Finite Group Databasebeta

← Group #13168605

Character table — Group #13168605

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666663334666666666121244443666121212121212121212121212244466121212121212121212121212121244444444121212126661212121212121212121212121244121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-111-1-1-111-1-11111111111-1-111-1-1111111-1-1-111-11111-1-11111-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1111-1-11111-1-1-11-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-11-1-1-1-1-111-1111
χ51111111111111111111111111111111-1-11111111111111111111-11111-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1111-111-1-11111-1-1111-1-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-111-11-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-11-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1111-1-1111-11-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-11111111-11111-1-1-11-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111111-11-1-1-111-1-111-1-111-1-1-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111111111-1-111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-11111-1-111-1-111-1-1-1-11111-1-1-11-1111-1-111-1-11111-1-1-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-11111-1-1-1-1-1-11-11111-1-1-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1111111111-1-1-1-1-1111-1-1111-1-11
χ17222222-12-12-1222-122-1-122-1-1-12-1-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-1220222-1-1-1-12200220000000022000000-1-1-1-102-1-100-1-1-1-1000200-1-100-1000
χ18222222-12-12-1222-122-1-122-1-1-12-1-12-1222200-1-1-1-1-12-1-122-1-1-1-1-1-1-220-2-2-2-1-11122002200000000-2-2000000111-10-2-1-10011-1-1000-20011001000
χ19222222-12-12-1222-122-1-122-1-1-12-1-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-12-2022211-1-1-2-200-2-200000000-2-2000000-1-1-11021100-1-111000-20011001000
χ20222222-12-12-1222-122-1-122-1-1-12-1-12-122-2-200-1-1-1-1-12-1-122-1-1-1-1-1-1-2-20-2-2-21111-2-200-2-2000000002200000011110-211001111000200-1-100-1000
χ21222222-12-12-1222-122-1-1-22-1-1-12-1-12-1-2-22200-1-1-1-11-211-2-21111112-20-222-1-1112200-2-200000000-2-2000000-1-1-110-2110011-1-10002001100-1000
χ22222222-12-12-1222-122-1-1-22-1-1-12-1-12-1-2-22200-1-1-1-11-211-2-2111111-2-202-2-2-1-1-1-12200-2-200000000220000001111021100-1-1-1-1000-200-1-1001000
χ23222222-12-12-1222-122-1-1-22-1-1-12-1-12-1-2-2-2-200-1-1-1-11-211-2-2111111220-2221111-2-200220000000022000000-1-1-1-10-2-1-1001111000-200-1-1001000
χ24222222-12-12-1222-122-1-1-22-1-1-12-1-12-1-2-2-2-200-1-1-1-11-211-2-2111111-2202-2-211-1-1-2-2002200000000-2-2000000111-102-1-100-1-1110002001100-1000
χ2522222-12-12-122222-1-12-12-12-1-1-12-1-12220022-1-1-1-12-1-1-1-1-122-1-1-1-12022-1-1002200220022-1-12200000000002-1-10-1-100-1-1-1-100-1-1200000-1-10-100
χ2622222-12-12-122222-1-12-12-12-1-1-12-1-12220022-1-1-1-12-1-1-1-1-122-1-1-1-1-202-21100-2-200220022-1-1-2-20000000000-2110-1100-1-11100-1-1-200000110100
