Finite Group Databasebeta

← Group #14297262

Character table — Group #14297262

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222224444445588888888888881010101010101012121212161616161616202020202020202020202020202020202424242424242424404040404040404060606060120120120120
order1223446664451012122210121215202020202020303030244666622446060606060604444441212121212121212121210101010202020204412121212121222448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111-1-11111111111111-1-1-1-1-1-1-11111111111-1-1ii−i−i-1-1iiii−i−i−i−i11111111i−i-1-1ii−i−i-1-1-1-1ii−i−i
χ6111111111111111-1-11111111111111-1-1-1-1-1-1-11111111111-1-1−i−iii-1-1−i−i−i−iiiii11111111−ii-1-1−i−iii-1-1-1-1−i−iii
χ7111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1i−i-1-1ii−i−i1111−i−iii
χ8111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iii-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1−ii-1-1−i−iii1111ii−i−i
χ9111111111-1-11111111-1-1111-1-1-1-111111111111-11-111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-11-11-11-11-1
χ10111111111-1-11111111-1-1111-1-1-1-111111111111-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-111111-11-1-11-11
χ11111111111-1-11111111-1-1111-1-1-1-11111111111-11-1111-1-1-1-1-1-111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-11-11-11-11
χ12111111111-1-11111111-1-1111-1-1-1-11111111111-11-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-11-111-11-1
χ13111111111-1-11111-1-11-1-1111-1-1-1-1111-1-1-1-1-1-1-11-11-111-1-1-1-111ii−i−i-1-1iiii−i−i−i−i11-1-111-1-1−ii11−i−iii-11-11i−i−ii
χ14111111111-1-11111-1-11-1-1111-1-1-1-1111-1-1-1-1-1-1-11-11-111-1-1-1-111−i−iii-1-1−i−i−i−iiiii11-1-111-1-1i−i11ii−i−i-11-11−iii−i
χ15111111111-1-11111-1-11-1-1111-1-1-1-1111-1-1-1-1-1-1-1-11-1111-1-1-1-111ii−i−i-1-1iiii−i−i−i−i-1-111-1-111−ii11−i−iii1-11-1−iii−i
χ16111111111-1-11111-1-11-1-1111-1-1-1-1111-1-1-1-1-1-1-1-11-1111-1-1-1-111−i−iii-1-1−i−i−i−iiiii-1-111-1-111i−i11ii−i−i1-11-1i−i−ii
χ172222-2-22222-222-2-22222-22-2-222-2-22222-2-222220000-2-222-2-22-20000-2-20000000000000000002-2000000000000
χ182222-2-22222-222-2-2-2-222-22-2-222-2-2222-222-2-2-2-20000-2-222-2-2-22000022000000000000000000-22000000000000
χ192222-2-2222-2222-2-2222-222-2-2-2-2222222-2-222220000-2-2-2-222-220000-2-2000000000000000000-22000000000000
χ202222-2-2222-2222-2-2-2-22-222-2-2-2-222222-222-2-2-2-20000-2-2-2-2222-20000220000000000000000002-2000000000000
χ21222-122-1-1-12222-1-1222-1-1-1222222-1-1-1222-1-1-1-10000-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-100000000
χ22222-122-1-1-12222-1-1222-1-1-1222222-1-1-1222-1-1-1-10000-1-1-1-1-1-122-2-2-2-2-1-11111111100000000-2-2-1-1111100000000
χ23222-122-1-1-12222-1-1-2-22-1-1-1222222-1-1-1-2-2-211110000-1-1-1-1-1-1-2-22i2i−2i−2i11−i−i−i−iiiii000000002i−2i11−i−iii00000000
χ24222-122-1-1-12222-1-1-2-22-1-1-1222222-1-1-1-2-2-211110000-1-1-1-1-1-1-2-2−2i−2i2i2i11iiii−i−i−i−i00000000−2i2i11ii−i−i00000000
χ25222-122-1-1-1-2-222-1-122211-122-2-2-2-2-1-1-1222-1-1-1-10000-1-11111-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-211111100000000
χ26222-122-1-1-1-2-222-1-122211-122-2-2-2-2-1-1-1222-1-1-1-10000-1-11111-2-2-2-2-2-2-1-111111111000000002211-1-1-1-100000000
χ27222-122-1-1-1-2-222-1-1-2-2211-122-2-2-2-2-1-1-1-2-2-211110000-1-11111222i2i−2i−2i11−i−i−i−iiiii00000000−2i2i-1-1ii−i−i00000000
χ28222-122-1-1-1-2-222-1-1-2-2211-122-2-2-2-2-1-1-1-2-2-211110000-1-1111122−2i−2i2i2i11iiii−i−i−i−i000000002i−2i-1-1−i−iii00000000
χ29222-1-2-2-1-1-12-22211222-11-1-2-222-2-2-1-1-12-2-2-1-1-1-1000011-1-1112-2000011−i3−i3i3i3−i3−i3i3i30000000000-11−i3i3−i3i300000000
χ30222-1-2-2-1-1-12-22211222-11-1-2-222-2-2-1-1-12-2-2-1-1-1-1000011-1-1112-2000011i3i3−i3−i3i3i3−i3−i30000000000-11i3−i3i3−i300000000
