Finite Group Databasebeta

← Group #14313775

Character table — Group #14313775

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1122244444444448888888810101010161616161616161620202020202024242424242440404040404040404040404040404848120120120120120120
order12236224566610101061215202030303044121210103030303060602441212124420202020688881224242424242424242020448888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1ii−i−i-1iiii−i−i−i−i11-1-1ii−i−i
χ611111111111111111111111-1-1-1-111111111-1-1-1-1-1-1111111-1−i−iii-1−i−i−i−iiiii11-1-1−i−iii
χ711111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1iiii−i−i−i−i-1-111−i−iii
χ811111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1−i−i−i−iiiii-1-111ii−i−i
χ911111-1-1111-1-1111-111111111111-1-1-1-1-1-1111-1-11-1-11-1-1-1-1-11i−ii−i-1ii−i−iii−i−i111-1i−ii−i
χ1011111-1-1111-1-1111-111111111111-1-1-1-1-1-1111-1-11-1-11-1-1-1-1-11−ii−ii-1−i−iii−i−iii111-1−ii−ii
χ1111111-1-1111-1-1111-111111111111-1-1-1-1-1-1111-1-11-1-1-1111111i−ii−i-1ii−i−iii−i−i-1-1-11−ii−ii
χ1211111-1-1111-1-1111-111111111111-1-1-1-1-1-1111-1-11-1-1-1111111−ii−ii-1−i−iii−i−iii-1-1-11i−ii−i
χ1311111-1-1111-1-1111-11111111-1-1-1-1-1-1-1-1-1-111-111-1111-1-1-1-1-1-11-1-11111-1-1-1-11111-111-1-11
χ1411111-1-1111-1-1111-11111111-1-1-1-1-1-1-1-1-1-111-111-1111-1-1-1-1-1-1-111-11-1-11111-1-111-11-111-1
χ1511111-1-1111-1-1111-11111111-1-1-1-1-1-1-1-1-1-111-111-111-111111-11-1-11111-1-1-1-111-1-11-1-111-1
χ1611111-1-1111-1-1111-11111111-1-1-1-1-1-1-1-1-1-111-111-111-111111-1-111-11-1-11111-1-1-1-11-11-1-11
χ17222222-2-22222222-2-22-2-222222222-222-2-2-2-2-22-2222000000-20000-20000000000000000
χ18222222-2-22222222-2-22-2-2222-2-2-2-22-222-2-2-2-22-22-2-2-20000002000020000000000000000
χ1922222-22-222-2-22222-22-2-22222222-22-2-222-2-2-2-222-2-2000000-2000020000000000000000
χ2022222-22-222-2-22222-22-2-2222-2-2-2-2-22-2-222-2-222-2-22200000020000-20000000000000000
χ21222-1-12222-1-1-1222-1-1-122-1-1-122-1-122-1-1-1-1-1-1222-1-1-1000000-12222-1-1-1-1-1-1-1-1-100000000
χ22222-1-12222-1-1-1222-1-1-122-1-1-122-1-122-1-1-1-1-1-1222-1-1-1000000-1-2-2-2-2-11111111100000000
χ23222-1-12222-1-1-1222-1-1-122-1-1-1-2-21122-1-1-1-1-1-1-2-2-211100000012i2i−2i−2i1−i−i−i−iiiii00000000
χ24222-1-12222-1-1-1222-1-1-122-1-1-1-2-21122-1-1-1-1-1-1-2-2-21110000001−2i−2i2i2i1iiii−i−i−i−i00000000
χ25222-1-12-2-22-1-1-122211-1-2-2-1-1-122-1-12-2-1-11111-22-2-1-1-1000000100001−i3i3−i3i3−i3i3−i3i300000000
χ26222-1-12-2-22-1-1-122211-1-2-2-1-1-122-1-12-2-1-11111-22-2-1-1-1000000100001i3−i3i3−i3i3−i3i3−i300000000
χ27222-1-12-2-22-1-1-122211-1-2-2-1-1-1-2-2112-2-1-111112-22111000000-10000-13−33−3−33−3300000000
χ28222-1-12-2-22-1-1-122211-1-2-2-1-1-1-2-2112-2-1-111112-22111000000-10000-1−33−333−33−300000000
χ29222-1-1-22-22-111222-11-1-2-2-1-1-122-1-1-2211-1-111-2-22-11100000010000-13−3−333−3−3300000000
χ30222-1-1-22-22-111222-11-1-2-2-1-1-122-1-1-2211-1-111-2-22-11100000010000-1−333−3−333−300000000
χ31222-1-1-22-22-111222-11-1-2-2-1-1-1-2-211-2211-1-11122-21-1-1000000-100001−i3i3i3−i3i3−i3−i3i300000000
χ32222-1-1-22-22-111222-11-1-2-2-1-1-1-2-211-2211-1-11122-21-1-1000000-100001i3−i3−i3i3−i3i3i3−i300000000
χ33222-1-1-2-222-1112221-1-122-1-1-122-1-1-2-21111-1-12-2-2-111000000-12i−2i2i−2i1−i−iii−i−iii00000000
χ34222-1-1-2-222-1112221-1-122-1-1-122-1-1-2-21111-1-12-2-2-111000000-1−2i2i−2i2i1ii−i−iii−i−i00000000
χ35222-1-1-2-222-1112221-1-122-1-1-1-2-211-2-21111-1-1-2221-1-100000012-2-22-1-1-11111-1-100000000
