Finite Group Databasebeta

← Group #13155472

Character table — Group #13155472

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444666688888888888812121212121212121212121212121212121212121818181824242424242424242424242424242424272727273636363636363636545472727272
order1222333446666666663336666666661212121212121212121288883666121212121212121244442424242424242424242424242424242488881212121212121212121212121212121222224444242424244412121212
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
χ91-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-1-1-1-11111111-1-11-1-1111-1-111-1-1i−ii−i11111111-1-1-1-1-1-1-1-111-1-1i−ii−ii−ii−iii−i−iii−i−i11-1-1i−ii−i11-1-11-1i−ii−i
χ101-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-1-1-1-11111111-1-11-1-1111-1-111-1-1i−i−ii11111111-1-1-1-1-1-1-1-1-1-111i−i−iii−i−iiii−i−i−i−iii-1-111i−i−ii-1-111-11i−i−ii
χ111-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-1-1-1-11111111-1-11-1-1111-1-111-1-1−iii−i11111111-1-1-1-1-1-1-1-1-1-111−iii−i−iii−i−i−iiiii−i−i-1-111−iii−i-1-111-11−iii−i
χ121-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-1-1-1-11111111-1-11-1-1111-1-111-1-1−ii−ii11111111-1-1-1-1-1-1-1-111-1-1−ii−ii−ii−ii−i−iii−i−iii11-1-1−ii−ii11-1-11-1−ii−ii
χ131-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-1-1-1-111111-1-1111-1-1111-1-111-1-1i−ii−i-1-1-1-1-1-1-1-11111111111-1-1i−ii−ii−ii−iii−i−iii−i−i-1-111−ii−ii11-1-1-11−ii−ii
χ141-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-1-1-1-111111-1-1111-1-1111-1-111-1-1i−i−ii-1-1-1-1-1-1-1-111111111-1-111i−i−iii−i−iiii−i−i−i−iii11-1-1−iii−i-1-1111-1−iii−i
χ151-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-1-1-1-111111-1-1111-1-1111-1-111-1-1−iii−i-1-1-1-1-1-1-1-111111111-1-111−iii−i−iii−i−i−iiiii−i−i11-1-1i−i−ii-1-1111-1i−i−ii
χ161-11-1111-11-1-1-1111-1-1-1111-1-1-1-1111-1-1-1-1-1-1-111111-1-1111-1-1111-1-111-1-1−ii−ii-1-1-1-1-1-1-1-11111111111-1-1−ii−ii−ii−ii−i−iii−i−iii-1-111i−ii−i11-1-1-11i−ii−i
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
χ19222222-12222-122-122-12-1-12-1-1-12-1-12-122-1-1-12-1-1-122222-1-1-1-12-12-1-1-1-1-1002222-1-1-1-1-1-122-1-1-1-1-1-10000002200-1-10000-1-1-1-10000002200000000-1-1
χ20222222-12222-122-122-12-1-12-1-1-12-1-12-122-1-1-12-1-1-122222-1-1-1-12-12-1-1-1-1-100-2-222-1-1-1-1-1-122-1-1-1-1-1-1000000-2-2001100001111000000-2-20000000011
χ21222222-12222-122-122-12-1-12-1-1-12-1-12-122-1-1-12-1-1-12-2-2-2-2-1-1-1-12-12-1-1-1-1-10022-2-2111111-2-21111110000002200-1-10000-1-1-1-1000000-2-20000000011
χ22222222-12222-122-122-12-1-12-1-1-12-1-12-122-1-1-12-1-1-12-2-2-2-2-1-1-1-12-12-1-1-1-1-100-2-2-2-2111111-2-2111111000000-2-20011000011110000002200000000-1-1
χ2322222-12222-122-122-12-12-1-12-1-1-12-1-122-12-1-1-12-1-122222-1-1-1-1-12-12-1-1-1-12200-1-122-1-1-1-1-1-122-1-1-1-100002200-1-100-1-1-1-1000000002200000000-1-100
χ2422222-12222-122-122-12-12-1-12-1-1-12-1-122-12-1-1-12-1-122222-1-1-1-1-12-12-1-1-1-1-2-200-1-122-1-1-1-1-1-122-1-1-1-10000-2-2001100111100000000-2-2000000001100
χ2522222-12222-122-122-12-12-1-12-1-1-12-1-122-12-1-1-12-1-12-2-2-2-2-1-1-1-1-12-12-1-1-1-1220011-2-2111111-2-2111100002200-1-100-1-1-1-100000000-2-2000000001100
χ2622222-12222-122-122-12-12-1-12-1-1-12-1-122-12-1-1-12-1-12-2-2-2-2-1-1-1-1-12-12-1-1-1-1-2-20011-2-2111111-2-211110000-2-20011001111000000002200000000-1-100
χ272222-12222-122-122-122-1-12-1-122-1-12-1-1-122222222-10000-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000002222-1-1-1-12222-1-1-1-1-1-1-1-100000000-1-1-1-1000000
χ282222-12222-122-122-122-1-12-1-122-1-12-1-1-122222222-10000-1-1-1-1-1-1-1-1-1-1-1-122-2-20000000000000000-2-2-2-2-1-11122-2-2-1-1-1-11111000000001111000000
