Finite Group Databasebeta

← Group #13156649

Character table — Group #13156649

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size11112222222222222222224444444444444444444444446666666666666666666666668888888888121212121212121212121212121212121212121212121212181818181818181818181818242424242424242424727272727272216
order1222333446666666661212121233366666666612121212121212121212121244448888121212121212121224242424242424243666121212121212121212121212121212121212242424242424242424242424888824242424242424244121212121212121244121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ51111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1111-1-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-200002222-2-2-2-2000000002222-2-2-2-2-2-2-2-2222222-2-2-2-20000000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2220000-2-2-2-22222000000002222-2-2-2-2-2-222-2-2-2-2-2-222220000000000000000000000000000000000000000
χ11222222-12222-1222-1-1222222-1-1-1-1-12-1-122-122-12222-1-1-1-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-122-1-1-1-102-1-1000
χ12222222-12222-1222-1-1222222-1-1-1-1-12-1-122-122-12222-1-1-1-1-1000022220000000022222222-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-211-2-211110-211000
χ13222222-12222-1222-1-1222222-1-1-1-1-12-1-122-122-12222-1-1-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-10000000000001111111111110000000000002-1-122-1-1-1-10-211000
χ14222222-12222-1222-1-1222222-1-1-1-1-12-1-122-122-12222-1-1-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000-211-2-2111102-1-1000
χ1522222-12222-1222-122-12222-12-122-1-12-1-1-1-1-1-12-1-1-1-122222222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000222-1-1-1-1-1-12000-1-10
χ1622222-12222-1222-122-12222-12-122-1-12-1-1-1-1-1-12-1-1-1-122222222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2111111-2000110
χ1722222-12222-1222-122-12222-12-122-1-12-1-1-1-1-1-12-1-1-1-122222-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000222-1-1-1-1-1-1-2000110
χ1822222-12222-1222-122-12222-12-122-1-12-1-1-1-1-1-12-1-1-1-122222-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000-2-2-21111112000-1-10
χ1922222-12-2-22-1222-122-1-2-2-2-2-12-122-1-12-1-1-1-111-21111-2-2-2-2-222-2-200002222-2-2-2-200000000-1-1-1-111111111-1-1-1-1-1-11111000000000000000000000000000−i3i3−i3−i3i3i30000−i3i30
χ2022222-12-2-22-1222-122-1-2-2-2-2-12-122-1-12-1-1-1-111-21111-2-2-2-2-222-2-200002222-2-2-2-200000000-1-1-1-111111111-1-1-1-1-1-11111000000000000000000000000000i3−i3i3i3−i3−i30000i3−i30
χ2122222-12-2-22-1222-122-1-2-2-2-2-12-122-1-12-1-1-1-111-21111-2-2-2-2-2-2-2220000-2-2-2-2222200000000-1-1-1-1111111-1-1111111-1-1-1-1000000000000000000000000000−i3i3−i3−i3i3i30000i3−i30
χ2222222-12-2-22-1222-122-1-2-2-2-2-12-122-1-12-1-1-1-111-21111-2-2-2-2-2-2-2220000-2-2-2-2222200000000-1-1-1-1111111-1-1111111-1-1-1-1000000000000000000000000000i3−i3i3i3−i3−i30000−i3i30
χ232222-12222-122-1-12222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ242222-12222-122-1-12222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111110000000000000000
χ252222-12222-122-1-12222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ262222-12222-122-1-12222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-10000000000000000
χ272222-122-2-2-122-1-122221111-1-12-1-12-1-12-1-12-2-2-2111111-21122-2-20000-1-1-1-111113333−3−3−3−3-1-1-1-1-2-21111-2-222-1-1-1-1111100003333−3−3−3−300003333−3−3−3−30000000000000000
χ282222-122-2-2-122-1-122221111-1-12-1-12-1-12-1-12-2-2-2111111-21122-2-20000-1-1-1-11111−3−3−3−33333-1-1-1-1-2-21111-2-222-1-1-1-111110000−3−3−3−333330000−3−3−3−333330000000000000000
