Finite Group Databasebeta

← Group #13155650

Character table — Group #13155650

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212121212121818181824242424242424242424242424242424272727273636363636363636545472727272
order12223334466666666633366666666612121212121212121212888836661212121212121212444424242424242424242424242424242424888812121212121212121212121212121212444422442424242444661212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ51111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ911-1-1111-11-1-111-1-1-1-11111-1-1-1-1111-1-11-1111-1-1-1-11ii−i−i1-1-1111-1-111-1-1i−ii−iiiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−iii−i−iii−i−iii−i−iii−i−i1-11-111-1-1i−i1-11-1
χ1011-1-1111-11-1-111-1-1-1-11111-1-1-1-1111-1-11-1111-1-1-1-11ii−i−i1-1-1111-1-111-1-1i−i−iiiiiiiiii−i−i−i−i−i−i−i−i-1-111ii−i−i−i−iiiii−i−i−i−iii−i−iii1-1-11-1-111−ii1-1-11
χ1111-1-1111-11-1-111-1-1-1-11111-1-1-1-1111-1-11-1111-1-1-1-11ii−i−i1-1-1111-1-111-1-1−iii−iiiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iii-111-1-1-111−ii-111-1
χ1211-1-1111-11-1-111-1-1-1-11111-1-1-1-1111-1-11-1111-1-1-1-11ii−i−i1-1-1111-1-111-1-1−ii−iiiiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−iii−i−iii−i−iii−i−iiiii−i−i-11-1111-1-1i−i-11-11
χ1311-1-1111-11-1-111-1-1-1-11111-1-1-1-1111-1-11-1111-1-1-1-11−i−iii1-1-1111-1-111-1-1i−ii−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii-11-1111-1-1−ii-11-11
χ1411-1-1111-11-1-111-1-1-1-11111-1-1-1-1111-1-11-1111-1-1-1-11−i−iii1-1-1111-1-111-1-1i−i−ii−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i-111-1-1-111i−i-111-1
χ1511-1-1111-11-1-111-1-1-1-11111-1-1-1-1111-1-11-1111-1-1-1-11−i−iii1-1-1111-1-111-1-1−iii−i−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−iiiii−i−i−i−iiiii−i−iii−i−i1-1-11-1-111i−i1-1-11
χ1611-1-1111-11-1-111-1-1-1-11111-1-1-1-1111-1-11-1111-1-1-1-11−i−iii1-1-1111-1-111-1-1−ii−ii−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii−i−iii−i−iii−i−iii−i−iii1-11-111-1-1−ii1-11-1
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000222200000000-2-20000
χ182222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-200002222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000-2-2-2-200000000220000
χ19222222-1222-12-1222-122-1-12-1-1-12-1-12-1-122-1-1-12-1-122222-1-1-1-12-12-1-1-1-1-1220022-1-1-1-1-1-122-1-1-1-1-1-100002-12-10000-1-1-1-1000000002200000000-1-100
χ20222222-1222-12-1222-122-1-12-1-1-12-1-12-1-122-1-1-12-1-122222-1-1-1-12-12-1-1-1-1-1-2-20022-1-1-1-1-1-122-1-1-1-1-1-10000-21-210000111100000000-2-2000000001100
χ21222222-1222-12-1222-122-1-12-1-1-12-1-12-1-122-1-1-12-1-12-2-2-2-2-1-1-1-12-12-1-1-1-1-12200-2-2111111-2-211111100002-12-10000-1-1-1-100000000-2-2000000001100
χ22222222-1222-12-1222-122-1-12-1-1-12-1-12-1-122-1-1-12-1-12-2-2-2-2-1-1-1-12-12-1-1-1-1-1-2-200-2-2111111-2-21111110000-21-2100001111000000002200000000-1-100