χ31222-1-2-2-1-1-12-22211-2-22-11-1-2-222-2-2-1-1-1-2221111000011-1-111-220000-1-133−3−3−3−33300000000001-13−3−3300000000
χ32222-1-2-2-1-1-12-22211-2-22-11-1-2-222-2-2-1-1-1-2221111000011-1-111-220000-1-1−3−33333−3−300000000001-1−333−300000000
χ33222-1-2-2-1-1-1-2222112221-1-1-2-2-2-222-1-1-12-2-2-1-1-1-100001111-1-1-22000011−i3−i3i3i3−i3−i3i3i300000000001-1i3−i3i3−i300000000
χ34222-1-2-2-1-1-1-2222112221-1-1-2-2-2-222-1-1-12-2-2-1-1-1-100001111-1-1-22000011i3i3−i3−i3i3i3−i3−i300000000001-1−i3i3−i3i300000000
χ35222-1-2-2-1-1-1-222211-2-221-1-1-2-2-2-222-1-1-1-222111100001111-1-12-20000-1-133−3−3−3−3330000000000-11−333−300000000
χ36222-1-2-2-1-1-1-222211-2-221-1-1-2-2-2-222-1-1-1-222111100001111-1-12-20000-1-1−3−33333−3−30000000000-113−3−3300000000
χ3722-222-2-2-2200222-222-20022-20000-2-22-22-22-2-22020-22-200000000002-200000000002200-2-200000000020-20000
χ3822-222-2-2-2200222-222-20022-20000-2-22-22-22-2-220-2022-200000000002-20000000000-2-20022000000000-2020000
χ3922-222-2-2-2200222-2-2-2-20022-20000-2-222-22-222-2020-22-20000000000-2200000000002200-2-2000000000-2020000
χ4022-222-2-2-2200222-2-2-2-20022-20000-2-222-22-222-20-2022-20000000000-220000000000-2-2002200000000020-20000
χ4122-22-22-2-220022-2222-2002-220000-2-22-2-222-2-2220-20-220000000000-22000000002200-2-2000000000020-200000
χ4222-22-22-2-220022-2222-2002-220000-2-22-2-222-2-22-2020-220000000000-2200000000-2-200220000000000-20200000
χ4322-22-22-2-220022-22-2-2-2002-220000-2-2222-2-222-220-20-2200000000002-2000000002200-2-20000000000-20200000
χ4422-22-22-2-220022-22-2-2-2002-220000-2-2222-2-222-2-2020-2200000000002-200000000-2-20022000000000020-200000
χ4544444444444-1-14400-144-1-1-1-1-1-1-1-1-1-100000004444-1-1-1-1-1-10000000000000000-1-1-1-1-1-1-1-10000000000000000
χ4644444444444-1-14400-144-1-1-1-1-1-1-1-1-1-10000000-4-4-4-4-1-1-1-1-1-10000000000000000111111110000000000000000
χ47444444444-4-4-1-14400-1-4-4-1-1-11111-1-1-100000004-44-4-1-111110000000000000000-1-111-1-1110000000000000000
χ48444444444-4-4-1-14400-1-4-4-1-1-11111-1-1-10000000-44-44-1-11111000000000000000011-1-111-1-10000000000000000
χ494444-4-44444-4-1-1-4-400-14-4-111-1-111-1-1-10000000000011-1-1110000000000000000−55−55−55−550000000000000000
χ504444-4-44444-4-1-1-4-400-14-4-111-1-111-1-1-10000000000011-1-11100000000000000005−55−55−55−50000000000000000
χ514444-4-4444-44-1-1-4-400-1-44-11111-1-1-1-1-1000000000001111-1-10000000000000000−555−5−555−50000000000000000
χ524444-4-4444-44-1-1-4-400-1-44-11111-1-1-1-1-1000000000001111-1-100000000000000005−5−555−5−550000000000000000
χ5344-444-4-4-4400-1-14-400100-1-11−55−5511-10000000040-4-11−55−550000000000000000−55-1-15−5110000000000000000
χ5444-444-4-4-4400-1-14-400100-1-11−55−5511-100000000-404-11−55−5500000000000000005−511−55-1-10000000000000000
χ5544-444-4-4-4400-1-14-400100-1-115−55−511-10000000040-4-115−55−500000000000000005−5-1-1−55110000000000000000
χ5644-444-4-4-4400-1-14-400100-1-115−55−511-100000000-404-115−55−50000000000000000−55115−5-1-10000000000000000
χ5744-44-44-4-4400-1-1-4400100-11-1−555−511-1000000040-401-1−555−50000000000000000-1-1−55115−50000000000000000
χ5844-44-44-4-4400-1-1-4400100-11-1−555−511-10000000-40401-1−555−50000000000000000115−5-1-1−550000000000000000
χ5944-44-44-4-4400-1-1-4400100-11-15−5−5511-1000000040-401-15−5−550000000000000000-1-15−511−550000000000000000
χ6044-44-44-4-4400-1-1-4400100-11-15−5−5511-10000000-40401-15−5−55000000000000000011−55-1-15−50000000000000000
χ6144-4-24-422-20044-2244-400-24-4000022-2-44-4-222-20000-220000000000-2200000000000000000000000000000000
χ6244-4-24-422-20044-22-4-4-400-24-4000022-24-442-2-220000-2200000000002-200000000000000000000000000000000