χ292222-12222-122-122-122-1-12-1-122-1-12-1-1-122222222-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000000000000000-2-2-2-211-1-1-2-2221111-1-1-1-1000000001111000000
χ302222-12222-122-122-122-1-12-1-122-1-12-1-1-122222222-10000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000000000000022221111-2-2-2-21111111100000000-1-1-1-1000000
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
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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
χ352-22-22222-2-2-2-2222-2-2-2222-2-2-2-2222-2-222222-2-2-2-2-200002-2-22-2-222-2-222000000000000000000000000000000000000000022-2-200000000-220000
χ362-22-22222-2-2-2-2222-2-2-2222-2-2-2-2222-2-222222-2-2-2-2-200002-2-22-2-222-2-2220000000000000000000000000000000000000000-2-222000000002-20000
χ372-22-222-1-22-2-2122-1-2-212-1-1-21112-1-1-21-2-21112-1-1-1222-2-2-111-12-1-21-1-111002i−2i22-1-1-1-1-1-1-2-21111110000002i−2i00−ii0000−i−iii0000002i−2i00000000−ii
χ382-22-222-1-22-2-2122-1-2-212-1-1-21112-1-1-21-2-21112-1-1-1222-2-2-111-12-1-21-1-11100−2i2i22-1-1-1-1-1-1-2-2111111000000−2i2i00i−i0000ii−i−i000000−2i2i00000000i−i
χ392-22-222-1-22-2-2122-1-2-212-1-1-21112-1-1-21-2-21112-1-1-12-2-222-111-12-1-21-1-111002i−2i-2-211111122-1-1-1-1-1-10000002i−2i00−ii0000−i−iii000000−2i2i00000000i−i
χ402-22-222-1-22-2-2122-1-2-212-1-1-21112-1-1-21-2-21112-1-1-12-2-222-111-12-1-21-1-11100−2i2i-2-211111122-1-1-1-1-1-1000000−2i2i00i−i0000ii−i−i0000002i−2i00000000−ii
χ412-22-22-12-22-21-22-12-21-2-12-11-211-12-11-2-21-211-12-1-1222-2-2-111-1-121-2-1-1112i−2i00-1-122-1-1-1-111-2-2111100002i−2i00−ii00−i−iii000000002i−2i00000000−ii00
χ422-22-22-12-22-21-22-12-21-2-12-11-211-12-11-2-21-211-12-1-1222-2-2-111-1-121-2-1-111−2i2i00-1-122-1-1-1-111-2-211110000−2i2i00i−i00ii−i−i00000000−2i2i00000000i−i00
χ432-22-22-12-22-21-22-12-21-2-12-11-211-12-11-2-21-211-12-1-12-2-222-111-1-121-2-1-1112i−2i0011-2-21111-1-122-1-1-1-100002i−2i00−ii00−i−iii00000000−2i2i00000000i−i00
χ442-22-22-12-22-21-22-12-21-2-12-11-211-12-11-2-21-211-12-1-12-2-222-111-1-121-2-1-111−2i2i0011-2-21111-1-122-1-1-1-10000−2i2i00i−i00ii−i−i000000002i−2i00000000−ii00
χ452-22-2-122-221-2-2-1221-2-2-1-1211-2-2-1-12111-2-2-2-22222-10000-111-1-1-111-1-1112i−2i2i−2i000000000000000022-2-2−ii−ii2i−2i2i−2i−i−iii−i−iii00000000-1-111000000
χ462-22-2-122-221-2-2-1221-2-2-1-1211-2-2-1-12111-2-2-2-22222-10000-111-1-1-111-1-1112i−2i−2i2i0000000000000000-2-222−iii−i2i−2i−2i2i−i−iiiii−i−i0000000011-1-1000000
χ472-22-2-122-221-2-2-1221-2-2-1-1211-2-2-1-12111-2-2-2-22222-10000-111-1-1-111-1-111−2i2i2i−2i0000000000000000-2-222i−i−ii−2i2i2i−2iii−i−i−i−iii0000000011-1-1000000
χ482-22-2-122-221-2-2-1221-2-2-1-1211-2-2-1-12111-2-2-2-22222-10000-111-1-1-111-1-111−2i2i−2i2i000000000000000022-2-2i−ii−i−2i2i−2i2iii−i−iii−i−i00000000-1-111000000
χ492-2-2222200-2-2-2-2-2-2222222-2-2-22-2-2-22200000000002−2−222-22-20000000000002−22−222−2−2−22−22−2−2222−2−2200000000000000002-2-2200002−2−22000000
χ502-2-2222200-2-2-2-2-2-2222222-2-2-22-2-2-22200000000002−2−222-22-20000000000002−22−222−2−2−22−22−2−222−222−20000000000000000-222-20000−222−2000000
χ512-2-2222200-2-2-2-2-2-2222222-2-2-22-2-2-2220000000000−222−22-22-2000000000000−22−22−2−2222−22−222−2−22−2−220000000000000000-222-200002−2−22000000
χ522-2-2222200-2-2-2-2-2-2222222-2-2-22-2-2-2220000000000−222−22-22-2000000000000−22−22−2−2222−22−222−2−2−222−200000000000000002-2-220000−222−2000000
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χ854-44-4-24-24-42-42-24-22-42-21-22-122-21-22-1-24-2-2-2-4222200001-1-112-1-21-1-1110000000000000000000000000000000000003i−3i−3i3i000000000000000000
χ864-44-4-24-24-42-42-24-22-42-21-22-122-21-22-1-24-2-2-2-4222200001-1-112-1-21-1-111000000000000000000000000000000000000−3i3i3i−3i000000000000000000
