Finite Group Databasebeta

← Group #13156657

Character table — Group #13156657

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size11112222222222222222224444444444444444444444446666666666666666666666668888888888121212121212121212121212121212121212121212121212181818181818181818181818242424242424242424727272727272216
order1222333446666666661212121233366666666612121212121212121212121244448888121212121212121224242424242424243666121212121212121212121212121212121212242424242424242424242424888824242424242424244121212121212121244121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1111-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111
χ51111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1
χ61111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-11
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-200002222-2-2-2-2000000002222-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000-2-2-2-22222000000002222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000000000000000
χ11222222-122222-122-1-1222222-1-122-12-1-1-1-1-12-1-122-1-1-1-1222222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002-1-122-1-1-1-102-1-1000
χ12222222-122222-122-1-1222222-1-122-12-1-1-1-1-12-1-122-1-1-1-1222222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-211-2-211110-211000
χ13222222-122222-122-1-1222222-1-122-12-1-1-1-1-12-1-122-1-1-1-1222-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000002-1-122-1-1-1-10-211000
χ14222222-122222-122-1-1222222-1-122-12-1-1-1-1-12-1-122-1-1-1-1222-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000-211-2-2111102-1-1000
χ15222222-1-2-2222-122-1-12-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-222-2-200002222-2-2-2-200000000-1-1-1-1111111-1-111-1-1-1-111110000000000000000000000000−i3i300−i3−i3i3i300−i3i3000
χ16222222-1-2-2222-122-1-12-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-222-2-200002222-2-2-2-200000000-1-1-1-1111111-1-111-1-1-1-111110000000000000000000000000i3−i300i3i3−i3−i300i3−i3000
χ17222222-1-2-2222-122-1-12-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-2-2-2220000-2-2-2-2222200000000-1-1-1-111111111-1-11111-1-1-1-10000000000000000000000000−i3i300−i3−i3i3i300i3−i3000
χ18222222-1-2-2222-122-1-12-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-2-2-2220000-2-2-2-2222200000000-1-1-1-111111111-1-11111-1-1-1-10000000000000000000000000i3−i300i3i3−i3−i300−i3i3000
χ1922222-122222-12-1-1222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2022222-122222-12-1-1222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111110000000000000000
χ2122222-122222-12-1-1222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2222222-122222-12-1-1222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-10000000000000000
χ2322222-12-2-222-12-1-12221111-12-1-1-12-12-1-1-12-2-2-2111111-21122-2-20000-1-1-1-111113333−3−3−3−3-1-1-1-1-2-2111122-2-2-1-1-1-1111100003333−3−3−3−300003333−3−3−3−30000000000000000
χ2422222-12-2-222-12-1-12221111-12-1-1-12-12-1-1-12-2-2-2111111-21122-2-20000-1-1-1-11111−3−3−3−33333-1-1-1-1-2-2111122-2-2-1-1-1-111110000−3−3−3−333330000−3−3−3−333330000000000000000
χ2522222-12-2-222-12-1-12221111-12-1-1-12-12-1-1-12-2-2-2111111-211-2-22200001111-1-1-1-13333−3−3−3−3-1-1-1-1-2-21111-2-2221111-1-1-1-100003333−3−3−3−30000−3−3−3−333330000000000000000
χ2622222-12-2-222-12-1-12221111-12-1-1-12-12-1-1-12-2-2-2111111-211-2-22200001111-1-1-1-1−3−3−3−33333-1-1-1-1-2-21111-2-2221111-1-1-1-10000−3−3−3−3333300003333−3−3−3−30000000000000000
χ272222-12222-1-1222222-12222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000222-1-1-1-1-1-12000-1-10
χ282222-12222-1-1222222-12222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2111111-2000110