χ2322222-122222-122-1-122-12-1-122-1-12-1-1-12-12222222-10000-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000002222-12-122-12-1-1-1-1-1-1-1-1-100000000-1-1-1-1000000
χ2422222-122222-122-1-122-12-1-122-1-12-1-1-12-12222222-10000-1-1-1-1-1-1-1-1-1-1-1-122-2-20000000000000000-2-2-2-2-12-12-21-21-1-1-1-11111000000001111000000
χ2522222-122222-122-1-122-12-1-122-1-12-1-1-12-12222222-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000000000000000-2-2-2-21-21-22-12-11111-1-1-1-1000000001111000000
χ2622222-122222-122-1-122-12-1-122-1-12-1-1-12-12222222-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000022221-21-2-21-211111111100000000-1-1-1-1000000
χ272222-12222-1222-1222-1-1-12-1-1-12-1-12-1222-1-1-12-1-1-122222-1-1-1-1-12-12-1-1-1-10022-1-122-1-1-1-1-1-122-1-1-1-100000000-12-120000-1-1-1-10000002200000000-1-1
χ282222-12222-1222-1222-1-1-12-1-1-12-1-12-1222-1-1-12-1-1-122222-1-1-1-1-12-12-1-1-1-100-2-2-1-122-1-1-1-1-1-122-1-1-1-1000000001-21-200001111000000-2-20000000011
χ292222-12222-1222-1222-1-1-12-1-1-12-1-12-1222-1-1-12-1-1-12-2-2-2-2-1-1-1-1-12-12-1-1-1-1002211-2-2111111-2-2111100000000-12-120000-1-1-1-1000000-2-20000000011
χ302222-12222-1222-1222-1-1-12-1-1-12-1-12-1222-1-1-12-1-1-12-2-2-2-2-1-1-1-1-12-12-1-1-1-100-2-211-2-2111111-2-21111000000001-21-2000011110000002200000000-1-1
χ3122-2-22222-2-2-222-2-2-2-22222-2-2-2-2222-2-2-22-2-2-22222-200002-2-22-2-222-2-22200000000000000000000000000000000000000002i2i−2i−2i00000000−2i2i0000
χ3222-2-22222-2-2-222-2-2-2-22222-2-2-2-2222-2-2-22-2-2-22222-200002-2-22-2-222-2-2220000000000000000000000000000000000000000−2i−2i2i2i000000002i−2i0000
χ3322-2-222-1-22-212-1-2-2-2122-1-1-21112-1-1-21-1-22-1-11-21122i2i−2i−2i-111-12-1-21-1-1112i−2i002i2i−i−i−i−i−i−i−2i−2iiiiiii00002i−i−2ii0000−i−iii000000002-200000000-1100
χ3422-2-222-1-22-212-1-2-2-2122-1-1-21112-1-1-21-1-22-1-11-21122i2i−2i−2i-111-12-1-21-1-111−2i2i002i2i−i−i−i−i−i−i−2i−2iiiiiii0000−2ii2i−i0000ii−i−i00000000-22000000001-100
χ3522-2-222-1-22-212-1-2-2-2122-1-1-21112-1-1-21-1-22-1-11-2112−2i−2i2i2i-111-12-1-21-1-1112i−2i00−2i−2iiiiiii2i2i−i−i−i−i−i−i00002i−i−2ii0000−i−iii00000000-22000000001-100
χ3622-2-222-1-22-212-1-2-2-2122-1-1-21112-1-1-21-1-22-1-11-2112−2i−2i2i2i-111-12-1-21-1-111−2i2i00−2i−2iiiiiii2i2i−i−i−i−i−i−i0000−2ii2i−i0000ii−i−i000000002-200000000-1100
χ3722-2-22-12-22-2-2-12-211-22-12-11-2-21-12-11121222-2-2-2-2-10000-111-1-1-111-1-1112i−2i2i−2i000000000000000022-2-2−i2ii−2i2i−i−2ii−i−iii−i−iii00000000-1-111000000
χ3822-2-22-12-22-2-2-12-211-22-12-11-2-21-12-11121222-2-2-2-2-10000-111-1-1-111-1-1112i−2i−2i2i0000000000000000-2-222−i2ii−2i−2ii2i−i−i−iiiii−i−i0000000011-1-1000000
χ3922-2-22-12-22-2-2-12-211-22-12-11-2-21-12-11121222-2-2-2-2-10000-111-1-1-111-1-111−2i2i2i−2i0000000000000000-2-222i−2i−i2i2i−i−2iiii−i−i−i−iii0000000011-1-1000000
χ4022-2-22-12-22-2-2-12-211-22-12-11-2-21-12-11121222-2-2-2-2-10000-111-1-1-111-1-111−2i2i−2i2i000000000000000022-2-2i−2i−i2i−2ii2i−iii−i−iii−i−i00000000-1-111000000
