Finite Group Databasebeta

← Group #14283906

Character table — Group #14283906

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122224444466668888888810101010151515151616161616161616162020202020202020202020202424242424404040404040404040484860606060606060606080120
order12223666451010104444412152020303030444422221220206060606060608888888812121212420202020424242424242424242020488888888124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111
χ31111111111111111111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-111111-1iiii−i−i−i−i11-1iiii−i−i−i−i-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-111111-1−i−i−i−iiiii11-1−i−i−i−iiiii-1-1
χ511111111111111111-1111111111111111-1-1-111-1-1-1-111-1-111-1-11111-11111-111-1-111-1-1-1-1111-1-111-1-1-1-1
χ611111111111111111-1111111111111111-1-1-111-1-1-1-1-1-111-1-1111111-11111-1-1-111-1-111-1-11-1-111-1-111-1-1
χ711111111111111111-11111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i−i−iii-1-1-1-1-111111ii−i−i−i−iii-1-1-1ii−i−i−i−iii11
χ811111111111111111-11111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iiiii−i−i-1-1-1-1-111111−i−iiiii−i−i-1-1-1−i−iiiii−i−i11
χ91111111111111-1-1-1-1111111111111-1-1-1-1111111111111111111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-11-1
χ101111111111111-1-1-1-1111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ111111111111111-1-1-1-111111111-1-1-1-11111111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-11−i−i−i−iiiii-11
χ121111111111111-1-1-1-111111111-1-1-1-11111111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-11iiii−i−i−i−i-11
χ131111111111111-1-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111111-1-1-1-1-111-1-111-1-111-1-1-111-1-111-11
χ141111111111111-1-1-1-1-111111111111-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-111-1-11111-111-1-111-1-1-11
χ151111111111111-1-1-1-1-11111111-1-1-1-11111-1-1-111-1-1-1-1ii−i−i−i−iii-1-1-1-11-1-1-1-11ii−i−i−i−iii111−i−iiiii−i−i1-1
χ161111111111111-1-1-1-1-11111111-1-1-1-11111-1-1-111-1-1-1-1−i−iiiii−i−i-1-1-1-11-1-1-1-11−i−iiiii−i−i111ii−i−i−i−iii1-1
χ1722222222-2222222-2-20-22-2-222222-2-22222000-2-2000000000000-2-2220-2-22200000000000-20000000000
χ1822222222-2222222-2-20-22-2-2222-2-222-2-2-2-2000-2-200000000000022-2-20-2-2220000000000020000000000
χ1922222222-22222-2-2220-22-2-222222-2-2-2-2-2-2000-2-2000000000000-2-222022-2-20000000000020000000000
χ2022222222-22222-2-2220-22-2-2222-2-2222222000-2-200000000000022-2-2022-2-200000000000-20000000000
χ212222-1-1-1-12222200002-1-122-1-1-122220000-122-1-1-1-1-1-122222222-1-1-1-1000002-1-1-1-1-1-1-1-100000000000-10
χ222222-1-1-1-12222200002-1-122-1-1-122220000-122-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-10000021111111100000000000-10
χ232222-1-1-1-12222200002-1-122-1-1-1-2-2-2-20000-122-1-1-1-1-1-12i2i2i2i−2i−2i−2i−2i111100000-2−i−i−i−iiiii0000000000010
χ242222-1-1-1-12222200002-1-122-1-1-1-2-2-2-20000-122-1-1-1-1-1-1−2i−2i−2i−2i2i2i2i2i111100000-2iiii−i−i−i−i0000000000010
χ252222-1-1-1-1222220000-2-1-122-1-1-1222200001-2-2-1-1111122-2-222-2-2-1-1-1-100000-2-1-111-1-1110000000000010
χ262222-1-1-1-1222220000-2-1-122-1-1-1222200001-2-2-1-11111-2-222-2-222-1-1-1-100000-211-1-111-1-10000000000010
χ272222-1-1-1-1222220000-2-1-122-1-1-1-2-2-2-200001-2-2-1-111112i2i−2i−2i−2i−2i2i2i1111000002−i−iiiii−i−i00000000000-10
