Finite Group Databasebeta

← Group #13156665

Character table — Group #13156665

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132
size11112222222222222222224444444444444444444444446666666666666666666666668888888888121212121212121212121212121212121212121212121212181818181818181818181818242424242424242424727272727272216
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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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-200002222-2-2-2-2000000002222-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000
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
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χ15222222-1-2-2222-122-12-1-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-222-2-200002222-2-2-2-200000000-1-1-1-1111111-1-111-1-1-1-11111000000000000000000000000000−i3i3−i3−i3i3i30000−i3i30
χ16222222-1-2-2222-122-12-1-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-222-2-200002222-2-2-2-200000000-1-1-1-1111111-1-111-1-1-1-11111000000000000000000000000000i3−i3i3i3−i3−i30000i3−i30
χ17222222-1-2-2222-122-12-1-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-2-2-2220000-2-2-2-2222200000000-1-1-1-111111111-1-11111-1-1-1-1000000000000000000000000000−i3i3−i3−i3i3i30000i3−i30
χ18222222-1-2-2222-122-12-1-2-2-2-22-1-122-12-1-1-1-1-1-211-2-21111-2-2-2-2-2220000-2-2-2-2222200000000-1-1-1-111111111-1-11111-1-1-1-1000000000000000000000000000i3−i3i3i3−i3−i30000−i3i30
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
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χ292222-12222-1-122222-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-10000000000001111111111110000000000002-1-122-1-1-1-10-211000
χ302222-12222-1-122222-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1000000000000111111111111000000000000-211-2-2111102-1-1000
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
χ4322-2-2-1222-21-122-2-2-21-222-2-2-1-12111-1-12-2-2112-21122-2-2-1-1-1000022-2-20000000022-2-222-2-2-111-1-11-1-111000000000000-1-111-1-111-1-11100000000000003−3003−33−3003−3000
χ4422-2-2-1222-21-122-2-2-21-222-2-2-1-12111-1-12-2-2112-21122-2-2-1-1-1000022-2-20000000022-2-222-2-2-111-1-11-1-111000000000000-1-111-1-111-1-1110000000000000−3300−33−3300−33000
χ4522-2-2-1222-21-122-2-2-21-222-2-2-1-12111-1-12-2-2112-21122-2-2-1-1-10000-2-22200000000-2-222-2-222-111-1-11-1-11100000000000011-1-111-1-111-1-100000000000003−3003−33−300−33000
χ4622-2-2-1222-21-122-2-2-21-222-2-2-1-12111-1-12-2-2112-21122-2-2-1-1-10000-2-22200000000-2-222-2-222-111-1-11-1-11100000000000011-1-111-1-111-1-10000000000000−3300−33−33003−3000
χ472-22-2222002-2-2-22-22-2-200002222-22-2-2-22-2-20000000000002-2002−22−22-22-200002−22−22−22−222-2-20000002-2002-22-200002−22−22−22−22−22−22−22−22−22−22−22−20000000000000000
χ482-22-2222002-2-2-22-22-2-200002222-22-2-2-22-2-20000000000002-200−22−222-22-20000−22−22−22−2222-2-20000002-2002-22-20000−22−22−22−22−22−22−22−22−22−22−22−220000000000000000
χ492-22-2222002-2-2-22-22-2-200002222-22-2-2-22-2-2000000000000-22002−22−2-22-2200002−22−22−22−222-2-2000000-2200-22-2200002−22−22−22−22−22−2−22−22−22−22−22−220000000000000000
χ502-22-2222002-2-2-22-22-2-200002222-22-2-2-22-2-2000000000000-2200−22−22-22-220000−22−22−22−2222-2-2000000-2200-22-220000−22−22−22−22−22−222−22−22−22−22−22−20000000000000000
χ512-22-22-12002-21-2-112-2-23−33−3-12-1-1121-21-11-20003−33−33−303−32-2002−22−2-11-113−33−3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23-1-111003−33−32-200-11-113−33−32−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230000000000000000
χ522-22-22-12002-21-2-112-2-23−33−3-12-1-1121-21-11-20003−33−33−303−32-200−22−22-11-113−33−3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23-1-111003−33−32-200-11-113−33−3−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230000000000000000
χ532-22-22-12002-21-2-112-2-23−33−3-12-1-1121-21-11-20003−33−33−303−3-22002−22−21-11-1−33−33ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23-1-111003−33−3-22001-11-1−33−332−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ230000000000000000
χ542-22-22-12002-21-2-112-2-23−33−3-12-1-1121-21-11-20003−33−33−303−3-2200−22−221-11-1−33−33−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23-1-111003−33−3-22001-11-1−33−33−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ230000000000000000
χ552-22-22-12002-21-2-112-2-2−33−33-12-1-1121-21-11-2000−33−33−330−332-2002−22−2-11-11−33−33ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7-1-11100−33−332-200-11-11−33−332−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70000000000000000
χ562-22-22-12002-21-2-112-2-2−33−33-12-1-1121-21-11-2000−33−33−330−332-200−22−22-11-11−33−33−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7-1-11100−33−332-200-11-11−33−33−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70000000000000000
χ572-22-22-12002-21-2-112-2-2−33−33-12-1-1121-21-11-2000−33−33−330−33-22002−22−21-11-13−33−3ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7-1-11100−33−33-22001-11-13−33−32−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ70000000000000000
χ582-22-22-12002-21-2-112-2-2−33−33-12-1-1121-21-11-2000−33−33−330−33-2200−22−221-11-13−33−3−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7-1-11100−33−33-22001-11-13−33−3−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ70000000000000000
χ592-2-2222200-2-2-2-2-22-2220000222-22-2-2-2-2-222000000000000002-22−2−2200002-2-222−2−222−2−222-22-2000000002-200002-2-222−2−222−2−222−2−222−2−222−2−222−2−220000000000000000
χ602-2-2222200-2-2-2-2-22-2220000222-22-2-2-2-2-222000000000000002-2−222−200002-2-22−222−2−222−22-22-2000000002-200002-2-22−222−2−222−2−222−2−222−2−222−2−222−20000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.