Finite Group Databasebeta

← Group #13169183

Character table — Group #13169183

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order1222333666666666333466666666612124444366612121212121212121212121224446612121212121212121212121212122266666661212121212121212121212121244444121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-111-1-1-1111111-1-1111111111111-1-1-111-11111-1-11111-1-11-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-11111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-111-1-1-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1-111-1-1-1-111-1111
χ51111111111111111111111111111111-1-11111111111111111111-11111-1-1-1-11111-1-11111-1-1-1-1-1-1111-111-1-11111-1-111-1-1-111-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-111111111111111111-1-1111-1-1-1-1-1-111-1-1-1-1-1-1111111111-1-11-1-1-1-111-1-1-1-1-1-11-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1111111-11-1-11-1-111-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-11-1-1-111-1-111-1-11-11-1111-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1111-1111111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1111-1111111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-11-1111-1-111-1-1111-11-1111-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-11111-1-1-1-1-1-1-1-111111111111-11111-1-1-1-1-1-1-11-1-11-1-111-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1111111111-1-1-1-11-1-11-1-1-1-1-1111-11-1
χ17222222-12-1222-1-122-1-122-1-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-102200022-1-1-1-100-1-1-1-12222-1-1-1-1000220-1-1-1-100-1-1-1-100200-1-100000000
χ18222222-12-1222-1-122-1-122-1-122-1-12-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-102-200022-1-11100-1-111-2-2-2-211110002-20-1-11100-1-11100-2001100000000
χ19222222-12-1222-1-122-1-122-1-122-1-12-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-10-22000-2-211-1-10011-1-122-2-21111000-22011-1-10011-1-100-2001100000000
χ20222222-12-1222-1-122-1-122-1-122-1-12-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-2-2000-2-21111001111-2-222-1-1-1-1000-2-20111100111100200-1-100000000
χ21222222-12-1222-1-122-1-12-2-1-122-1-12-1-1112222-1-1-1-1-2-2-2-2111111110-2-200022111100-1-1-1-12222-1-1-1-1000-2-20111100-1-1-1-100-2001100000000
χ22222222-12-1222-1-122-1-12-2-1-122-1-12-1-11122-2-2-1-1-1-1-2-2-2-2111111110-220002211-1-100-1-111-2-2-2-21111000-22011-1-100-1-11100200-1-100000000
χ23222222-12-1222-1-122-1-12-2-1-122-1-12-1-111-2-222-1-1-1-1-2-2-2-21111111102-2000-2-2-1-1110011-1-122-2-211110002-20-1-1110011-1-100200-1-100000000
χ24222222-12-1222-1-122-1-12-2-1-122-1-12-1-111-2-2-2-2-1-1-1-1-2-2-2-211111111022000-2-2-1-1-1-1001111-2-222-1-1-1-1000220-1-1-1-100111100-2001100000000
χ2522222-1222-12-122-122-1-122-1-1-12-1-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-1220222-1-12200-1-1220000000000-1-1-1-102-1-100-1-1-1-1002200000-1-100-1000
χ2622222-1222-12-122-122-1-122-1-1-12-1-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-1-220-2-2-2-1-1220011220000000000111-10-2-1-10011-1-100-2-20000011001000