χ874-44-4-24-2-442-42-24-22-42-21-22-122-21-22-12-42224-2-2-2-200001-1-11-212-111-1-1004i−4i0000000000000000000000−2i2i00−2i2i0000ii−i−i000000000000000000
χ884-44-4-24-2-442-42-24-22-42-21-22-122-21-22-12-42224-2-2-2-200001-1-11-212-111-1-100−4i4i00000000000000000000002i−2i002i−2i0000−i−iii000000000000000000
χ894-44-4-2-244-422-4-2-2422-41-2-2-12221-2-2-12-2-24-2-22-422200001-1-11-121-2-1-111000000000000000000000000000000003i−3i−3i3i0000000000000000000000
χ904-44-4-2-244-422-4-2-2422-41-2-2-12221-2-2-12-2-24-2-22-422200001-1-11-121-2-1-11100000000000000000000000000000000−3i3i3i−3i0000000000000000000000
χ914-44-4-2-24-4422-4-2-2422-41-2-2-12221-2-2-1222-422-24-2-2-200001-1-111-2-1211-1-14i−4i0000000000000000000000−2i2i00−2i2i00ii−i−i0000000000000000000000
χ924-44-4-2-24-4422-4-2-2422-41-2-2-12221-2-2-1222-422-24-2-2-200001-1-111-2-1211-1-1−4i4i00000000000000000000002i−2i002i−2i00−i−iii0000000000000000000000
χ934-4-4444-200-4-42-4-4244-24-2-2-422-2-4224-2000000000022−22−2222-22-2200000000000022−22−22−2−222−22222−222−2−200000000000000000000000000000000000000
χ944-4-4444-200-4-42-4-4244-24-2-2-422-2-4224-20000000000−222222−22-22-22000000000000−22222−222−2−222−22−22−2−22200000000000000000000000000000000000000
χ954-4-444-2400-42-4-42-44-24-24-22-42-22-42-24000000000022−22−2222-22-22000000000000−2222−22−2−2222−2−222222−2−200000000000000000000000000000000000000
χ964-4-444-2400-42-4-42-44-24-24-22-42-22-42-240000000000−222222−22-22-220000000000002−2−222222−2−2−2222−22−2−22200000000000000000000000000000000000000
χ974-4-444-2-200-422-4224-2-2-2-2122-1122-1-2-20003i−3i00−3i3i022−22−22221-11-10000−3i3i3i−3i0000−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ32−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ300000000000000000000000000000000000000
χ984-4-444-2-200-422-4224-2-2-2-2122-1122-1-2-20003i−3i00−3i3i0−222222−221-11-10000−3i3i3i−3i00002−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ3−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ300000000000000000000000000000000000000
χ994-4-444-2-200-422-4224-2-2-2-2122-1122-1-2-2000−3i3i003i−3i022−22−22221-11-100003i−3i−3i3i0000−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ32−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ300000000000000000000000000000000000000
χ1004-4-444-2-200-422-4224-2-2-2-2122-1122-1-2-2000−3i3i003i−3i0−222222−221-11-100003i−3i−3i3i00002−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ3−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ300000000000000000000000000000000000000
χ1014-4-44-244002-4-42-4-4-244-2-2422-4422-4-2-200000000000000-22-22000000000000000000000000000022−22−2222000000000000000000000000−222−2000000
χ1024-4-44-244002-4-42-4-4-244-2-2422-4422-4-2-200000000000000-22-220000000000000000000000000000−222222−220000000000000000000000002−2−22000000
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
χ1098-88-8-4-4-48-8444-4-4-4444222-2-2-2-2222-2-2-4-4-42244-2-240000-111-1-2-22211-1-10000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4-88444-4-4-4444222-2-2-2-2222-2-2444-2-2-4-422-40000-111-122-2-2-1-1110000000000000000000000000000000000000000000000000000000000
χ1118-8-88-48-4004-844-84-48-4-42-44-24-44-24-42000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-480044-844-8-4-482-4-4-244-4-2442-4000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-400444444-4-4-4222-2-2-22-2-2-2220006i−6i00−6i6i00000-11-1100003i−3i−3i3i0000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-400444444-4-4-4222-2-2-22-2-2-222000−6i6i006i−6i00000-11-110000−3i3i3i−3i0000000000000000000000000000000000000000000000000000000000

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