Finite Group Databasebeta

← Group #13155666

Character table — Group #13155666

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212121212121818181824242424242424242424242424242424272727273636363636363636545472727272
order1222333446666666663336666666661212121212121212121288883666121212121212121244442424242424242424242424242424242488881212121212121212121212121212121244444444242424244412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111
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
χ61111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-11111-1-1
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
χ91-11-1111-11-1-1-11-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-11ii−i−i1-1-1111-1-111-1-1i−ii−iiiiiiiii−i−i−i−i−i−i−i−i11-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−i1-11-111-1-1i−i1-11-1
χ101-11-1111-11-1-1-11-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-11ii−i−i1-1-1111-1-111-1-1i−i−iiiiiiiiii−i−i−i−i−i−i−i−i-1-111i−i−iii−i−iiii−i−i−i−iii−i−iii1-1-11-1-111−ii1-1-11
χ111-11-1111-11-1-1-11-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-11ii−i−i1-1-1111-1-111-1-1−iii−iiiiiiiii−i−i−i−i−i−i−i−i-1-111−iii−i−iii−i−i−iiiii−i−i−i−iii-111-1-1-111−ii-111-1
χ121-11-1111-11-1-1-11-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-11ii−i−i1-1-1111-1-111-1-1−ii−iiiiiiiiii−i−i−i−i−i−i−i−i11-1-1−ii−ii−ii−ii−i−iii−i−iiiii−i−i-11-1111-1-1i−i-11-11
χ131-11-1111-11-1-1-11-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-11−i−iii1-1-1111-1-111-1-1i−ii−i−i−i−i−i−i−i−i−iiiiiiiii11-1-1i−ii−ii−ii−iii−i−iii−i−i−i−iii-11-1111-1-1−ii-11-11
χ141-11-1111-11-1-1-11-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-11−i−iii1-1-1111-1-111-1-1i−i−ii−i−i−i−i−i−i−i−iiiiiiiii-1-111i−i−iii−i−iiii−i−i−i−iiiii−i−i-111-1-1-111i−i-111-1
χ151-11-1111-11-1-1-11-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-11−i−iii1-1-1111-1-111-1-1−iii−i−i−i−i−i−i−i−i−iiiiiiiii-1-111−iii−i−iii−i−i−iiiii−i−iii−i−i1-1-11-1-111i−i1-1-11
χ161-11-1111-11-1-1-11-1-1-111111-1-1-1-1111-1-1-11111-1-1-1-11−i−iii1-1-1111-1-111-1-1−ii−ii−i−i−i−i−i−i−i−iiiiiiiii11-1-1−ii−ii−ii−ii−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
χ19222222-12222-122-122-12-1-12-1-1-12-1-12-122-1-1-12-1-1-122222-1-1-1-12-12-1-1-1-1-1002222-1-1-1-1-1-122-1-1-1-1-1-1000000-1-100220000-1-1-1-10000002200000000-1-1
χ20222222-12222-122-122-12-1-12-1-1-12-1-12-122-1-1-12-1-1-122222-1-1-1-12-12-1-1-1-1-100-2-222-1-1-1-1-1-122-1-1-1-1-1-10000001100-2-200001111000000-2-20000000011
χ21222222-12222-122-122-12-1-12-1-1-12-1-12-122-1-1-12-1-1-12-2-2-2-2-1-1-1-12-12-1-1-1-1-10022-2-2111111-2-2111111000000-1-100220000-1-1-1-1000000-2-20000000011
χ22222222-12222-122-122-12-1-12-1-1-12-1-12-122-1-1-12-1-1-12-2-2-2-2-1-1-1-12-12-1-1-1-1-100-2-2-2-2111111-2-21111110000001100-2-2000011110000002200000000-1-1
χ2322222-12222-122-122-12-12-1-12-1-1-12-1-122-12-1-1-12-1-122222-1-1-1-1-12-12-1-1-1-12200-1-122-1-1-1-1-1-122-1-1-1-10000-1-1002200-1-1-1-1000000002200000000-1-100
χ2422222-12222-122-122-12-12-1-12-1-1-12-1-122-12-1-1-12-1-122222-1-1-1-1-12-12-1-1-1-1-2-200-1-122-1-1-1-1-1-122-1-1-1-100001100-2-200111100000000-2-2000000001100