χ2722222-12-12-122222-1-12-12-12-1-1-12-1-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-120-22-1-1002200-2-200-2-211-2-200000000002-1-101-10011-1-10011-200000110100
χ2822222-12-12-122222-1-12-12-12-1-1-12-1-122200-2-2-1-1-1-12-1-1-1-1-122-1-1-1-1-20-2-21100-2-200-2-200-2-211220000000000-2110110011110011200000-1-10-100
χ2922222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-20022-1-1-1-1-211111-2-2111120-2-2-1-100-2-2002200-2-2-1-12200000000002-1-101100111100-1-1-200000-1-10100
χ3022222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-20022-1-1-1-1-211111-2-21111-20-22110022002200-2-2-1-1-2-20000000000-21101-10011-1-100-1-1200000110-100
χ3122222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-200-2-2-1-1-1-1-211111-2-21111202-2-1-100-2-200-2-2002211-2-200000000002-1-10-1100-1-1110011200000110-100
χ3222222-12-12-122222-1-12-1-2-12-1-1-12-1-12-2-200-2-2-1-1-1-1-211111-2-21111-202211002200-2-2002211220000000000-2110-1-100-1-1-1-10011-200000-1-10100
χ332222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-10220002200-1-1-1-1-1-1-1-12200220022-1-1-1-1000220-1-1-1-100-1-1-1-100-1-100000000
χ342222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-102-20002200-1-111-1-111-2-200-2-200-2-211110002-20-1-11100-1-111001100000000
χ352222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-10-22000-2-20011-1-111-1-12200-2-200-2-21111000-22011-1-10011-1-1001100000000
χ362222-1222222-1-1-122-1-122-1-122-1-12-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-2-2000-2-20011111111-2-200220022-1-1-1-1000-2-20111100111100-1-100000000
χ372222-1222222-1-1-122-1-12-2-1-122-1-12-1-1112222-1-1-1-1-2-2-2-2111111110-2-20002200-1-1-1-111112200-2-200221111000-2-20111100-1-1-1-100-1-100000000
χ382222-1222222-1-1-122-1-12-2-1-122-1-12-1-11122-2-2-1-1-1-1-2-2-2-2111111110-220002200-1-11111-1-1-2-2002200-2-2-1-1-1-1000-22011-1-100-1-111001100000000
χ392222-1222222-1-1-122-1-12-2-1-122-1-12-1-111-2-222-1-1-1-1-2-2-2-21111111102-2000-2-20011-1-1-1-11122002200-2-2-1-1-1-10002-20-1-1110011-1-1001100000000
χ402222-1222222-1-1-122-1-12-2-1-122-1-12-1-111-2-2-2-2-1-1-1-1-2-2-2-211111111022000-2-2001111-1-1-1-1-2-200-2-200221111000220-1-1-1-100111100-1-100000000
χ4122-2-2222-22-2-22-2-2-222220-2-2-22-2-2-2220000002-2-22000000000000000000000000000000002-22i−2i2i−2i002i2i−2i−2i000000000000000000002i−2i2-20000
χ4222-2-2222-22-2-22-2-2-222220-2-2-22-2-2-2220000002-2-22000000000000000000000000000000002-2−2i2i−2i2i00−2i−2i2i2i00000000000000000000−2i2i2-20000
χ4322-2-2222-22-2-22-2-2-222220-2-2-22-2-2-2220000002-2-2200000000000000000000000000000000-222i−2i−2i2i002i2i−2i−2i00000000000000000000−2i2i-220000
χ4422-2-2222-22-2-22-2-2-222220-2-2-22-2-2-2220000002-2-2200000000000000000000000000000000-22−2i2i2i−2i00−2i−2i2i2i000000000000000000002i−2i-220000
χ452-2-22222-2-222-2-22-2-22220-2-2-2-2222-2-2002i−2i2i−2i22-2-20000000000000000002i−2i002i−2i2i−2i00002i−2i0000002-200000000000000002i−2i2i−2i002-200000000
χ462-2-22222-2-222-2-22-2-22220-2-2-2-2222-2-2002i−2i−2i2i22-2-20000000000000000002i−2i002i−2i−2i2i0000−2i2i000000-2200000000000000002i−2i−2i2i00-2200000000