χ6344-4-2-4422-200442-244-400-2-44000022-2-4-44-222-200002-200000000002-200000000000000000000000000000000
χ6444-4-2-4422-200442-2-4-4-400-2-44000022-244-42-2-2200002-20000000000-2200000000000000000000000000000000
χ654-4040000-4004-4004-4000400000000-4000400-40000000000002-22-2002-22-22-22-2000000000000000000000000
χ664-4040000-4004-4004-4000400000000-4000400-4000000000000-22-2200-22-22-22-22000000000000000000000000
χ674-4040000-4004-400-44000400000000-4000-40040000000000002i−2i−2i2i002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ684-4040000-4004-400-44000400000000-4000-4004000000000000−2i2i2i−2i00−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ694-40-200−2i32i32004-4004-4000-2000000−2i32i32000-2−2i32i320000000000002-22-200−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i3000000000000000000000000
χ704-40-200−2i32i32004-4004-4000-2000000−2i32i32000-2−2i32i32000000000000-22-22001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i3000000000000000000000000
χ714-40-200−2i32i32004-400-44000-2000000−2i32i3200022i3−2i3-20000000000002i−2i−2i2i00−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ592ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ432ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ59000000000000000000000000
χ724-40-200−2i32i32004-400-44000-2000000−2i32i3200022i3−2i3-2000000000000−2i2i2i−2i002ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ432ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ59−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59000000000000000000000000
χ734-40-2002i3−2i32004-4004-4000-20000002i3−2i32000-22i3−2i320000000000002-22-200−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i3000000000000000000000000
χ744-40-2002i3−2i32004-4004-4000-20000002i3−2i32000-22i3−2i32000000000000-22-22001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i3000000000000000000000000
χ754-40-2002i3−2i32004-400-44000-20000002i3−2i320002−2i32i3-20000000000002i−2i−2i2i00−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ432ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ592ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ43000000000000000000000000
χ764-40-2002i3−2i32004-400-44000-20000002i3−2i320002−2i32i3-2000000000000−2i2i2i−2i002ζ11+2ζ23+2ζ47+2ζ59−2ζ11−2ζ23−2ζ47−2ζ592ζ7+2ζ19+2ζ31+2ζ43−2ζ7−2ζ19−2ζ31−2ζ43−2ζ11−2ζ23−2ζ47−2ζ592ζ11+2ζ23+2ζ47+2ζ59−2ζ7−2ζ19−2ζ31−2ζ432ζ7+2ζ19+2ζ31+2ζ43000000000000000000000000
χ77888-488-4-4-488-2-2-4-400-2-4-41-2-2-2-2-2-2111000000000001111110000000000000000000000000000000000000000
χ78888-488-4-4-4-8-8-2-2-4-400-2441-2-222221110000000000011-1-1-1-10000000000000000000000000000000000000000
χ79888-4-8-8-4-4-48-8-2-24400-2-44122-2-22211100000000000-1-111-1-10000000000000000000000000000000000000000
χ80888-4-8-8-4-4-4-88-2-24400-24-412222-2-211100000000000-1-1-1-1110000000000000000000000000000000000000000
χ8188-8-48-844-400-2-2-44002001-22−2525−2525-1-11000000000001-15−55−50000000000000000000000000000000000000000
χ8288-8-48-844-400-2-2-44002001-2225−2525−25-1-11000000000001-1−55−550000000000000000000000000000000000000000
χ8388-8-4-8844-400-2-24-40020012-2−252525−25-1-1100000000000-115−5−550000000000000000000000000000000000000000
χ8488-8-4-8844-400-2-24-40020012-225−25−2525-1-1100000000000-11−555−50000000000000000000000000000000000000000
χ8516-160160000-1600-440000000-4000000004000000000000000000000000000000000000000000000000000000000
χ8616-160-800−8i38i3800-44000000020000002i3−2i3-2000000000000000000000000000000000000000000000000000000000
χ8716-160-8008i3−8i3800-4400000002000000−2i32i3-2000000000000000000000000000000000000000000000000000000000

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