-2-4422-2442-244000-4-2-4422-2-44-4-222-2000000002-2000000002-200000000000000000000000000000
χ5644-4-2-4422-2442-2-4-4000-4-2-4422-24-442-2-22000000002-200000000-2200000000000000000000000000000
χ574-4040000-44-4004-4000040000-4000400-4000000000000002i−2i2i−2i002i−2i2i−2i2i−2i2i−2i000000000000000000000
χ584-4040000-44-4004-4000040000-4000400-400000000000000−2i2i−2i2i00−2i2i−2i2i−2i2i−2i2i000000000000000000000
χ594-4040000-44-400-44000040000-4000-4004000000000000002-2-22002-22-2-22-22000000000000000000000
χ604-4040000-44-400-44000040000-4000-400400000000000000-222-200-22-222-22-2000000000000000000000
χ614-40-200−2i32i324-4004-40000-200−2i32i32000-2−2i32i32000000000000002i−2i2i−2i00−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43000000000000000000000
χ624-40-200−2i32i324-4004-40000-200−2i32i32000-2−2i32i3200000000000000−2i2i−2i2i002ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ592ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ432ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ592ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ43000000000000000000000
χ634-40-200−2i32i324-400-440000-200−2i32i3200022i3−2i3-2000000000000002-2-2200−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i3000000000000000000000
χ644-40-200−2i32i324-400-440000-200−2i32i3200022i3−2i3-200000000000000-222-2001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i3000000000000000000000
χ654-40-2002i3−2i324-4004-40000-2002i3−2i32000-22i3−2i32000000000000002i−2i2i−2i00−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59000000000000000000000
χ664-40-2002i3−2i324-4004-40000-2002i3−2i32000-22i3−2i3200000000000000−2i2i−2i2i002ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ432ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ592ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ432ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ59000000000000000000000
χ674-40-2002i3−2i324-400-440000-2002i3−2i320002−2i32i3-2000000000000002-2-2200−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i3000000000000000000000
χ684-40-2002i3−2i324-400-440000-2002i3−2i320002−2i32i3-200000000000000-222-2001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i3000000000000000000000
χ698888-8-8888-2-2-8-800000-2-222-2-2-200000000000000022000000000000000000000000000000000000000
χ70888-488-4-4-4-2-2-4-4008-4-4-21-2-2111000000000-2-2111111000000000000000000000000000000000000000
χ71888-488-4-4-4-2-2-4-400-844-21-2-211100000000022-1-1-1-111000000000000000000000000000000000000000
χ72888-4-8-8-4-4-4-2-244000−4i34i3-212211100000000000i3i3−i3−i3-1-1000000000000000000000000000000000000000
χ73888-4-8-8-4-4-4-2-2440004i3−4i3-212211100000000000−i3−i3i3i3-1-1000000000000000000000000000000000000000
χ7488-888-8-8-88-2-28-8000002-2-2222-2000000000000000-22000000000000000000000000000000000000000
χ7588-8-48-844-4-2-2-440000021-22-1-1100000000000−i15i15i15−i151-1000000000000000000000000000000000000000
χ7688-8-48-844-4-2-2-440000021-22-1-1100000000000i15−i15−i15i151-1000000000000000000000000000000000000000
χ7788-8-4-8844-4-2-24-400000212-2-1-11000000000−25255−55−5-11000000000000000000000000000000000000000
χ7888-8-4-8844-4-2-24-400000212-2-1-1100000000025−25−55−55-11000000000000000000000000000000000000000
χ7916-160160000-16-4400000000-40000400000000000000000000000000000000000000000000000000000000
χ8016-160-800−8i38i38-44000000002002i3−2i3-200000000000000000000000000000000000000000000000000000000
χ8116-160-8008i3−8i38-4400000000200−2i32i3-200000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.