Finite Group Databasebeta

← Group #13156429

Character table — Group #13156429

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123
size11112222222222222222224444444444444444444444446666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121212242424242424363636363636363636363636727272216
order122233344666666666121212123336666666661212121212121212121212124412121212366612121212121224466666666881212121212121212121224242424242424242424242424242424121212121212448812121212242424242664
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-11
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-11
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-200-2-2-2-2-2-2-2-200220000222200000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22002222222200-2-20000-2-2-2-200000000000000000000000000000000000000
χ11222222-12222-1-1222-122222-1-12-1-1-122-1-12-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-1022000000002200222200002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-10
χ12222222-12222-1-1222-122222-1-12-1-1-122-1-12-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-102200000000-2-20022220000-2-2-2-2111111111111-1-1-1-1-1-1000000000000-2110
χ13222222-12222-1-1222-122222-1-12-1-1-122-1-12-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-10-2-2000000002200-2-2-2-200002222-1-1-1-1-1-1-1-1-1-1-1-1111111000000000000-2110
χ14222222-12222-1-1222-122222-1-12-1-1-122-1-12-1-122-1-12222-1-1-1000000-1-1-1-1-1-1-1-1-1-10-2-200000000-2-200-2-2-2-20000-2-2-2-21111111111111111110000000000002-1-10
χ1522222-122222222-1-12-122222-1-122-1-1-12-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-10022-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12200-1-1-1-100000000
χ1622222-122222222-1-12-122222-1-122-1-1-12-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-222-1-1-1-1-1-100221111-1-1-1-10000000000000000-2-21111-2-200111100000000
χ1722222-122222222-1-12-122222-1-122-1-1-12-1-1-12-1-122-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-1-222-2-211111100-2-2-1-1-1-11111000000000000000022-1-1-1-1-2-200111100000000
χ1822222-122222222-1-12-122222-1-122-1-1-12-1-1-12-1-122-1-1-1-1222-2-21111-1-1-1-1-1-1-1-1-1-1-2-2-2-2-211111100-2-2111111110000000000000000-2-211112200-1-1-1-100000000
χ1922222-12-2-222222-1-12-1-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-222-1-1-1-1-1-1-1-1111111-200-2-21111110022−i3−i3i3i3-1-1-1-1000000000000000000−i3−i3i3i30000−i3−i3i3i300000000
χ2022222-12-2-222222-1-12-1-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-222-1-1-1-1-1-1-1-1111111-200-2-21111110022i3i3−i3−i3-1-1-1-1000000000000000000i3i3−i3−i30000i3i3−i3−i300000000
χ2122222-12-2-222222-1-12-1-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-2-2-21111-1-1-1-111111120022-1-1-1-1-1-100-2-2−i3−i3i3i31111000000000000000000−i3−i3i3i30000i3i3−i3−i300000000
χ2222222-12-2-222222-1-12-1-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-2-2-21111-1-1-1-111111120022-1-1-1-1-1-100-2-2i3i3−i3−i31111000000000000000000i3i3−i3−i30000−i3−i3i3i300000000
χ232222-12222-1-122-12222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-1200-1-122-1-1-1-122-1-10000-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000220000-1-1-1-10000
χ242222-12222-1-122-12222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1222222-1-1-1-122-1-1-1-1200-1-122-1-1-1-1-2-2-1-10000-1-1-1-11111-2-2-2-21111111100000000-2-2000011110000
χ252222-12222-1-122-12222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-20011-2-21111221100001111-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2000011110000