χ2722222-1222-12-122-122-1-122-1-1-12-1-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-12-2022211-2-200-1-1-2-20000000000-1-1-11021100-1-11100-2-20000011001000
χ2822222-1222-12-122-122-1-122-1-1-12-1-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-2-20-2-2-211-2-20011-2-2000000000011110-211001111002200000-1-100-1000
χ2922222-1222-12-122-122-1-1-22-1-1-12-1-12-1-2-22200-1-1-1-11-211-2-21111112-20-222-1-1-2-20011220000000000-1-1-110-2110011-1-1002-2000001100-1000
χ3022222-1222-12-122-122-1-1-22-1-1-12-1-12-1-2-22200-1-1-1-11-211-2-2111111-2-202-2-2-1-1-2-200-1-12200000000001111021100-1-1-1-100-2200000-1-1001000
χ3122222-1222-12-122-122-1-1-22-1-1-12-1-12-1-2-2-2-200-1-1-1-11-211-2-2111111220-22211220011-2-20000000000-1-1-1-10-2-1-100111100-2200000-1-1001000
χ3222222-1222-12-122-122-1-1-22-1-1-12-1-12-1-2-2-2-200-1-1-1-11-211-2-2111111-2202-2-2112200-1-1-2-20000000000111-102-1-100-1-111002-2000001100-1000
χ332222-122-122-12222-1-12-12-12-1-1-12-1-12220022-1-1-1-12-1-1-1-1-122-1-1-1-12022-1-1000022220022-1-10000002-1-10-1-100-1-1-1-100-1-1000220000-1-10-100
χ342222-122-122-12222-1-12-12-12-1-1-12-1-12220022-1-1-1-12-1-1-1-1-122-1-1-1-1-202-211000022-2-20022-1-1000000-2110-1100-1-11100-1-1000-2-20000110100
χ352222-122-122-12222-1-12-12-12-1-1-12-1-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-120-22-1-10000-2-22200-2-2110000002-1-101-10011-1-10011000-2-20000110100
χ362222-122-122-12222-1-12-12-12-1-1-12-1-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2-2110000-2-2-2-200-2-211000000-2110110011110011000220000-1-10-100
χ372222-122-122-12222-1-12-1-2-12-1-1-12-1-12-2-20022-1-1-1-1-211111-2-2111120-2-2-1-10000-2-2-2-20022-1-10000002-1-101100111100-1-10002-20000-1-10100
χ382222-122-122-12222-1-12-1-2-12-1-1-12-1-12-2-20022-1-1-1-1-211111-2-21111-20-22110000-2-2220022-1-1000000-21101-10011-1-100-1-1000-220000110-100
χ392222-122-122-12222-1-12-1-2-12-1-1-12-1-12-2-200-2-2-1-1-1-1-211111-2-21111202-2-1-1000022-2-200-2-2110000002-1-10-1100-1-1110011000-220000110-100
χ402222-122-122-12222-1-12-1-2-12-1-1-12-1-12-2-200-2-2-1-1-1-1-211111-2-21111-2022110000222200-2-211000000-2110-1-100-1-1-1-100110002-20000-1-10100
χ412-2-22222-2-2-2222-2-2-22220-2-2-2-2222-2-2002i−2i2i−2i22-2-20000000000000000002i−2i0000002i−2i2i−2i2i−2i2-222-2-20000000000002i−2i2i−2i000000000000000
χ422-2-22222-2-2-2222-2-2-22220-2-2-2-2222-2-2002i−2i−2i2i22-2-20000000000000000002i−2i0000002i−2i−2i2i−2i2i-22-2-2220000000000002i−2i−2i2i000000000000000
χ432-2-22222-2-2-2222-2-2-22220-2-2-2-2222-2-200−2i2i2i−2i22-2-2000000000000000000−2i2i000000−2i2i2i−2i2i−2i-22-2-222000000000000−2i2i2i−2i000000000000000
χ442-2-22222-2-2-2222-2-2-22220-2-2-2-2222-2-200−2i2i−2i2i22-2-2000000000000000000−2i2i000000−2i2i−2i2i−2i2i2-222-2-2000000000000−2i2i−2i2i000000000000000
χ452-2-2222-1-21-222-11-2-2-1-12011-2-2-1-12113−32i−2i2i−2i-1-11100003−33−333−3−30000002i−2i−i3i3−i3i300−ii−ii2i−2i2-2-1-111000000−i3i3−i3i300−ii−ii000003−300000000
χ462-2-2222-1-21-222-11-2-2-1-12011-2-2-1-12113−32i−2i−2i2i-1-11100003−33−333−3−30000002i−2i−i3i3i3−i300−iii−i−2i2i-2211-1-1000000−i3i3i3−i300−iii−i00000−3300000000