χ2522222-12222-122-122-12-12-1-12-1-1-12-1-122-12-1-1-12-1-12-2-2-2-2-1-1-1-1-12-12-1-1-1-1220011-2-2111111-2-211110000-1-1002200-1-1-1-100000000-2-2000000001100
χ2622222-12222-122-122-12-12-1-12-1-1-12-1-122-12-1-1-12-1-12-2-2-2-2-1-1-1-1-12-12-1-1-1-1-2-20011-2-2111111-2-2111100001100-2-2001111000000002200000000-1-100
χ272222-12222-122-122-122-1-12-1-122-1-12-1-1-122222222-10000-1-1-1-1-1-1-1-1-1-1-1-12222000000000000000022222222-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1000000
χ282222-12222-122-122-122-1-12-1-122-1-12-1-1-122222222-10000-1-1-1-1-1-1-1-1-1-1-1-122-2-20000000000000000-2-2-2-222-2-2-1-111-1-1-1-11111000000001111000000
χ292222-12222-122-122-122-1-12-1-122-1-12-1-1-122222222-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000000000000000-2-2-2-2-2-22211-1-11111-1-1-1-1000000001111000000
χ302222-12222-122-122-122-1-12-1-122-1-12-1-1-122222222-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000000002222-2-2-2-211111111111100000000-1-1-1-1000000
χ3122-2-222200222-2-2-2-2-2-2222222-2-2-2-2-2-200000000002−22−222-2-20000000000002−22−222−2−22−22−222−2−22−22−200000000000000002-22-200002−22−2000000
χ3222-2-222200222-2-2-2-2-2-2222222-2-2-2-2-2-200000000002−22−222-2-20000000000002−22−222−2−22−22−222−2−2−22−220000000000000000-22-220000−22−22000000
χ3322-2-222200222-2-2-2-2-2-2222222-2-2-2-2-2-20000000000−22−2222-2-2000000000000−22−22−2−222−22−22−2−2222−22−20000000000000000-22-2200002−22−2000000
χ3422-2-222200222-2-2-2-2-2-2222222-2-2-2-2-2-20000000000−22−2222-2-2000000000000−22−22−2−222−22−22−2−222−22−2200000000000000002-22-20000−22−22000000
χ352-22-22222-2-2-2-22-2-2-222222-2-2-2-2222-2-22-2-2-2-22222-200002-2-22-2-222-2-22200000000000000000000000000000000000000002i2i−2i−2i00000000−2i2i0000
χ362-22-22222-2-2-2-22-2-2-222222-2-2-2-2222-2-22-2-2-2-22222-200002-2-22-2-222-2-2220000000000000000000000000000000000000000−2i−2i2i2i000000002i−2i0000
χ372-22-222-1-22-2-212-21-22-12-1-1-21112-1-1-21-22-1-1-1-211122i2i−2i−2i-111-12-1-21-1-111002i−2i2i2i−i−i−i−i−i−i−2i−2iiiiiii000000−ii002i−2i0000−i−iii0000002-200000000-11
χ382-22-222-1-22-2-212-21-22-12-1-1-21112-1-1-21-22-1-1-1-211122i2i−2i−2i-111-12-1-21-1-11100−2i2i2i2i−i−i−i−i−i−i−2i−2iiiiiii000000i−i00−2i2i0000ii−i−i000000-22000000001-1
χ392-22-222-1-22-2-212-21-22-12-1-1-21112-1-1-21-22-1-1-1-21112−2i−2i2i2i-111-12-1-21-1-111002i−2i−2i−2iiiiiii2i2i−i−i−i−i−i−i000000−ii002i−2i0000−i−iii000000-22000000001-1
χ402-22-222-1-22-2-212-21-22-12-1-1-21112-1-1-21-22-1-1-1-21112−2i−2i2i2i-111-12-1-21-1-11100−2i2i−2i−2iiiiiii2i2i−i−i−i−i−i−i000000i−i00−2i2i0000ii−i−i0000002-200000000-11
χ412-22-22-12-22-21-221-2-2-12-12-11-211-12-11-2-2-12-1-11-21122i2i−2i−2i-111-1-121-2-1-1112i−2i00−i−i2i2i−i−i−i−iii−2i−2iiiii0000−ii002i−2i00−i−iii000000002-200000000-1100
χ422-22-22-12-22-21-221-2-2-12-12-11-211-12-11-2-2-12-1-11-21122i2i−2i−2i-111-1-121-2-1-111−2i2i00−i−i2i2i−i−i−i−iii−2i−2iiiii0000i−i00−2i2i00ii−i−i00000000-22000000001-100