χ36222-1-1-2-222-1112221-1-122-1-1-1-2-211-2-21111-1-1-2221-1-10000001-222-2-111-1-1-1-11100000000
χ3744444444-1444-1-1-144-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000044-1-1-1-100000000000000-1-1000000
χ3844444444-1444-1-1-144-1-1-1-1-1-10000-1-1-1-1-1-1-1-1000000-4-411110000000000000011000000
χ39444444-4-4-1444-1-1-1-4-4-111-1-1-10000-11-1-1111100000000−5−55500000000000000−55000000
χ40444444-4-4-1444-1-1-1-4-4-111-1-1-10000-11-1-111110000000055−5−5000000000000005−5000000
χ4144444-44-4-14-4-4-1-1-14-4-111-1-1-100001-111-1-11100000000−5−555000000000000005−5000000
χ4244444-44-4-14-4-4-1-1-14-4-111-1-1-100001-111-1-1110000000055−5−500000000000000−55000000
χ4344444-4-44-14-4-4-1-1-1-44-1-1-1-1-1-10000111111-1-10000004-4111100000000000000-1-1000000
χ4444444-4-44-14-4-4-1-1-1-44-1-1-1-1-1-10000111111-1-1000000-44-1-1-1-10000000000000011000000
χ4544-4440004-400-4-4400400-4-444-44400000000000-4000000000000000000000000000000
χ4644-4440004-400-4-4400400-4-44-44-4-4000000000004000000000000000000000000000000
χ4744-4-2-200042−2i32i3-4-4400-20022-24-4-2-200−2i32i300000002−2i32i30000000000000000000000000000
χ4844-4-2-200042−2i32i3-4-4400-20022-2-442200−2i32i30000000-22i3−2i30000000000000000000000000000
χ4944-4-2-2000422i3−2i3-4-4400-20022-24-4-2-2002i3−2i3000000022i3−2i30000000000000000000000000000
χ5044-4-2-2000422i3−2i3-4-4400-20022-2-4422002i3−2i30000000-2−2i32i30000000000000000000000000000
χ51888-4-4888-2-4-4-4-2-2-2-4-41-2-21110000-2-21111110000000000000000000000000000000000
χ52888-4-48-8-8-2-4-4-4-2-2-2441221110000-2211-1-1-1-10000000000000000000000000000000000
χ53888-4-4-88-8-2-444-2-2-2-4412211100002-2-1-111-1-10000000000000000000000000000000000
χ54888-4-4-8-88-2-444-2-2-24-41-2-2111000022-1-1-1-1110000000000000000000000000000000000
χ5588-888000-2-80022-200-2−252522-20000000000−25250000000000000000000000000000000000
χ5688-888000-2-80022-200-225−2522-2000000000025−250000000000000000000000000000000000
χ5788-8-4-4000-24−4i34i322-2001−2525-1-11000000i3−i3−i15i155−50000000000000000000000000000000000
χ5888-8-4-4000-24−4i34i322-200125−25-1-11000000i3−i3i15−i15−550000000000000000000000000000000000
χ5988-8-4-4000-244i3−4i322-2001−2525-1-11000000−i3i3i15−i155−50000000000000000000000000000000000
χ6088-8-4-4000-244i3−4i322-200125−25-1-11000000−i3i3−i15i15−550000000000000000000000000000000000
χ618-808-8000800000-80080000-80000000000000000000000000000000000000000000000
χ628-808-8000-2000−2525200-200−2525200000000000000000000−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ592ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ470000000000000000000000
χ638-808-8000-2000−2525200-200−25252000000000000000000002ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ59−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ470000000000000000000000
χ648-808-8000-200025−25200-20025−252000000000000000000002ζ7−2ζ23−2ζ43+2ζ47−2ζ7+2ζ23+2ζ43−2ζ472ζ11−2ζ19+2ζ31−2ζ59−2ζ11+2ζ19−2ζ31+2ζ590000000000000000000000
χ658-808-8000-200025−25200-20025−25200000000000000000000−2ζ7+2ζ23+2ζ43−2ζ472ζ7−2ζ23−2ζ43+2ζ47−2ζ11+2ζ19−2ζ31+2ζ592ζ11−2ζ19+2ζ31−2ζ590000000000000000000000
χ668-80-44000800000-800-4000040043−43000000000000000000000000000000000000000000
χ678-80-44000800000-800-40000400−4343000000000000000000000000000000000000000000
χ6816-160-88000-4000−454540020025−25-20000000000000000000000000000000000000000000000
χ6916-160-88000-400045−45400200−2525-20000000000000000000000000000000000000000000000

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