χ262222-12222-1-122-12222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-20011-2-21111-2-211000011111111-2-2-2-21111111100000000220000-1-1-1-10000
χ272222-122-2-2-1-122-122221111-12-1-1-12-1-1-12-12-2-2-2111111-211222222-1-1-1-1-2-21111-20011-2-2111100-1-10000-1-1-1-133−3−300003333−3−3−3−30000000000000033−3−30000
χ282222-122-2-2-1-122-122221111-12-1-1-12-1-1-12-12-2-2-2111111-211222222-1-1-1-1-2-21111-20011-2-2111100-1-10000-1-1-1-1−3−3330000−3−3−3−3333300000000000000−3−3330000
χ292222-122-2-2-1-122-122221111-12-1-1-12-1-1-12-12-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-21111200-1-122-1-1-1-100110000111133−3−300003333−3−3−3−300000000000000−3−3330000
χ302222-122-2-2-1-122-122221111-12-1-1-12-1-1-12-12-2-2-2111111-211-2-2-2-2-2-2-1-1-1-1-2-21111200-1-122-1-1-1-1001100001111−3−3330000−3−3−3−333330000000000000033−3−30000
χ3122-2-22222-2-2-2-2222-2-2-222-2-2222-2-2-2-2-2222-2-22-2-2-222-2-22220000002-2-222-222-2-20000000000000000000000000000000000000000000002i−2i002i−2i2i−2i00000000
χ3222-2-22222-2-2-2-2222-2-2-222-2-2222-2-2-2-2-2222-2-22-2-2-222-2-22220000002-2-222-222-2-2000000000000000000000000000000000000000000000−2i2i00−2i2i−2i2i00000000
χ3322-2-2222-22-2-2-2222-2-2-2-2-222222-2-2-2-2-2222-22-2222-2-222-2-2-20000002-2-22-22-2-22202i−2i0000000000002i−2i2i−2i000000000000000000002i−2i2i−2i2i−2i0000000000000000
χ3422-2-2222-22-2-2-2222-2-2-2-2-222222-2-2-2-2-2222-22-2222-2-222-2-2-20000002-2-22-22-2-2220−2i2i000000000000−2i2i−2i2i00000000000000000000−2i2i−2i2i−2i2i0000000000000000
χ3522-2-222-1-22-2-21-122-21-2-2-222-1-12111-2-2-1-121-1-22-1-1-2-222111000000-111-11-111-1-102i−2i0000000000002i−2i2i−2i0000000033−3−333−3−333−3−3−ii−ii−ii0000000000000−i3i30
χ3622-2-222-1-22-2-21-122-21-2-2-222-1-12111-2-2-1-121-1-22-1-1-2-222111000000-111-11-111-1-102i−2i0000000000002i−2i2i−2i00000000−3−333−3−333−3−333−ii−ii−ii0000000000000i3−i30
χ3722-2-222-1-22-2-21-122-21-2-2-222-1-12111-2-2-1-121-1-22-1-1-2-222111000000-111-11-111-1-10−2i2i000000000000−2i2i−2i2i0000000033−3−333−3−333−3−3i−ii−ii−i0000000000000i3−i30
χ3822-2-222-1-22-2-21-122-21-2-2-222-1-12111-2-2-1-121-1-22-1-1-2-222111000000-111-11-111-1-10−2i2i000000000000−2i2i−2i2i00000000−3−333−3−333−3−333i−ii−ii−i0000000000000−i3i30
χ3922-2-22-122-2-2-2-222-11-2122-2-22-1-1-2-21112-1-11-2-11-2-2-1-11122200−i3−i3i3i3-111-1-11-1-11100000−i3i3−i3−i3i3i300003−3−33−i3−i3i3i30000000000000000003−3−332i−2i00−ii−ii00000000
χ4022-2-22-122-2-2-2-222-11-2122-2-22-1-1-2-21112-1-11-2-11-2-2-1-11122200−i3−i3i3i3-111-1-11-1-11100000−i3i3−i3−i3i3i30000−333−3−i3−i3i3i3000000000000000000−333−3−2i2i00i−ii−i00000000
χ4122-2-22-122-2-2-2-222-11-2122-2-22-1-1-2-21112-1-11-2-11-2-2-1-11122200i3i3−i3−i3-111-1-11-1-11100000i3−i3i3i3−i3−i300003−3−33i3i3−i3−i30000000000000000003−3−33−2i2i00i−ii−i00000000
χ4222-2-22-122-2-2-2-222-11-2122-2-22-1-1-2-21112-1-11-2-11-2-2-1-11122200i3i3−i3−i3-111-1-11-1-11100000i3−i3i3i3−i3−i30000−333−3i3i3−i3−i3000000000000000000−333−32i−2i00−ii−ii00000000
χ4322-2-22-12-22-2-2-222-11-21-2-2222-1-1-2-21112-1-1121-12211-1-1-2-2-200−i3−i3i3i3-111-11-111-1-102i−2i00i3−i3i3i3−i3−i30000−ii−ii−i3−i3i3i300000000000000002i−2i−ii−ii00003−3−3300000000
χ4422-2-22-12-22-2-2-222-11-21-2-2222-1-1-2-21112-1-1121-12211-1-1-2-2-200−i3−i3i3i3-111-11-111-1-10−2i2i00i3−i3i3i3−i3−i30000i−ii−i−i3−i3i3i30000000000000000−2i2ii−ii−i0000−333−300000000
