Finite Group Databasebeta

← Group #13156538

Character table — Group #13156538

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size11112222222222222222224444444444444444444444446666666666666666666666668888888888121212121212121212121212121212121212121212121212181818181818181818181818242424242424242424727272727272216
order1222333446666666661212121233366666666612121212121212121212121288888888242424242424242424242424242424243666121212121212242424242424242424242424242424242424242424242424444412121212121212124121212121212121244121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ51111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-111-1
χ61111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-2-2-2-2-200000000000000000000000022-2-22222-2-2-2-20000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000002222-2-2-2-2-2-2000000000000000000000000-2-222-2-2-2-222220000000000000000
χ11222222-12222-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ12222222-12222-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111110000000000000000
χ13222222-12222-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ14222222-12222-122-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-10000000000000000
χ15222222-1-2-222-122-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111000000003333−3−3−3−33333−3−3−3−3-1-1-1-1-2-2111100003333−3−3−3−300003333−3−3−3−322-2-2-1-1-1-111110000000000000000
χ16222222-1-2-222-122-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111000000003333−3−3−3−3−3−3−3−33333-1-1-1-1-2-2111100003333−3−3−3−30000−3−3−3−33333-2-2221111-1-1-1-10000000000000000
χ17222222-1-2-222-122-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-2111100000000−3−3−3−333333333−3−3−3−3-1-1-1-1-2-211110000−3−3−3−3333300003333−3−3−3−3-2-2221111-1-1-1-10000000000000000
χ18222222-1-2-222-122-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-2111100000000−3−3−3−33333−3−3−3−33333-1-1-1-1-2-211110000−3−3−3−333330000−3−3−3−3333322-2-2-1-1-1-111110000000000000000
χ1922222-12222-122-1222-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000222-1-1-1-1-1-10200-1-10
χ2022222-12222-122-1222-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-21111110-200110
χ2122222-12222-122-1222-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000222-1-1-1-1-1-10-200110
χ2222222-12222-122-1222-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000-2-2-21111110200-1-10
χ232222-12222-122-1222-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002-1-122-1-1-1-120-1-1000
χ242222-12222-122-1222-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-211-2-21111-2011000
χ252222-12222-122-1222-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000002-1-122-1-1-1-1-2011000
χ262222-12222-122-1222-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000-211-2-2111120-1-1000
χ2722-2-22222-2-2-2222-2-2-2-222-2-2222-2-2-2-2-2-22222-222-2-2-22-2-2222i2i−2i−2i00002i2i−2i−2i2i2i−2i−2i000000002-2-222-222-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ2822-2-22222-2-2-2222-2-2-2-222-2-2222-2-2-2-2-2-22222-222-2-2-22-2-222−2i−2i2i2i0000−2i−2i2i2i−2i−2i2i2i000000002-2-222-222-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ2922-2-2222-22-2-2222-2-2-2-2-2-222222-2-2-2-2-2-2222-22-2-2222-222-2-200002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i2-2-22-22-2-2220000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ3022-2-2222-22-2-2222-2-2-2-2-2-222222-2-2-2-2-2-2222-22-2-2222-222-2-20000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i2-2-22-22-2-222000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ3122-2-222-12-2-2-2-12211-2-2-1-1112-1-1-2-21111-1-122-2-1-111-2211-1-12i2i−2i−2i0000−i−iii−i−iii−i3−i3i3i3i3i3−i3−i3-111-12-2-1-1112i2i−2i−2i−i−iii−i−iii0000−i3−i3i3i3i3i3−i3−i3000033−3−333−3−30000000000000000
χ3222-2-222-12-2-2-2-12211-2-2-1-1112-1-1-2-21111-1-122-2-1-111-2211-1-12i2i−2i−2i0000−i−iii−i−iiii3i3−i3−i3−i3−i3i3i3-111-12-2-1-1112i2i−2i−2i−i−iii−i−iii0000i3i3−i3−i3−i3−i3i3i30000−3−333−3−3330000000000000000
χ3322-2-222-12-2-2-2-12211-2-2-1-1112-1-1-2-21111-1-122-2-1-111-2211-1-1−2i−2i2i2i0000ii−i−iii−i−i−i3−i3i3i3i3i3−i3−i3-111-12-2-1-111−2i−2i2i2iii−i−iii−i−i0000−i3−i3i3i3i3i3−i3−i30000−3−333−3−3330000000000000000
χ3422-2-222-12-2-2-2-12211-2-2-1-1112-1-1-2-21111-1-122-2-1-111-2211-1-1−2i−2i2i2i0000ii−i−iii−i−ii3i3−i3−i3−i3−i3i3i3-111-12-2-1-111−2i−2i2i2iii−i−iii−i−i0000i3i3−i3−i3−i3−i3i3i3000033−3−333−3−30000000000000000