χ432-22-22-12-22-21-221-2-2-12-12-11-211-12-11-2-2-12-1-11-2112−2i−2i2i2i-111-1-121-2-1-1112i−2i00ii−2i−2iiiii−i−i2i2i−i−i−i−i0000−ii002i−2i00−i−iii00000000-22000000001-100
χ442-22-22-12-22-21-221-2-2-12-12-11-211-12-11-2-2-12-1-11-2112−2i−2i2i2i-111-1-121-2-1-111−2i2i00ii−2i−2iiiii−i−i2i2i−i−i−i−i0000i−i00−2i2i00ii−i−i000000002-200000000-1100
χ452-22-2-122-221-2-2-1-2-2122-1-1211-2-2-1-121112222-2-2-2-2-10000-111-1-1-111-1-1112i−2i2i−2i000000000000000022-2-22i−2i2i−2i−ii−ii−i−iii−i−iii00000000-1-111000000
χ462-22-2-122-221-2-2-1-2-2122-1-1211-2-2-1-121112222-2-2-2-2-10000-111-1-1-111-1-1112i−2i−2i2i0000000000000000-2-2222i−2i−2i2i−iii−i−i−iiiii−i−i0000000011-1-1000000
χ472-22-2-122-221-2-2-1-2-2122-1-1211-2-2-1-121112222-2-2-2-2-10000-111-1-1-111-1-111−2i2i2i−2i0000000000000000-2-222−2i2i2i−2ii−i−iiii−i−i−i−iii0000000011-1-1000000
χ482-22-2-122-221-2-2-1-2-2122-1-1211-2-2-1-121112222-2-2-2-2-10000-111-1-1-111-1-111−2i2i−2i2i000000000000000022-2-2−2i2i−2i2ii−ii−iii−i−iii−i−i00000000-1-111000000
χ492-2-2222200-2-2-2-2222-2-2222-2-2-22-2-2-2220000000000i2−i2−i2i22-22-2000000000000i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2−i2i2i22−2−2200000000000000002i−2i−2i2i00002−2−22000000
χ502-2-2222200-2-2-2-2222-2-2222-2-2-22-2-2-2220000000000i2−i2−i2i22-22-2000000000000i2−i2i2−i2i2i2−i2−i2−i2i2−i2i2−i2−i2i2i2−222−20000000000000000−2i2i2i−2i0000−222−2000000
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χ834-44-44-2-2-44-422422-4-2-2-2-2122-1-1-2-2122-4-2-21122-1-14−4i−4i4i4i1-1-11-2-22211-1-100002i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii00000000000000000000000000000000000000
χ844-44-4-2444-42-4-4-2-4-4244-2-2422-4-4-2-2422-2-4-4-4-4444420000-222-222-2-222-2-20000000000000000000000000000000000000000000000000000000000
χ854-44-4-24-24-42-42-2-4224-2-21-22-122-21-22-1-2-42224-2-2-2200001-1-112-1-21-1-1110000000000000000000000000000000000003i−3i−3i3i000000000000000000
χ864-44-4-24-24-42-42-2-4224-2-21-22-122-21-22-1-2-42224-2-2-2200001-1-112-1-21-1-111000000000000000000000000000000000000−3i3i3i−3i000000000000000000
χ874-44-4-24-2-442-42-2-4224-2-21-22-122-21-22-124-2-2-2-4222-200001-1-11-212-111-1-1004i−4i0000000000000000000000−2i2i00−2i2i0000ii−i−i000000000000000000
χ884-44-4-24-2-442-42-2-4224-2-21-22-122-21-22-124-2-2-2-4222-200001-1-11-212-111-1-100−4i4i00000000000000000000002i−2i002i−2i0000−i−iii000000000000000000
χ894-44-4-2-244-422-4-22-42-241-2-2-12221-2-2-12-22-422-24-2-2200001-1-11-121-2-1-111000000000000000000000000000000003i−3i−3i3i0000000000000000000000
χ904-44-4-2-244-422-4-22-42-241-2-2-12221-2-2-12-22-422-24-2-2200001-1-11-121-2-1-11100000000000000000000000000000000−3i3i3i−3i0000000000000000000000
χ914-44-4-2-24-4422-4-22-42-241-2-2-12221-2-2-122-24-2-22-422-200001-1-111-2-1211-1-14i−4i0000000000000000000000−2i2i00−2i2i00ii−i−i0000000000000000000000
χ924-44-4-2-24-4422-4-22-42-241-2-2-12221-2-2-122-24-2-22-422-200001-1-111-2-1211-1-1−4i4i00000000000000000000002i−2i002i−2i00−i−iii0000000000000000000000
χ934-4-4444-200-4-42-44-24-424-2-2-422-2-4224-200000000002i2−2i2−2i22i2-22-220000000000002i2−2i2−i2i2−i2−i2i2i2−2i22i2i2−i2i2i2−i2−i200000000000000000000000000000000000000