χ292222-122-2-2-122-1-122221111-1-12-1-12-1-12-1-12-2-2-2111111-211-2-22200001111-1-1-1-13333−3−3−3−3-1-1-1-1-2-2111122-2-21111-1-1-1-100003333−3−3−3−30000−3−3−3−333330000000000000000
χ302222-122-2-2-122-1-122221111-1-12-1-12-1-12-1-12-2-2-2111111-211-2-22200001111-1-1-1-1−3−3−3−33333-1-1-1-1-2-2111122-2-21111-1-1-1-10000−3−3−3−3333300003333−3−3−3−30000000000000000
χ3122-2-22222-2222-2-2-2-2-2-222-2-2222-2-2-2222-2-2-22-2-222-2-2-2-2222000022-2-20000000022-2-222-2-22-2-222-222-2-200000000000022-2-222-2-222-2-20000000000000000000000000000
χ3222-2-22222-2222-2-2-2-2-2-222-2-2222-2-2-2222-2-2-22-2-222-2-2-2-22220000-2-22200000000-2-222-2-2222-2-222-222-2-2000000000000-2-222-2-222-2-2220000000000000000000000000000
χ3322-2-2222-22222-2-2-2-2-2-2-2-222222-2-2-2222-2-2-2-222-2-22222-2-2-20000000000000000000000002-2-22-22-2-22200000000000000000000000022-2-222-2-222-2-20000000000000000
χ3422-2-2222-22222-2-2-2-2-2-2-2-222222-2-2-2222-2-2-2-222-2-22222-2-2-20000000000000000000000002-2-22-22-2-222000000000000000000000000-2-222-2-222-2-2220000000000000000
χ3522-2-222-12-222-1-2-2-211-222-2-22-1-11112-1-1-2-212-2122-2-211-1-1-1000022-2-20000000022-2-222-2-2-111-1-11-1-111000000000000-1-111-1-111-1-11100000000000003−3003−33−3003−3000
χ3622-2-222-12-222-1-2-2-211-222-2-22-1-11112-1-1-2-212-2122-2-211-1-1-1000022-2-20000000022-2-222-2-2-111-1-11-1-111000000000000-1-111-1-111-1-1110000000000000−3300−33−3300−33000
χ3722-2-222-12-222-1-2-2-211-222-2-22-1-11112-1-1-2-212-2122-2-211-1-1-10000-2-22200000000-2-222-2-222-111-1-11-1-11100000000000011-1-111-1-111-1-100000000000003−3003−33−300−33000
χ3822-2-222-12-222-1-2-2-211-222-2-22-1-11112-1-1-2-212-2122-2-211-1-1-10000-2-22200000000-2-222-2-222-111-1-11-1-11100000000000011-1-111-1-111-1-10000000000000−3300−33−33003−3000
χ3922-2-2-1222-2-12211-2-2-2-2-1-111-1-1211-2-1-1211-22-2-2-1-111112-1-1000022-2-233−3−333−3−3-1-111-1-111-111-12-2-1-111000033−3−333−3−322-2-2-1-111-1-111000033−3−3−3−3330000000000000000
χ4022-2-2-1222-2-12211-2-2-2-2-1-111-1-1211-2-1-1211-22-2-2-1-111112-1-1000022-2-2−3−333−3−333-1-111-1-111-111-12-2-1-1110000−3−333−3−33322-2-2-1-111-1-1110000−3−33333−3−30000000000000000
χ4122-2-2-1222-2-12211-2-2-2-2-1-111-1-1211-2-1-1211-22-2-2-1-111112-1-10000-2-22233−3−333−3−311-1-111-1-1-111-12-2-1-111000033−3−333−3−3-2-22211-1-111-1-10000−3−33333−3−30000000000000000
χ4222-2-2-1222-2-12211-2-2-2-2-1-111-1-1211-2-1-1211-22-2-2-1-111112-1-10000-2-222−3−333−3−33311-1-111-1-1-111-12-2-1-1110000−3−333−3−333-2-22211-1-111-1-1000033−3−3−3−3330000000000000000
χ4322-2-2-122-22-12211-2-2-2-211-1-1-1-1211-2-1-1211-2-22211-1-1-1-1-2110000000033−3−3−3−33333−3−3−3−333-111-1-2211-1-1000033−3−3−3−333000033−3−3−3−333-2-22211-1-111-1-10000000000000000
χ4422-2-2-122-22-12211-2-2-2-211-1-1-1-1211-2-1-1211-2-22211-1-1-1-1-2110000000033−3−3−3−333−3−33333−3−3-111-1-2211-1-1000033−3−3−3−3330000−3−33333−3−322-2-2-1-111-1-1110000000000000000
χ4522-2-2-122-22-12211-2-2-2-211-1-1-1-1211-2-1-1211-2-22211-1-1-1-1-21100000000−3−33333−3−333−3−3−3−333-111-1-2211-1-10000−3−33333−3−3000033−3−3−3−33322-2-2-1-111-1-1110000000000000000
χ4622-2-2-122-22-12211-2-2-2-211-1-1-1-1211-2-1-1211-2-22211-1-1-1-1-21100000000−3−33333−3−3−3−33333−3−3-111-1-2211-1-10000−3−33333−3−30000−3−33333−3−3-2-22211-1-111-1-10000000000000000