χ292222-12222-1-1222222-12222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000222-1-1-1-1-1-1-2000110
χ302222-12222-1-1222222-12222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000-2-2-21111112000-1-10
χ3122-2-22222-2-2222-2-2-2-2-222-2-2222-2-2-2222-2-2-2-22-2-2-222-2-2222000022-2-20000000022-2-222-2-22-2-222-222-2-200000000000022-2-222-2-222-2-20000000000000000000000000000
χ3222-2-22222-2-2222-2-2-2-2-222-2-2222-2-2-2222-2-2-2-22-2-2-222-2-22220000-2-22200000000-2-222-2-2222-2-222-222-2-2000000000000-2-222-2-222-2-2220000000000000000000000000000
χ3322-2-2222-22-2222-2-2-2-2-2-2-222222-2-2-2222-2-2-22-2222-2-222-2-2-20000000000000000000000002-2-22-22-2-22200000000000000000000000022-2-222-2-222-2-20000000000000000
χ3422-2-2222-22-2222-2-2-2-2-2-2-222222-2-2-2222-2-2-22-2222-2-222-2-2-20000000000000000000000002-2-22-22-2-222000000000000000000000000-2-222-2-222-2-2220000000000000000
χ3522-2-22-122-2-22-1211-2-2-2-1-111-12-111-2-12-111-2-22-211-1-1112-1-1000022-2-233−3−333−3−3-1-111-1-111-111-12-2-1-111000033−3−333−3−322-2-2-1-111-1-111000033−3−3−3−3330000000000000000
χ3622-2-22-122-2-22-1211-2-2-2-1-111-12-111-2-12-111-2-22-211-1-1112-1-1000022-2-2−3−333−3−333-1-111-1-111-111-12-2-1-1110000−3−333−3−33322-2-2-1-111-1-1110000−3−33333−3−30000000000000000
χ3722-2-22-122-2-22-1211-2-2-2-1-111-12-111-2-12-111-2-22-211-1-1112-1-10000-2-22233−3−333−3−311-1-111-1-1-111-12-2-1-111000033−3−333−3−3-2-22211-1-111-1-10000−3−33333−3−30000000000000000
χ3822-2-22-122-2-22-1211-2-2-2-1-111-12-111-2-12-111-2-22-211-1-1112-1-10000-2-222−3−333−3−33311-1-111-1-1-111-12-2-1-1110000−3−333−3−333-2-22211-1-111-1-1000033−3−3−3−3330000000000000000
χ3922-2-22-12-22-22-1211-2-2-211-1-1-12-111-2-12-111-22-22-1-111-1-1-2110000000033−3−3−3−33333−3−3−3−333-111-1-2211-1-1000033−3−3−3−333000033−3−3−3−333-2-22211-1-111-1-10000000000000000
χ4022-2-22-12-22-22-1211-2-2-211-1-1-12-111-2-12-111-22-22-1-111-1-1-2110000000033−3−3−3−333−3−33333−3−3-111-1-2211-1-1000033−3−3−3−3330000−3−33333−3−322-2-2-1-111-1-1110000000000000000
χ4122-2-22-12-22-22-1211-2-2-211-1-1-12-111-2-12-111-22-22-1-111-1-1-21100000000−3−33333−3−333−3−3−3−333-111-1-2211-1-10000−3−33333−3−3000033−3−3−3−33322-2-2-1-111-1-1110000000000000000
χ4222-2-22-12-22-22-1211-2-2-211-1-1-12-111-2-12-111-22-22-1-111-1-1-21100000000−3−33333−3−3−3−33333−3−3-111-1-2211-1-10000−3−33333−3−30000−3−33333−3−3-2-22211-1-111-1-10000000000000000
χ4322-2-2-1222-21-122-2-2-2-2122-2-2-1-12111-1-12-2-2112-21122-2-2-1-1-1000022-2-20000000022-2-222-2-2-111-1-11-1-111000000000000-1-111-1-111-1-1110000000000000003−33−33−300003−30
χ4422-2-2-1222-21-122-2-2-2-2122-2-2-1-12111-1-12-2-2112-21122-2-2-1-1-1000022-2-20000000022-2-222-2-2-111-1-11-1-111000000000000-1-111-1-111-1-111000000000000000−33−33−330000−330
χ4522-2-2-1222-21-122-2-2-2-2122-2-2-1-12111-1-12-2-2112-21122-2-2-1-1-10000-2-22200000000-2-222-2-222-111-1-11-1-11100000000000011-1-111-1-111-1-10000000000000003−33−33−30000−330
χ4622-2-2-1222-21-122-2-2-2-2122-2-2-1-12111-1-12-2-2112-21122-2-2-1-1-10000-2-22200000000-2-222-2-222-111-1-11-1-11100000000000011-1-111-1-111-1-1000000000000000−33−33−3300003−30