χ4122-2-2-122-221-2221-2-2-2-1-1-12111-2-1-121-22-2-1-1-1-211122i2i−2i−2i-111-1-121-2-1-111002i−2i−i−i2i2i−i−i−i−iii−2i−2iiiii00000000−i2ii−2i0000−i−iii0000002-200000000-11
χ4222-2-2-122-221-2221-2-2-2-1-1-12111-2-1-121-22-2-1-1-1-211122i2i−2i−2i-111-1-121-2-1-11100−2i2i−i−i2i2i−i−i−i−iii−2i−2iiiii00000000i−2i−i2i0000ii−i−i000000-22000000001-1
χ4322-2-2-122-221-2221-2-2-2-1-1-12111-2-1-121-22-2-1-1-1-21112−2i−2i2i2i-111-1-121-2-1-111002i−2iii−2i−2iiiii−i−i2i2i−i−i−i−i00000000−i2ii−2i0000−i−iii000000-22000000001-1
χ4422-2-2-122-221-2221-2-2-2-1-1-12111-2-1-121-22-2-1-1-1-21112−2i−2i2i2i-111-1-121-2-1-11100−2i2iii−2i−2iiiii−i−i2i2i−i−i−i−i00000000i−2i−i2i0000ii−i−i0000002-200000000-11
χ452-22-2222002-2-2-2-22-22-222222-2-2-2-2-2-2200000000002−22−222-2-20000000000002−22−222−2−22−22−222−2−2i2−i2i2−i200000000000000002i−2i2i−2i0000i2−i2i2−i2000000
χ462-22-2222002-2-2-2-22-22-222222-2-2-2-2-2-2200000000002−22−222-2-20000000000002−22−222−2−22−22−222−2−2−i2i2−i2i20000000000000000−2i2i−2i2i0000−i2i2−i2i2000000
χ472-22-2222002-2-2-2-22-22-222222-2-2-2-2-2-220000000000−22−2222-2-2000000000000−22−22−2−222−22−22−2−222i2−i2i2−i20000000000000000−2i2i−2i2i0000i2−i2i2−i2000000
χ482-22-2222002-2-2-2-22-22-222222-2-2-2-2-2-220000000000−22−2222-2-2000000000000−22−22−2−222−22−22−2−222−i2i2−i2i200000000000000002i−2i2i−2i0000−i2i2−i2i2000000
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χ884-44-4-24400-2-4-4-424-442-2-24-2-22-422-4240000000000−2222−2222-2-2220000000000002−2−222222−2−22−2−222222−2−200000000000000000000000000000000000000
χ894-44-4-24-200-22-4224-4-22-21-2-21-122-122-20003i−3i003i−3i022−2222−2211-1-100003i−3i3i−3i0000−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ3−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ300000000000000000000000000000000000000
χ904-44-4-24-200-22-4224-4-22-21-2-21-122-122-20003i−3i003i−3i0−2222−222211-1-100003i−3i3i−3i00002−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ32−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ300000000000000000000000000000000000000
χ914-44-4-24-200-22-4224-4-22-21-2-21-122-122-2000−3i3i00−3i3i022−2222−2211-1-10000−3i3i−3i3i0000−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ3−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ300000000000000000000000000000000000000
χ924-44-4-24-200-22-4224-4-22-21-2-21-122-122-2000−3i3i00−3i3i0−2222−222211-1-10000−3i3i−3i3i00002−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ32−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ300000000000000000000000000000000000000
χ934-4-4444-200-4-2-424-442-44-2-2-42-2-2-4224200000000002i2−2i2−2i22i2-22-220000000000002i2−2i2−i2i2−i2−i2i2i2−2i22i2i2−i2i2i2−i2−i200000000000000000000000000000000000000
χ944-4-4444-200-4-2-424-442-44-2-2-42-2-2-422420000000000−2i22i22i2−2i2-22-22000000000000−2i22i2i2−i2i2i2−i2−i22i2−2i2−i2i2−i2−i2i2i200000000000000000000000000000000000000