χ472-22-222200-2-2-22-2-22-2200002222-2-2-2-2-22-220000000000002-200−i2i2−i2i22-22-20000−i2i2−i2i2−i2i2−i2i222-2-2000000002-22-22-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ482-22-222200-2-2-22-2-22-2200002222-2-2-2-2-22-220000000000002-200i2−i2i2−i22-22-20000i2−i2i2−i2i2−i2i2−i222-2-2000000002-22-22-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ492-22-222200-2-2-22-2-22-2200002222-2-2-2-2-22-22000000000000-2200−i2i2−i2i2-22-220000−i2i2−i2i2−i2i2−i2i222-2-200000000-22-22-220000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000000000
χ502-22-222200-2-2-22-2-22-2200002222-2-2-2-2-22-22000000000000-2200i2−i2i2−i2-22-220000i2−i2i2−i2i2−i2i2−i222-2-200000000-22-22-220000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000000000
χ512-22-2-122001-2-2-11-22-223−33−3-1-12-11-211-2-1120003−33−33−303−32-200−i2i2−i2i2-11-113−33−3ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-1-111003−33−3002-2-11-113−33−3−i2i2−i2i2ζ5+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
χ522-22-2-122001-2-2-11-22-223−33−3-1-12-11-211-2-1120003−33−33−303−32-200i2−i2i2−i2-11-113−33−3−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-1-111003−33−3002-2-11-113−33−3i2−i2i2−i2−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
χ532-22-2-122001-2-2-11-22-223−33−3-1-12-11-211-2-1120003−33−33−303−3-2200−i2i2−i2i21-11-1−33−33ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23-1-111003−33−300-221-11-1−33−33−i2i2−i2i2ζ5+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
χ542-22-2-122001-2-2-11-22-223−33−3-1-12-11-211-2-1120003−33−33−303−3-2200i2−i2i2−i21-11-1−33−33−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23-1-111003−33−300-221-11-1−33−33i2−i2i2−i2−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
χ552-22-2-122001-2-2-11-22-22−33−33-1-12-11-211-2-112000−33−33−330−332-200−i2i2−i2i2-11-11−33−33ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7-1-11100−33−33002-2-11-11−33−33−i2i2−i2i2ζ13+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
χ562-22-2-122001-2-2-11-22-22−33−33-1-12-11-211-2-112000−33−33−330−332-200i2−i2i2−i2-11-11−33−33−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7-1-11100−33−33002-2-11-11−33−33i2−i2i2−i2−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
χ572-22-2-122001-2-2-11-22-22−33−33-1-12-11-211-2-112000−33−33−330−33-2200−i2i2−i2i21-11-13−33−3ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7-1-11100−33−3300-221-11-13−33−3−i2i2−i2i2ζ13+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
χ12588-8-8-4-4-48-8-4-4-4444444-4-444222-2-2-2222-2-2-2-44422-2-2-2-2-422000000000000000000000000-111-12-2-1-1110000000000000000000000000000000000000000000000000000
χ12688-8-8-4-4-4-88-4-4-444444444-4-4222-2-2-2222-2-2-24-4-4-2-222224-2-2000000000000000000000000-111-1-2211-1-10000000000000000000000000000000000000000000000000000
χ1278-88-88-4-400-8448-84-44-40000-4-42-44-244-2-44200000000000000000000000000000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ1288-88-8-4-4-400444-444-44-443−4343−432222-2-2-2-2-22-22000−2323−2323−23230−2323000000000000000000000000-1-111003−33−30000000000000000000000000000000000000000000000000000
χ1298-88-8-4-4-400444-444-44-4−4343−43432222-2-2-2-2-22-2200023−2323−2323−23023−23000000000000000000000000-1-11100−33−330000000000000000000000000000000000000000000000000000
χ1308-8-888-4-400-844-88-44-440000-4-424-4244-24-4-20000000000000000000000000000000000002-22-20000000000000000000000000000000000000000000000000000000000
χ1318-8-88-4-4-4004444-4-44-4443−43−4343222-222-2-2-2-22-2000−232323−2323−230−2323000000000000000000000000-11-11003−3−330000000000000000000000000000000000000000000000000000
χ1328-8-88-4-4-4004444-4-44-44−434343−43222-222-2-2-2-22-200023−23−2323−2323023−23000000000000000000000000-11-1100−333−30000000000000000000000000000000000000000000000000000

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