χ472-22-222200-2-2-2-22-22-2200002222-2-2-2-2-22-22000000000000002i−2i2−22−200002i−2i2i−2i2−22−22−22−222-2-2000000002i−2i00002i−2i2i−2i2−22−22−22−22−22−2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ482-22-222200-2-2-2-22-22-2200002222-2-2-2-2-22-22000000000000002i−2i−22−2200002i−2i2i−2i−22−22−22−2222-2-2000000002i−2i00002i−2i2i−2i−22−22−22−22−22−22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ492-22-222200-2-2-2-22-22-2200002222-2-2-2-2-22-2200000000000000−2i2i2−22−20000−2i2i−2i2i2−22−22−22−222-2-200000000−2i2i0000−2i2i−2i2i2−22−22−22−22−22−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ502-22-222200-2-2-2-22-22-2200002222-2-2-2-2-22-2200000000000000−2i2i−22−220000−2i2i−2i2i−22−22−22−2222-2-200000000−2i2i0000−2i2i−2i2i−22−22−22−22−22−22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ512-22-22-1200-2-21-2-112-223−33−3-12-1-11-21-21-1120003−33−33−303−3002i−2i2−22−2−i3i3−i3i3−ii−iiζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23-1-111003−33−3002i−2i−i3i3−i3i3−ii−ii2−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ230000000000000000
χ522-22-22-1200-2-21-2-112-223−33−3-12-1-11-21-21-1120003−33−33−303−3002i−2i−22−22−i3i3−i3i3−ii−ii−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23-1-111003−33−3002i−2i−i3i3−i3i3−ii−ii−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ230000000000000000
χ532-22-22-1200-2-21-2-112-223−33−3-12-1-11-21-21-1120003−33−33−303−300−2i2i2−22−2i3−i3i3−i3i−ii−iζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23-1-111003−33−300−2i2ii3−i3i3−i3i−ii−i2−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ230000000000000000
χ542-22-22-1200-2-21-2-112-223−33−3-12-1-11-21-21-1120003−33−33−303−300−2i2i−22−22i3−i3i3−i3i−ii−i−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23-1-111003−33−300−2i2ii3−i3i3−i3i−ii−i−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ230000000000000000
χ552-22-22-1200-2-21-2-112-22−33−33-12-1-11-21-21-112000−33−33−330−33002i−2i2−22−2i3−i3i3−i3−ii−iiζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7-1-11100−33−33002i−2ii3−i3i3−i3−ii−ii2−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ70000000000000000
χ562-22-22-1200-2-21-2-112-22−33−33-12-1-11-21-21-112000−33−33−330−33002i−2i−22−22i3−i3i3−i3−ii−ii−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7-1-11100−33−33002i−2ii3−i3i3−i3−ii−ii−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ70000000000000000
χ572-22-22-1200-2-21-2-112-22−33−33-12-1-11-21-21-112000−33−33−330−3300−2i2i2−22−2−i3i3−i3i3i−ii−iζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7-1-11100−33−3300−2i2i−i3i3−i3i3i−ii−i2−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ70000000000000000
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χ1248888-4-4-4-8-8-4-4-4-4-4-4-4-4-44444222222222222444-2-2-2-2-2-24-2-2000000000000000000000000-1-1-1-1-2-211110000000000000000000000000000000000000000000000000000
χ12588-8-8-4-4-48-84-4-4-444444-4-444222-2-2-2222-2-2-24-44-2-222-2-2-422000000000000000000000000-111-12-2-1-1110000000000000000000000000000000000000000000000000000
χ12688-8-8-4-4-4-884-4-4-44444444-4-4222-2-2-2222-2-2-2-44-422-2-2224-2-2000000000000000000000000-111-1-2211-1-10000000000000000000000000000000000000000000000000000
χ1278-88-8-48-40044-848-8-44-40000-42-4-44-24-24-44200000000000000000000000000000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ1288-88-8-4-4-4004444-44-44-443−4343−432222-2-2-2-2-22-22000−2323−2323−23230−2323000000000000000000000000-1-111003−33−30000000000000000000000000000000000000000000000000000
χ1298-88-8-4-4-4004444-44-44-4−4343−43432222-2-2-2-2-22-2200023−2323−2323−23023−23000000000000000000000000-1-11100−33−330000000000000000000000000000000000000000000000000000
χ1308-8-88-48-400-44-84-884-440000-42-44-424-244-4-20000000000000000000000000000000000002-22-20000000000000000000000000000000000000000000000000000000000
χ1318-8-88-4-4-400-44444-44-4443−43−4343222-222-2-2-2-22-200023−23−232323−230−2323000000000000000000000000-11-11003−3−330000000000000000000000000000000000000000000000000000
χ1328-8-88-4-4-400-44444-44-44−434343−43222-222-2-2-2-22-2000−232323−23−2323023−23000000000000000000000000-11-1100−333−30000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.