χ944-4-4444-200-4-42-44-24-424-2-2-422-2-4224-20000000000−2i22i22i2−2i2-22-22000000000000−2i22i2i2−i2i2i2−i2−i22i2−2i2−i2i2−i2−i2i2i200000000000000000000000000000000000000
χ954-4-444-2400-42-4-4-2442-4-24-22-42-22-42-2400000000002i2−2i2−2i22i2-22-22000000000000−i2i22i2−2i2−i2−i2i2i2i2−i2−2i22i2i2i2−i2−i200000000000000000000000000000000000000
χ964-4-444-2400-42-4-4-2442-4-24-22-42-22-42-240000000000−2i22i22i2−2i2-22-22000000000000i2−i2−2i22i2i2i2−i2−i2−i2i22i2−2i2−i2−i2i2i200000000000000000000000000000000000000
χ974-4-444-2-200-422-4-2-2422-2-2122-1122-1-2-20003i−3i00−3i3i02i2−2i2−2i22i21-11-100003i−3i−3i3i0000−i2i2−i2i2−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ3i2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ300000000000000000000000000000000000000
χ984-4-444-2-200-422-4-2-2422-2-2122-1122-1-2-20003i−3i00−3i3i0−2i22i22i2−2i21-11-100003i−3i−3i3i0000i2−i2i2−i2ζ−2ζ3−2ζ+ζ3−ζ+2ζ32ζ−ζ3−i2i2−i2i2−ζ+2ζ32ζ−ζ3ζ−2ζ3−2ζ+ζ300000000000000000000000000000000000000
χ994-4-444-2-200-422-4-2-2422-2-2122-1122-1-2-2000−3i3i003i−3i02i2−2i2−2i22i21-11-10000−3i3i3i−3i0000−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ3i2−i2i2−i2−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ300000000000000000000000000000000000000
χ1004-4-444-2-200-422-4-2-2422-2-2122-1122-1-2-2000−3i3i003i−3i0−2i22i22i2−2i21-11-10000−3i3i3i−3i0000i2−i2i2−i2−2ζ+ζ3ζ−2ζ32ζ−ζ3−ζ+2ζ3−i2i2−i2i22ζ−ζ3−ζ+2ζ3−2ζ+ζ3ζ−2ζ300000000000000000000000000000000000000
χ1014-4-44-244002-4-4244-2-4-4-2-2422-4422-4-2-200000000000000-22-22000000000000000000000000000022−22−2222000000000000000000000000−222−2000000
χ1024-4-44-244002-4-4244-2-4-4-2-2422-4422-4-2-200000000000000-22-220000000000000000000000000000−222222−220000000000000000000000002−2−22000000
χ1038888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-40000-1-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000000000000
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
χ10588-8-8-48-400-48-44-844-84-42-4-42-444-244-20000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4800-4-4844-844-82-4-42-4-44-244-240000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-400-4-4-4444444222222-2-2-2-2-2-20006i−6i006i−6i00000-1-1110000−3i3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ10888-8-8-4-4-400-4-4-4444444222222-2-2-2-2-2-2000−6i6i00−6i6i00000-1-11100003i−3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-48-8444-4444-4-4222-2-2-2-2222-2-2-444-2-2-4-42240000-111-1-2-22211-1-10000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-88444-4444-4-4222-2-2-2-2222-2-24-4-42244-2-2-40000-111-122-2-2-1-1110000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-4004-8448-4-4-84-42-44-24-44-24-42000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-480044-84-48-44-82-4-4-244-4-2442-4000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4004444-4-4-444222-2-2-22-2-2-2220006i−6i00−6i6i00000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4004444-4-4-444222-2-2-22-2-2-222000−6i6i006i−6i00000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000000000

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