χ472-2-2222-1-21-222-11-2-2-1-12011-2-2-1-12113−3−2i2i2i−2i-1-11100003−33−333−3−3000000−2i2ii3−i3−i3i300i−i−ii2i−2i-2211-1-1000000i3−i3−i3i300i−i−ii00000−3300000000
χ482-2-2222-1-21-222-11-2-2-1-12011-2-2-1-12113−3−2i2i−2i2i-1-11100003−33−333−3−3000000−2i2ii3−i3i3−i300i−ii−i−2i2i2-2-1-111000000i3−i3i3−i300i−ii−i000003−300000000
χ492-2-2222-1-21-222-11-2-2-1-12011-2-2-1-1211−332i−2i2i−2i-1-1110000−33−33−3−3330000002i−2ii3−i3i3−i300−ii−ii2i−2i2-2-1-111000000i3−i3i3−i300−ii−ii00000−3300000000
χ502-2-2222-1-21-222-11-2-2-1-12011-2-2-1-1211−332i−2i−2i2i-1-1110000−33−33−3−3330000002i−2ii3−i3−i3i300−iii−i−2i2i-2211-1-1000000i3−i3−i3i300−iii−i000003−300000000
χ512-2-2222-1-21-222-11-2-2-1-12011-2-2-1-1211−33−2i2i2i−2i-1-1110000−33−33−3−333000000−2i2i−i3i3i3−i300i−i−ii2i−2i-2211-1-1000000−i3i3i3−i300i−i−ii000003−300000000
χ522-2-2222-1-21-222-11-2-2-1-12011-2-2-1-1211−33−2i2i−2i2i-1-1110000−33−33−3−333000000−2i2i−i3i3−i3i300i−ii−i−2i2i2-2-1-111000000−i3i3−i3i300i−ii−i00000−3300000000
χ5344444-2-24-2-24-2-2-2-24-21-24-21-2-2-21-2-21-2-244001111-24-2-2-2-2111111040000-2-2-2-20000-2-20000000000000-2001100001100000000000000000
χ5444444-2-24-2-24-2-2-2-24-21-24-21-2-2-21-2-21-2-2-4-4001111-24-2-2-2-21111110-4000022220000220000000000000200-1-10000-1-100000000000000000
χ5544444-2-24-2-24-2-2-2-24-21-2-4-21-2-2-21-2-2122440011112-42222-1-1-1-1-1-10-40000-2-2220000-2-20000000000000200-1-100001100000000000000000
χ5644444-2-24-2-24-2-2-2-24-21-2-4-21-2-2-21-2-2122-4-40011112-42222-1-1-1-1-1-104000022-2-20000220000000000000-200110000-1-100000000000000000
χ574444-24-2-2-24-24-2-24-21-2-241-2-2-21-2-21-2-2-2004411114-2-2-211-2-211110040000000-2-20000-2-2-2-20000000000-200011000011000000000000000
χ584444-24-2-2-24-24-2-24-21-2-241-2-2-21-2-21-2-2-200-4-411114-2-2-211-2-2111100-40000000220000222200000000002000-1-10000-1-1000000000000000
χ594444-24-2-2-24-24-2-24-21-2-2-41-2-2-21-2-21-22200441111-4222-1-122-1-1-1-100-40000000220000-2-2-2-200000000002000-1-1000011000000000000000
χ604444-24-2-2-24-24-2-24-21-2-2-41-2-2-21-2-21-22200-4-41111-4222-1-122-1-1-1-10040000000-2-2000022220000000000-2000110000-1-1000000000000000
χ614444-2-24-24-2-2-244-2-2-2-214-2-211-2-21-2-24400001111-2-211-2-2-2-211114004-2-2000000-2-2000000000000-21100-20000110000000000000000000
χ624444-2-24-24-2-2-244-2-2-2-214-2-211-2-21-2-24400001111-2-211-2-2-2-21111-400-422000000220000000000002-1-10020000-1-10000000000000000000
χ634444-2-24-24-2-2-244-2-2-2-21-4-2-211-2-21-2-2-4-40000111122-1-12222-1-1-1-1400-4-2-200000022000000000000-2110020000-1-10000000000000000000
χ644444-2-24-24-2-2-244-2-2-2-21-4-2-211-2-21-2-2-4-40000111122-1-12222-1-1-1-1-400422000000-2-20000000000002-1-100-20000110000000000000000000
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χ764-44-4444-4-44-4-4-44-444440-4-4-44-4-4-4440000004-4-44000000000000000000000000000000000000000000000000000000000000000000000
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χ814-44-4-2442-442-4-44-4-2-24-202-42-22-42-24000000-222-2000000000000000000000000000000000000000000000000000000000000000−2i32i30000
