Finite Group Databasebeta

← Group #13156611

Character table — Group #13156611

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size11112222222222222222224444444444444444444444446666666666666666666666668888888888121212121212121212121212121212121212121212121212181818181818181818181818242424242424242424727272727272216
order12223334466666666612121212333666666666121212121212121212121212444488881212121212121212242424242424242436661212121212121212121212121212121212122424242424242424242424248888242424242424242441212121212121212246612122
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-200002222-2-2-2-2000000002222-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000
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
χ11222222-12222222-1-1-1222222-1-122-1-12-1-1-1-1-1-1222-1-1-1-1222222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002-1-122-1-1-1-120-1-1000
χ12222222-12222222-1-1-1222222-1-122-1-12-1-1-1-1-1-1222-1-1-1-1222222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-211-2-21111-2011000
χ13222222-12222222-1-1-1222222-1-122-1-12-1-1-1-1-1-1222-1-1-1-1222-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-11111111111110000000000000000000000002-1-122-1-1-1-1-2011000
χ14222222-12222222-1-1-1222222-1-122-1-12-1-1-1-1-1-1222-1-1-1-1222-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000-211-2-2111120-1-1000
χ15222222-1-2-222222-1-1-12-2-2-2-22-1-122-1-12-1-1-1-111-2-2-21111-2-2-222-2-200002222-2-2-2-200000000-1-1-1-1111111-1-111-1-1-1-111110000000000000000000000000−i3i300−i3−i3i3i300−i3i3000
χ16222222-1-2-222222-1-1-12-2-2-2-22-1-122-1-12-1-1-1-111-2-2-21111-2-2-222-2-200002222-2-2-2-200000000-1-1-1-1111111-1-111-1-1-1-111110000000000000000000000000i3−i300i3i3−i3−i300i3−i3000
χ17222222-1-2-222222-1-1-12-2-2-2-22-1-122-1-12-1-1-1-111-2-2-21111-2-2-2-2-2220000-2-2-2-2222200000000-1-1-1-111111111-1-11111-1-1-1-10000000000000000000000000−i3i300−i3−i3i3i300i3−i3000
χ18222222-1-2-222222-1-1-12-2-2-2-22-1-122-1-12-1-1-1-111-2-2-21111-2-2-2-2-2220000-2-2-2-2222200000000-1-1-1-111111111-1-11111-1-1-1-10000000000000000000000000i3−i300i3i3−i3−i300−i3i3000
χ1922222-122222-1-1-12222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ2022222-122222-1-1-12222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111110000000000000000
χ2122222-122222-1-1-12222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ2222222-122222-1-1-12222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-10000000000000000
χ2322222-12-2-222-1-1-122221111-12-1-1-122-1-1-1-12-2-2-2111111-21122-2-20000-1-1-1-111113333−3−3−3−3-1-1-1-1-2-2111122-2-2-1-1-1-1111100003333−3−3−3−300003333−3−3−3−30000000000000000
χ2422222-12-2-222-1-1-122221111-12-1-1-122-1-1-1-12-2-2-2111111-21122-2-20000-1-1-1-11111−3−3−3−33333-1-1-1-1-2-2111122-2-2-1-1-1-111110000−3−3−3−333330000−3−3−3−333330000000000000000
χ2522222-12-2-222-1-1-122221111-12-1-1-122-1-1-1-12-2-2-2111111-211-2-22200001111-1-1-1-13333−3−3−3−3-1-1-1-1-2-21111-2-2221111-1-1-1-100003333−3−3−3−30000−3−3−3−333330000000000000000
χ2622222-12-2-222-1-1-122221111-12-1-1-122-1-1-1-12-2-2-2111111-211-2-22200001111-1-1-1-1−3−3−3−33333-1-1-1-1-2-21111-2-2221111-1-1-1-10000−3−3−3−3333300003333−3−3−3−30000000000000000
χ272222-12222-1-1222222-12222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000222-1-1-1-1-1-10200-1-10
χ282222-12222-1-1222222-12222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-21111110-200110