χ4522-2-22-12-22-2-2-222-11-21-2-2222-1-1-2-21112-1-1121-12211-1-1-2-2-200i3i3−i3−i3-111-11-111-1-102i−2i00−i3i3−i3−i3i3i30000−ii−iii3i3−i3−i300000000000000002i−2i−ii−ii0000−333−300000000
χ4622-2-22-12-22-2-2-222-11-21-2-2222-1-1-2-21112-1-1121-12211-1-1-2-2-200i3i3−i3−i3-111-11-111-1-10−2i2i00−i3i3−i3−i3i3i30000i−ii−ii3i3−i3−i30000000000000000−2i2ii−ii−i00003−3−3300000000
χ472-22-2222002-2-2-2-2-222-200002222-2-22-2-2-2-220000000000002i−2i2i−2i2i−2i22-2-2000000000000000002−22i−2i00002i−2i2i−2i2−22−22−22−22−22−22−22−200000000−i2i20000−i2i2−i2i20000
χ482-22-2222002-2-2-2-2-222-200002222-2-22-2-2-2-220000000000002i−2i2i−2i2i−2i22-2-200000000000000000−222i−2i00002i−2i2i−2i−22−22−22−22−22−22−22−2200000000i2−i20000i2−i2i2−i20000
χ492-22-2222002-2-2-2-2-222-200002222-2-22-2-2-2-22000000000000−2i2i−2i2i−2i2i22-2-2000000000000000002−2−2i2i0000−2i2i−2i2i2−22−22−22−22−22−22−22−200000000i2−i20000i2−i2i2−i20000
χ502-22-2222002-2-2-2-2-222-200002222-2-22-2-2-2-22000000000000−2i2i−2i2i−2i2i22-2-200000000000000000−22−2i2i0000−2i2i−2i2i−22−22−22−22−22−22−22−2200000000−i2i20000−i2i2−i2i20000
χ512-22-2-12200-11-2-21-222-23−33−3-12-1-11-2-111-2120003−33−33−303−32i−2i2i−2i2i−2i-1-111003−33−3000−i3i300−i3i3−i3i32−2−ii0000−ii−iiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ522-22-2-12200-11-2-21-222-23−33−3-12-1-11-2-111-2120003−33−33−303−32i−2i2i−2i2i−2i-1-111003−33−3000−i3i300−i3i3−i3i3−22−ii0000−ii−ii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ532-22-2-12200-11-2-21-222-23−33−3-12-1-11-2-111-2120003−33−33−303−3−2i2i−2i2i−2i2i-1-111003−33−3000i3−i300i3−i3i3−i32−2i−i0000i−ii−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ542-22-2-12200-11-2-21-222-23−33−3-12-1-11-2-111-2120003−33−33−303−3−2i2i−2i2i−2i2i-1-111003−33−3000i3−i300i3−i3i3−i3−22i−i0000i−ii−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ552-22-2-12200-11-2-21-222-2−33−33-12-1-11-2-111-212000−33−33−330−332i−2i2i−2i2i−2i-1-11100−33−33000i3−i300i3−i3i3−i32−2−ii0000−ii−iiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ562-22-2-12200-11-2-21-222-2−33−33-12-1-11-2-111-212000−33−33−330−332i−2i2i−2i2i−2i-1-11100−33−33000i3−i300i3−i3i3−i3−22−ii0000−ii−ii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ572-22-2-12200-11-2-21-222-2−33−33-12-1-11-2-111-212000−33−33−330−33−2i2i−2i2i−2i2i-1-11100−33−33000−i3i300−i3i3−i3i32−2i−i0000i−ii−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ582-22-2-12200-11-2-21-222-2−33−33-12-1-11-2-111-212000−33−33−330−33−2i2i−2i2i−2i2i-1-11100−33−33000−i3i300−i3i3−i3i3−22i−i0000i−ii−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ59444444-2-4-444-2-2444-24-4-4-4-4-2-24-2-2-244-2-24-22-4-422-4-4-4-4222000000-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
χ6044444-2-24444-2-24-2-2-2-24444-21-2-2-21-2-2-21-21-2-2-2-2-2-2-2-2-2-2-2-20000001111111111044000000000000-2-2-2-200000000000000000000-2-211110000000000000000
χ6144444-2-24444-2-24-2-2-2-24444-21-2-2-21-2-2-21-21-2-2-2-2-2-2-2-2-2-2-2-200000011111111110-4-400000000000022220000000000000000000022-1-1-1-10000000000000000
χ6244444-2-2-4-444-2-24-2-2-2-2-4-4-4-4-21-2-2-21-2-2-21-212222222222220000001111-1-1-1-1-1-1000000000000000−2i3−2i32i32i30000000000000000000000i3i3−i3−i30000000000000000
χ6344444-2-2-4-444-2-24-2-2-2-2-4-4-4-4-21-2-2-21-2-2-21-212222222222220000001111-1-1-1-1-1-10000000000000002i32i3−2i3−2i30000000000000000000000−i3−i3i3i30000000000000000
χ644444-24-244-2-2-2-2-244-24-2-2-2-21-2-211-2-2-21-2-2-2-24411-2-2-2-2-2110000001111-2-2111100000000000440000000000-2-2-2-2-2-2-2-2111111110000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.