χ824-44-4-2442-442-4-44-4-2-24-202-42-22-42-24000000-222-20000000000000000000000000000000000000000000000000000000000000002i3−2i30000
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χ844-4-444-24-4-424-24-42-44-2-20-42224-2-2-4200−4i4i00-2-2220000000000000000002i−2i000000−4i4i00000000000000000000002i−2i00000000000000000
χ854-4-444-2-2-4224-2-222-4-21-202-122-21-22-123−234i−4i0011-1-1000023−23−33−3−333000000−2i2i−2i32i30000−2i2i0000000000000000i3−i30000i−i00000000000000000
χ864-4-444-2-2-4224-2-222-4-21-202-122-21-22-123−23−4i4i0011-1-1000023−23−33−3−3330000002i−2i2i3−2i300002i−2i0000000000000000−i3i30000−ii00000000000000000
χ874-4-444-2-2-4224-2-222-4-21-202-122-21-22-1−23234i−4i0011-1-10000−23233−333−3−3000000−2i2i2i3−2i30000−2i2i0000000000000000−i3i30000i−i00000000000000000
χ884-4-444-2-2-4224-2-222-4-21-202-122-21-22-1−2323−4i4i0011-1-10000−23233−333−3−30000002i−2i−2i32i300002i−2i0000000000000000i3−i30000−ii00000000000000000
χ894-4-44-2442-4-4-244-4-42-24-202-422-24-22-400004i−4i-2-22200000000000000000000000000004i−4i−2i2i00000000000000000000−2i2i000000000000000
χ904-4-44-2442-4-4-244-4-42-24-202-422-24-22-40000−4i4i-2-2220000000000000000000000000000−4i4i2i−2i000000000000000000002i−2i000000000000000
χ914-4-44-24-222-4-24-22-421-2-20-12221-2-2-1223−23004i−4i11-1-10000−3323−23−3−3330000000000−2i32i30000−2i2i−2i2i00000000000000i3−i30000i−i000000000000000
χ924-4-44-24-222-4-24-22-421-2-20-12221-2-2-1223−2300−4i4i11-1-10000−3323−23−3−33300000000002i3−2i300002i−2i2i−2i00000000000000−i3i30000−ii000000000000000
χ934-4-44-24-222-4-24-22-421-2-20-12221-2-2-12−2323004i−4i11-1-100003−3−232333−3−300000000002i3−2i30000−2i2i−2i2i00000000000000−i3i30000i−i000000000000000
χ944-4-44-24-222-4-24-22-421-2-20-12221-2-2-12−232300−4i4i11-1-100003−3−232333−3−30000000000−2i32i300002i−2i2i−2i00000000000000i3−i30000−ii000000000000000
χ958888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-48-44-8444-4-8-42-40-42-444-244-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-4-4-4-84-844842-4-402-4-44-244-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4-4-444444-442220222-2-2-2-2-2-2000000-11-11006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-4-444444-442220222-2-2-2-2-2-2000000-11-1100−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1018-88-88-4-4-84-4-844-448-42-404-24-44-24-420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-48-44484-84-4-8-42-4-40-244-4-2442-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-484-8-444-884-4-4-42044-2244-2-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-444-4444-44-42220-2-2-22-2-2-222000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-444-4444-44-42220-2-2-22-2-2-222000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-484-84-4-48-844-4-42044-2-2-4-424400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-4444-4-4-44442220-2-2-2-2222-2-243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-4444-4-4-44442220-2-2-2-2222-2-2−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).