χ292222-12222-1-1222222-12222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000222-1-1-1-1-1-10-200110
χ302222-12222-1-1222222-12222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000-2-2-21111110200-1-10
χ3122-2-2222002-2-22-22-2-2-200002222-22-2-2-22-2-2000000000000002i−2i22−2−200002i2i−2i−2i22−2−222−2−222-2-2000000002i−2i00002i2i−2i−2i22−2−222−2−222−2−2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3222-2-2222002-2-22-22-2-2-200002222-22-2-2-22-2-2000000000000002i−2i−2−22200002i2i−2i−2i−2−222−2−22222-2-2000000002i−2i00002i2i−2i−2i−2−222−2−222−2−222i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3322-2-2222002-2-22-22-2-2-200002222-22-2-2-22-2-200000000000000−2i2i22−2−20000−2i−2i2i2i22−2−222−2−222-2-200000000−2i2i0000−2i−2i2i2i22−2−222−2−222−2−2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3422-2-2222002-2-22-22-2-2-200002222-22-2-2-22-2-200000000000000−2i2i−2−2220000−2i−2i2i2i−2−222−2−22222-2-200000000−2i2i0000−2i−2i2i2i−2−222−2−222−2−222−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3522-2-22-12002-21-112-2-2-23−33−3-12-1-112-211-11-20003−333−3−303−3002i−2i22−2−2−i3−i3i3i3−i−iiiζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23-1-1110033−3−3002i−2i−i3−i3i3i3−i−iii22−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ230000000000000000
χ3622-2-22-12002-21-112-2-2-23−33−3-12-1-112-211-11-20003−333−3−303−3002i−2i−2−222−i3−i3i3i3−i−iii−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23-1-1110033−3−3002i−2i−i3−i3i3i3−i−iii−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ230000000000000000
χ3722-2-22-12002-21-112-2-2-23−33−3-12-1-112-211-11-20003−333−3−303−300−2i2i22−2−2i3i3−i3−i3ii−i−iζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23-1-1110033−3−300−2i2ii3i3−i3−i3ii−i−i22−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23i2i2−i2−i2−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ230000000000000000
χ3822-2-22-12002-21-112-2-2-23−33−3-12-1-112-211-11-20003−333−3−303−300−2i2i−2−222i3i3−i3−i3ii−i−i−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23-1-1110033−3−300−2i2ii3i3−i3−i3ii−i−i−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−i2−i2i2i2ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ230000000000000000
χ3922-2-22-12002-21-112-2-2-2−33−33-12-1-112-211-11-2000−33−3−3330−33002i−2i22−2−2i3i3−i3−i3−i−iiiζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7-1-11100−3−333002i−2ii3i3−i3−i3−i−iii22−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ70000000000000000
χ4022-2-22-12002-21-112-2-2-2−33−33-12-1-112-211-11-2000−33−3−3330−33002i−2i−2−222i3i3−i3−i3−i−iii−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7-1-11100−3−333002i−2ii3i3−i3−i3−i−iii−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ70000000000000000
χ4122-2-22-12002-21-112-2-2-2−33−33-12-1-112-211-11-2000−33−3−3330−3300−2i2i22−2−2−i3−i3i3i3ii−i−iζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7-1-11100−3−33300−2i2i−i3−i3i3i3ii−i−i22−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7i2i2−i2−i2−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ70000000000000000
χ4222-2-22-12002-21-112-2-2-2−33−33-12-1-112-211-11-2000−33−3−3330−3300−2i2i−2−222−i3−i3i3i3ii−i−i−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7-1-11100−3−33300−2i2i−i3−i3i3i3ii−i−i−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−i2−i2i2i2ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ70000000000000000