χ282222-1-1-1-1222220000-2-1-122-1-1-1-2-2-2-200001-2-2-1-11111−2i−2i2i2i2i2i−2i−2i1111000002ii−i−i−i−iii00000000000-10
χ292-22-22-2-2202-2-22002i−2i002002-2-2002i−2i22-2-20000000001+i−1−i001−i−1+i002i−2i0002i−2i0001+i−1−i001−i−1+i000001−i−1+i001+i−1−i0000
χ302-22-22-2-2202-2-22002i−2i002002-2-2002i−2i22-2-2000000000−1−i1+i00−1+i1−i002i−2i0002i−2i000−1−i1+i00−1+i1−i00000−1+i1−i00−1−i1+i0000
χ312-22-22-2-2202-2-22002i−2i002002-2-200−2i2i-2-2220000000001−i−1+i001+i−1−i00−2i2i0002i−2i0001−i−1+i001+i−1−i00000−1−i1+i00−1+i1−i0000
χ322-22-22-2-2202-2-22002i−2i002002-2-200−2i2i-2-222000000000−1+i1−i00−1−i1+i00−2i2i0002i−2i000−1+i1−i00−1−i1+i000001+i−1−i001−i−1+i0000
χ332-22-22-2-2202-2-2200−2i2i002002-2-2002i−2i-2-2220000000001+i−1−i001−i−1+i002i−2i000−2i2i0001+i−1−i001−i−1+i00000−1+i1−i00−1−i1+i0000
χ342-22-22-2-2202-2-2200−2i2i002002-2-2002i−2i-2-222000000000−1−i1+i00−1+i1−i002i−2i000−2i2i000−1−i1+i00−1+i1−i000001−i−1+i001+i−1−i0000
χ352-22-22-2-2202-2-2200−2i2i002002-2-200−2i2i22-2-20000000001−i−1+i001+i−1−i00−2i2i000−2i2i0001−i−1+i001+i−1−i000001+i−1−i001−i−1+i0000
χ362-22-22-2-2202-2-2200−2i2i002002-2-200−2i2i22-2-2000000000−1+i1−i00−1−i1+i00−2i2i000−2i2i000−1+i1−i00−1−i1+i00000−1−i1+i00−1+i1−i0000
χ372-2-222-22-202-22-22i−2i0000200-2-222i−2i002-22-2000000000001+i−1−i001−i−1+i002i−2i0002i−2i0001+i−1−i001−i−1+i000001−i−1+i001+i−1−i00
χ382-2-222-22-202-22-22i−2i0000200-2-222i−2i002-22-200000000000−1−i1+i00−1+i1−i002i−2i0002i−2i000−1−i1+i00−1+i1−i00000−1+i1−i00−1−i1+i00
χ392-2-222-22-202-22-22i−2i0000200-2-22−2i2i00-22-22000000000001−i−1+i001+i−1−i00−2i2i0002i−2i0001−i−1+i001+i−1−i00000−1−i1+i00−1+i1−i00
χ402-2-222-22-202-22-22i−2i0000200-2-22−2i2i00-22-2200000000000−1+i1−i00−1−i1+i00−2i2i0002i−2i000−1+i1−i00−1−i1+i000001+i−1−i001−i−1+i00
χ412-2-222-22-202-22-2−2i2i0000200-2-222i−2i00-22-22000000000001+i−1−i001−i−1+i002i−2i000−2i2i0001+i−1−i001−i−1+i00000−1+i1−i00−1−i1+i00
χ422-2-222-22-202-22-2−2i2i0000200-2-222i−2i00-22-2200000000000−1−i1+i00−1+i1−i002i−2i000−2i2i000−1−i1+i00−1+i1−i000001−i−1+i001+i−1−i00
χ432-2-222-22-202-22-2−2i2i0000200-2-22−2i2i002-22-2000000000001−i−1+i001+i−1−i00−2i2i000−2i2i0001−i−1+i001+i−1−i000001+i−1−i001−i−1+i00
χ442-2-222-22-202-22-2−2i2i0000200-2-22−2i2i002-22-200000000000−1+i1−i00−1−i1+i00−2i2i000−2i2i000−1+i1−i00−1−i1+i00000−1−i1+i00−1+i1−i00
χ45444444444-1-1-1-1444444-1-1-1-1-1-1000000004-1-1-1-1-1-1-1-10000000000004-1-1-1-1000000000-1-100000000000
χ46444444444-1-1-1-14444-44-1-1-1-1-1-100000000-411-1-11111000000000000-4-1-1-1-10000000001100000000000
χ47444444444-1-1-1-1-4-4-4-444-1-1-1-1-1-1000000004-1-1-1-1-1-1-1-1000000000000-411110000000001100000000000
χ48444444444-1-1-1-1-4-4-4-4-44-1-1-1-1-1-100000000-411-1-1111100000000000041111000000000-1-100000000000
χ4944444444-4-1-1-1-144-4-40-4-111-1-1-1000000000−5511−5−555000000000000011-1-1000000000−5500000000000
χ5044444444-4-1-1-1-144-4-40-4-111-1-1-10000000005−51155−5−5000000000000011-1-10000000005−500000000000
χ5144444444-4-1-1-1-1-4-4440-4-111-1-1-1000000000−5511−5−5550000000000000-1-1110000000005−500000000000
χ5244444444-4-1-1-1-1-4-4440-4-111-1-1-10000000005−51155−5−50000000000000-1-111000000000−5500000000000
χ534444-2-2-2-2-44444000002-2-4-4-2-2-244-4-400000002200000000000022-2-2000000000000000000000000000
χ544444-2-2-2-2-44444000002-2-4-4-2-2-2-4-444000000022000000000000-2-222000000000000000000000000000