χ954-4-444-2400-442-442-2-4-4-24-22-44-22-42-2200000000000000-22-2200000000000000000000000000002i2−2i2−2i22i2000000000000000000000000−i2i2i2−i2000000
χ964-4-444-2400-442-442-2-4-4-24-22-44-22-42-2200000000000000-22-220000000000000000000000000000−2i22i22i2−2i2000000000000000000000000i2−i2−i2i2000000
χ974-4-44-2440024-4-4-2-44-42-2-2422-2422-4-2-400000000002i2−2i2−2i22i2-22-22000000000000−i2i22i2−2i2−i2−i2i2i2i2−i2−2i22i2i2i2−i2−i200000000000000000000000000000000000000
χ984-4-44-2440024-4-4-2-44-42-2-2422-2422-4-2-40000000000−2i22i22i2−2i2-22-22000000000000i2−i2−2i22i2i2i2−i2−i2−i2i22i2−2i2−i2−i2i2i200000000000000000000000000000000000000
χ994-4-44-24-2002-2-42-2-4422-21-22-11-22-12-220003i−3i00−3i3i02i2−2i2−2i22i21-11-100003i−3i−3i3i0000−i2i2−i2i2−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ3i2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ300000000000000000000000000000000000000
χ1004-4-44-24-2002-2-42-2-4422-21-22-11-22-12-220003i−3i00−3i3i0−2i22i22i2−2i21-11-100003i−3i−3i3i0000i2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ3−i2i2−i2i2−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ300000000000000000000000000000000000000
χ1014-4-44-24-2002-2-42-2-4422-21-22-11-22-12-22000−3i3i003i−3i02i2−2i2−2i22i21-11-10000−3i3i3i−3i0000−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ3i2−i2i2−i2−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ300000000000000000000000000000000000000
χ1024-4-44-24-2002-2-42-2-4422-21-22-11-22-12-22000−3i3i003i−3i0−2i22i22i2−2i21-11-10000−3i3i3i−3i0000i2−i2i2−i2−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ3−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ300000000000000000000000000000000000000
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χ1048888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-240000-1-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-48-844-4-44444-4222-2-2-2-2222-2-24-44-2-2-4-42240000-111-1-2-22211-1-10000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-8844-4-44444-4222-2-2-2-2222-2-2-44-42244-2-2-40000-111-122-2-2-1-1110000000000000000000000000000000000000000000000000000000000
χ1078-88-88-4-4008444-8-44-4-8-4-42-4-44-244-2420000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4800-4-84-84-44842-4-42-444-244-2-40000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-400-44444-44-4422222-2-2-2-2-2-220006i−6i006i−6i00000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-400-44444-44-4422222-2-2-2-2-2-22000−6i6i00−6i6i00000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-400-8-44484-44-8-4-4244-4244-2-4-2000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-4800484-8-44-4-842-4-4-24-4-4-24424000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4004-444-44-444222-2-222-2-2-22-20006i−6i00−6i6i00000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4004-444-44-444222-2-222-2-2-22-2000−6i6i006i−6i00000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.