χ432-22-222200-22-2-22-22-2-20000222-22-22-2-2-22-20000000000002i−2i002−22−22i−2i2i−2i00002−22−22−22−22-22-20000002i−2i002i−2i2i−2i00002−22−22−22−22−22−2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ442-22-222200-22-2-22-22-2-20000222-22-22-2-2-22-20000000000002i−2i00−22−222i−2i2i−2i0000−22−22−22−222-22-20000002i−2i002i−2i2i−2i0000−22−22−22−22−22−22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ452-22-222200-22-2-22-22-2-20000222-22-22-2-2-22-2000000000000−2i2i002−22−2−2i2i−2i2i00002−22−22−22−22-22-2000000−2i2i00−2i2i−2i2i00002−22−22−22−22−22−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ462-22-222200-22-2-22-22-2-20000222-22-22-2-2-22-2000000000000−2i2i00−22−22−2i2i−2i2i0000−22−22−22−222-22-2000000−2i2i00−2i2i−2i2i0000−22−22−22−22−22−22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ472-22-22-1200-2211-1-22-2-23−3−33-12-11-1-22111-1-2000−333−33−303−32i−2i002−22−2−ii−ii−i3i3−i3i3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23-11-11003−33−32i−2i00−ii−ii−i3i3−i3i32−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ70000000000000000
χ482-22-22-1200-2211-1-22-2-23−3−33-12-11-1-22111-1-2000−333−33−303−32i−2i00−22−22−ii−ii−i3i3−i3i3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23-11-11003−33−32i−2i00−ii−ii−i3i3−i3i3−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ70000000000000000
χ492-22-22-1200-2211-1-22-2-23−3−33-12-11-1-22111-1-2000−333−33−303−3−2i2i002−22−2i−ii−ii3−i3i3−i3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23-11-11003−33−3−2i2i00i−ii−ii3−i3i3−i32−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ70000000000000000
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χ1224-4-44-2-24-4422-222-4-44-222-2-21-2-2-1-1221-222-2-44-2112-2-222-1-10000000000000000−232323−2323−23−23231-1-112-2-111-100000000000000003−3−33−333−30000000000000000000000000000
χ1238888-4-4-488-4-4-4-4-4-4-4-4-4-4-4-4-4222222222222-4-4-4222222-422000000000000000000000000-1-1-1-122-1-1-1-10000000000000000000000000000000000000000000000000000
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
χ12588-8-8-48-400-44-88-8-44440000-42-4-442-244-44-200000000000000000000000000000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ12688-8-8-4-4-400-444-44-444443−4343−432222-22-2-2-22-2-2000−2323−23−2323230−2323000000000000000000000000-1-1110033−3−30000000000000000000000000000000000000000000000000000
χ12788-8-8-4-4-400-444-44-4444−4343−43432222-22-2-2-22-2-200023−232323−23−23023−23000000000000000000000000-1-11100−3−3330000000000000000000000000000000000000000000000000000
χ1288-88-8-48-4004-4-8-884-4440000-42-44-4-22444-4-20000000000000000000000000000000000002-22-20000000000000000000000000000000000000000000000000000000000
χ1298-88-8-4-4-4004-444-44-44443−43−4343222-22-22-2-2-22-200023−23−2323−23230−2323000000000000000000000000-11-11003−33−30000000000000000000000000000000000000000000000000000
χ1308-88-8-4-4-4004-444-44-444−434343−43222-22-22-2-2-22-2000−232323−2323−23023−23000000000000000000000000-11-1100−33−330000000000000000000000000000000000000000000000000000
χ1318-8-88-4-4-48-844-44444-4-4-4-444222-2-2-2-222-2-22-444-2-22-2-22-422000000000000000000000000-111-12-2-111-10000000000000000000000000000000000000000000000000000
χ1328-8-88-4-4-4-8844-44444-4-444-4-4222-2-2-2-222-2-224-4-422-222-24-2-2000000000000000000000000-111-1-221-1-110000000000000000000000000000000000000000000000000000

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