χ472-2-22222-2-222-2-22-2-22220-2-2-2-2222-2-200−2i2i2i−2i22-2-2000000000000000000−2i2i00−2i2i2i−2i00002i−2i000000-220000000000000000−2i2i2i−2i00-2200000000
χ482-2-22222-2-222-2-22-2-22220-2-2-2-2222-2-200−2i2i−2i2i22-2-2000000000000000000−2i2i00−2i2i−2i2i0000−2i2i0000002-20000000000000000−2i2i−2i2i002-200000000
χ492-2-22-122-2-22211-1-2-2-1-12011-2-2-1-12113−32i−2i2i−2i-1-11100003−33−333−3−30000002i−2i00−ii−ii−i3i3−i3i32i−2i0000002-23−33−3000000−i3i3−i3i300−ii−ii00-1100000000
χ502-2-22-122-2-22211-1-2-2-1-12011-2-2-1-12113−32i−2i−2i2i-1-11100003−33−333−3−30000002i−2i00−iii−i−i3i3i3−i3−2i2i000000-22−33−33000000−i3i3i3−i300−iii−i001-100000000
χ512-2-22-122-2-22211-1-2-2-1-12011-2-2-1-12113−3−2i2i2i−2i-1-11100003−33−333−3−3000000−2i2i00i−i−iii3−i3−i3i32i−2i000000-22−33−33000000i3−i3−i3i300i−i−ii001-100000000
χ522-2-22-122-2-22211-1-2-2-1-12011-2-2-1-12113−3−2i2i−2i2i-1-11100003−33−333−3−3000000−2i2i00i−ii−ii3−i3i3−i3−2i2i0000002-23−33−3000000i3−i3i3−i300i−ii−i00-1100000000
χ532-2-22-122-2-22211-1-2-2-1-12011-2-2-1-1211−332i−2i2i−2i-1-1110000−33−33−3−3330000002i−2i00−ii−iii3−i3i3−i32i−2i0000002-2−33−33000000i3−i3i3−i300−ii−ii00-1100000000
χ542-2-22-122-2-22211-1-2-2-1-12011-2-2-1-1211−332i−2i−2i2i-1-1110000−33−33−3−3330000002i−2i00−iii−ii3−i3−i3i3−2i2i000000-223−33−3000000i3−i3−i3i300−iii−i001-100000000
χ552-2-22-122-2-22211-1-2-2-1-12011-2-2-1-1211−33−2i2i2i−2i-1-1110000−33−33−3−333000000−2i2i00i−i−ii−i3i3i3−i32i−2i000000-223−33−3000000−i3i3i3−i300i−i−ii001-100000000
χ562-2-22-122-2-22211-1-2-2-1-12011-2-2-1-1211−33−2i2i−2i2i-1-1110000−33−33−3−333000000−2i2i00i−ii−i−i3i3−i3i3−2i2i0000002-2−33−33000000−i3i3−i3i300i−ii−i00-1100000000
χ5744444-2-2-2-2-2-2444-2-2-2-214-2-211-2-21-2-24400001111-2-211-2-2-2-211114004-2-200-2-20000000000000000000000-21100-20000110000000000000000
χ5844444-2-2-2-2-2-2444-2-2-2-214-2-211-2-21-2-24400001111-2-211-2-2-2-21111-400-422002200000000000000000000002-1-10020000-1-10000000000000000
χ5944444-2-2-2-2-2-2444-2-2-2-21-4-2-211-2-21-2-2-4-40000111122-1-12222-1-1-1-1400-4-2-200220000000000000000000000-2110020000-1-10000000000000000
χ6044444-2-2-2-2-2-2444-2-2-2-21-4-2-211-2-21-2-2-4-40000111122-1-12222-1-1-1-1-40042200-2-200000000000000000000002-1-100-20000110000000000000000
χ614444-24-24-24-2-2-2-2-24-21-24-21-2-2-21-2-21-2-244001111-24-2-2-2-2111111040000-2-200-2-200-2-20000000000000000000-2001100001100000000000000
χ624444-24-24-24-2-2-2-2-24-21-24-21-2-2-21-2-21-2-2-4-4001111-24-2-2-2-21111110-4000022002200220000000000000000000200-1-10000-1-100000000000000
χ634444-24-24-24-2-2-2-2-24-21-2-4-21-2-2-21-2-2122440011112-42222-1-1-1-1-1-10-40000-2-200-2-200220000000000000000000200-1-100001100000000000000
χ644444-24-24-24-2-2-2-2-24-21-2-4-21-2-2-21-2-2122-4-40011112-42222-1-1-1-1-1-104000022002200-2-20000000000000000000-200110000-1-100000000000000
χ654444-2-24-24-24-2-2-24-21-2-241-2-2-21-2-21-2-2-2004411114-2-2-211-2-21111004000000000-2-200-2-2-2-20000000000000000-200011000011000000000000