χ3522-2-222-1-22-2-2-12211-2-211-1-12-1-1-2-21111-1-12-2211-1-12-2-1-11100002i2i−2i−2i−i3−i3i3i3i3i3−i3−i3−i−iii−i−iii-111-1-2211-1-10000−i3−i3i3i3i3i3−i3−i32i2i−2i−2i−i−iii−i−iii0000−3−33333−3−30000000000000000
χ3622-2-222-1-22-2-2-12211-2-211-1-12-1-1-2-21111-1-12-2211-1-12-2-1-11100002i2i−2i−2ii3i3−i3−i3−i3−i3i3i3−i−iii−i−iii-111-1-2211-1-10000i3i3−i3−i3−i3−i3i3i32i2i−2i−2i−i−iii−i−iii000033−3−3−3−3330000000000000000
χ3722-2-222-1-22-2-2-12211-2-211-1-12-1-1-2-21111-1-12-2211-1-12-2-1-1110000−2i−2i2i2i−i3−i3i3i3i3i3−i3−i3ii−i−iii−i−i-111-1-2211-1-10000−i3−i3i3i3i3i3−i3−i3−2i−2i2i2iii−i−iii−i−i000033−3−3−3−3330000000000000000
χ3822-2-222-1-22-2-2-12211-2-211-1-12-1-1-2-21111-1-12-2211-1-12-2-1-1110000−2i−2i2i2ii3i3−i3−i3−i3−i3i3i3ii−i−iii−i−i-111-1-2211-1-10000i3i3−i3−i3−i3−i3i3i3−2i−2i2i2iii−i−iii−i−i0000−3−33333−3−30000000000000000
χ3922-2-22-12-22-2122-1-2-2-21-2-222-12-111-2-2112-1-1-2-1-2-2-1-121221100002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i-111-11-111-1-1000000000000−i−iii−i−iii−i−iii000000000000000−i3i3−i3−i3i3i300003−30
χ4022-2-22-12-22-2122-1-2-2-21-2-222-12-111-2-2112-1-1-2-1-2-2-1-121221100002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i-111-11-111-1-1000000000000−i−iii−i−iii−i−iii000000000000000i3−i3i3i3−i3−i30000−330
χ4122-2-22-12-22-2122-1-2-2-21-2-222-12-111-2-2112-1-1-2-1-2-2-1-12122110000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i-111-11-111-1-1000000000000ii−i−iii−i−iii−i−i000000000000000−i3i3−i3−i3i3i30000−330
χ4222-2-22-12-22-2122-1-2-2-21-2-222-12-111-2-2112-1-1-2-1-2-2-1-12122110000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i-111-11-111-1-1000000000000ii−i−iii−i−iii−i−i000000000000000i3−i3i3i3−i3−i300003−30
χ4322-2-2-1222-21-22-12-2-21-222-2-2-1-121111-2-2-12-1-1-2-1-1-2-21211222i2i−2i−2i00002i2i−2i−2i2i2i−2i−2i00000000-111-1-11-1-111−i−iii−i−iii−i−iii0000000000000000000000000−i3i300−i3i3−i3i3003−3000
χ4422-2-2-1222-21-22-12-2-21-222-2-2-1-121111-2-2-12-1-1-2-1-1-2-21211222i2i−2i−2i00002i2i−2i−2i2i2i−2i−2i00000000-111-1-11-1-111−i−iii−i−iii−i−iii0000000000000000000000000i3−i300i3−i3i3−i300−33000
χ4522-2-2-1222-21-22-12-2-21-222-2-2-1-121111-2-2-12-1-1-2-1-1-2-2121122−2i−2i2i2i0000−2i−2i2i2i−2i−2i2i2i00000000-111-1-11-1-111ii−i−iii−i−iii−i−i0000000000000000000000000−i3i300−i3i3−i3i300−33000
χ4622-2-2-1222-21-22-12-2-21-222-2-2-1-121111-2-2-12-1-1-2-1-1-2-2121122−2i−2i2i2i0000−2i−2i2i2i−2i−2i2i2i00000000-111-1-11-1-111ii−i−iii−i−iii−i−i0000000000000000000000000i3−i300i3−i3i3−i3003−3000
χ472-22-2222002-2-2-2-22-2-2200002222-22-22-2-2-2-20000000000002−22−2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i222-2-20000002−22−22−22−22−22−2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2002i−2i00002i−2i2i−2i0000000000000000
χ482-22-2222002-2-2-2-22-2-2200002222-22-22-2-2-2-20000000000002−22−2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i222-2-20000002−22−22−22−22−22−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200−2i2i0000−2i2i−2i2i0000000000000000
χ492-22-2222002-2-2-2-22-2-2200002222-22-22-2-2-2-2000000000000−22−22−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i222-2-2000000−22−22−22−22−22−22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200−2i2i0000−2i2i−2i2i0000000000000000
χ502-22-2222002-2-2-2-22-2-2200002222-22-22-2-2-2-2000000000000−22−22i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i222-2-2000000−22−22−22−22−22−22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2002i−2i00002i−2i2i−2i0000000000000000
χ512-22-222-1002-21-2-2-11-223−33−32-1-12-2-11-1111-2003−33−3003−33−32−22−2−i2i2−i2i2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-1-111003−33−32−22−2ζ5−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−ζ23002i−2i−i3i3−i3i3−ii−ii0000000000000000
χ522-22-222-1002-21-2-2-11-223−33−32-1-12-2-11-1111-2003−33−3003−33−32−22−2i2−i2i2−i2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-1-111003−33−32−22−2ζ5−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+ζ2300−2i2ii3−i3i3−i3i−ii−i0000000000000000
χ532-22-222-1002-21-2-2-11-223−33−32-1-12-2-11-1111-2003−33−3003−33−3−22−22−i2i2−i2i2−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-1-111003−33−3−22−22−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−ζ2300−2i2ii3−i3i3−i3i−ii−i0000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.