χ5544-4-444-4-4044-4-4000000400-44-400004-4-44000000000000000000000000000000000000000000000000
χ5644-4-444-4-4044-4-4000000400-44-40000-444-4000000000000000000000000000000000000000000000000
χ574-44-4-222-204-4-44000000-200-222004i−4i00000000000002+2i−2−2i002−2i−2+2i00−2i2i00000000−1−i1+i00−1+i1−i000000000000000
χ584-44-4-222-204-4-44000000-200-222004i−4i0000000000000−2−2i2+2i00−2+2i2−2i00−2i2i000000001+i−1−i001−i−1+i000000000000000
χ594-44-4-222-204-4-44000000-200-22200−4i4i00000000000002−2i−2+2i002+2i−2−2i002i−2i00000000−1+i1−i00−1−i1+i000000000000000
χ604-44-4-222-204-4-44000000-200-22200−4i4i0000000000000−2+2i2−2i00−2−2i2+2i002i−2i000000001−i−1+i001+i−1−i000000000000000
χ614-4-44-22-2204-44-4000000-20022-24i−4i000000000000000002+2i−2−2i002−2i−2+2i00−2i2i00000000−1−i1+i00−1+i1−i0000000000000
χ624-4-44-22-2204-44-4000000-20022-24i−4i00000000000000000−2−2i2+2i00−2+2i2−2i00−2i2i000000001+i−1−i001−i−1+i0000000000000
χ634-4-44-22-2204-44-4000000-20022-2−4i4i000000000000000002−2i−2+2i002+2i−2−2i002i−2i00000000−1+i1−i00−1−i1+i0000000000000
χ644-4-44-22-2204-44-4000000-20022-2−4i4i00000000000000000−2+2i2−2i00−2−2i2+2i002i−2i000000001−i−1+i001+i−1−i0000000000000
χ658888-4-4-4-48-2-2-2-200008-41-2-211100000000-4-2-2111111000000000000000000000000000000000000000
χ668888-4-4-4-48-2-2-2-20000-8-41-2-21110000000042211-1-1-1-1000000000000000000000000000000000000000
χ678888-4-4-4-4-8-2-2-2-2000004122111000000000−2525-1-155−5−5000000000000000000000000000000000000000
χ688888-4-4-4-4-8-2-2-2-200000412211100000000025−25-1-1−5−555000000000000000000000000000000000000000
χ6988-8-888-8-80-2-222000000-2−25252-2200000000000−25250000000000000000000000000000000000000000000
χ7088-8-888-8-80-2-222000000-225−252-220000000000025−250000000000000000000000000000000000000000000
χ7188-8-8-4-444088-8-8000000-4004-4400000000000000000000000000000000000000000000000000000000
χ7288-8-8-4-4440-2-2220000001−2525-11-1000000000005−5ζ7+ζ11+ζ19+ζ23−ζ31−ζ43−ζ47−ζ59−ζ7−ζ11−ζ19−ζ23+ζ31+ζ43+ζ47+ζ59−ζ7+ζ11+ζ19−ζ23−ζ31+ζ43+ζ47−ζ59ζ7−ζ11−ζ19+ζ23+ζ31−ζ43−ζ47+ζ59000000000000000000000000000000000000000
χ7388-8-8-4-4440-2-2220000001−2525-11-1000000000005−5−ζ7−ζ11−ζ19−ζ23+ζ31+ζ43+ζ47+ζ59ζ7+ζ11+ζ19+ζ23−ζ31−ζ43−ζ47−ζ59ζ7−ζ11−ζ19+ζ23+ζ31−ζ43−ζ47+ζ59−ζ7+ζ11+ζ19−ζ23−ζ31+ζ43+ζ47−ζ59000000000000000000000000000000000000000
χ7488-8-8-4-4440-2-222000000125−25-11-100000000000−55−ζ7+ζ11+ζ19−ζ23−ζ31+ζ43+ζ47−ζ59ζ7−ζ11−ζ19+ζ23+ζ31−ζ43−ζ47+ζ59−ζ7−ζ11−ζ19−ζ23+ζ31+ζ43+ζ47+ζ59ζ7+ζ11+ζ19+ζ23−ζ31−ζ43−ζ47−ζ59000000000000000000000000000000000000000
χ7588-8-8-4-4440-2-222000000125−25-11-100000000000−55ζ7−ζ11−ζ19+ζ23+ζ31−ζ43−ζ47+ζ59−ζ7+ζ11+ζ19−ζ23−ζ31+ζ43+ζ47−ζ59ζ7+ζ11+ζ19+ζ23−ζ31−ζ43−ζ47−ζ59−ζ7−ζ11−ζ19−ζ23+ζ31+ζ43+ζ47+ζ59000000000000000000000000000000000000000
χ768-88-88-8-880-222-2008i−8i00-200-222000000000000000000000000000000−2i2i000000000000000000000000
χ778-88-88-8-880-222-200−8i8i00-200-2220000000000000000000000000000002i−2i000000000000000000000000
χ788-8-888-88-80-22-228i−8i0000-20022-200000000000000000000000000000000−2i2i0000000000000000000000
χ798-8-888-88-80-22-22−8i8i0000-20022-2000000000000000000000000000000002i−2i0000000000000000000000
χ8016-1616-16-888-80-444-40000002002-2-200000000000000000000000000000000000000000000000000000000
χ8116-16-1616-88-880-44-44000000200-2-2200000000000000000000000000000000000000000000000000000000

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