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χ674444-2-24-24-24-2-2-24-21-2-2-41-2-2-21-2-21-22200441111-4222-1-122-1-1-1-100-4000000000-2-20022-2-200000000000000002000-1-1000011000000000000
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χ834-44-44-2-2-2222-44-4-22-2-210-2-21-122-1220000001-11-100−3i3i0000−3i3i−3i3i00002i3−2i30023−2300000000000000000000000−i3i30000000−330000000000000000
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χ894-4-444-242-4-24-4-44-42-24-202-422-24-22-40000−4i4i-2-222000000000000000000000000−4i4i00002i−2i000000000000000000000000002i−2i000000000000
χ904-4-44-24-2-424-222-22-4-21-202-122-21-22-123−234i−4i0011-1-1000023−23−33−3−333000000−2i2i00−2i2i00−2i32i30000000000000000000000i3−i30000i−i00000000000000
χ914-4-44-24-2-424-222-22-4-21-202-122-21-22-123−23−4i4i0011-1-1000023−23−33−3−3330000002i−2i002i−2i002i3−2i30000000000000000000000−i3i30000−ii00000000000000
χ924-4-44-24-2-424-222-22-4-21-202-122-21-22-1−23234i−4i0011-1-10000−23233−333−3−3000000−2i2i00−2i2i002i3−2i30000000000000000000000−i3i30000i−i00000000000000
χ934-4-44-24-2-424-222-22-4-21-202-122-21-22-1−2323−4i4i0011-1-10000−23233−333−3−30000002i−2i002i−2i00−2i32i30000000000000000000000i3−i30000−ii00000000000000
χ944-4-44-2-242-4-2422-2-421-2-20-12221-2-2-1223−23004i−4i11-1-10000−3323−23−3−333000000000000−2i2i00−2i32i3−2i2i00000000000000000000i3−i30000i−i000000000000
χ954-4-44-2-242-4-2422-2-421-2-20-12221-2-2-1223−2300−4i4i11-1-10000−3323−23−3−3330000000000002i−2i002i3−2i32i−2i00000000000000000000−i3i30000−ii000000000000
χ964-4-44-2-242-4-2422-2-421-2-20-12221-2-2-12−2323004i−4i11-1-100003−3−232333−3−3000000000000−2i2i002i3−2i3−2i2i00000000000000000000−i3i30000i−i000000000000
χ974-4-44-2-242-4-2422-2-421-2-20-12221-2-2-12−232300−4i4i11-1-100003−3−232333−3−30000000000002i−2i00−2i32i32i−2i00000000000000000000i3−i30000−ii000000000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-88-4-44-4448-8-84-4-4-42044-2244-2-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-48-4-8-4-84-44448-42-404-24-44-24-420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-48484-8-444-8-42-4-40-244-4-2442-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4-44-444-4444-42220-2-2-22-2-2-222000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-44-444-4444-42220-2-2-22-2-2-222000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-48-484-844-44-4-8-42-40-42-444-244-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-48-4-84-84-44842-4-402-4-44-244-240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4-44444-44-442220222-2-2-2-2-2-2000000-11-11006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4-44444-44-442220222-2-2-2-2-2-2000000-11-1100−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000
χ1098-8-888-4-444-4-4-8-8844-4-42044-2-2-4-424400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-444-4-444-4442220-2-2-2-2222-2-243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-444-4-444-4442220-2-2-2-2222-2-2−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000000

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