Finite Group Databasebeta

← Group #13155995

Character table — Group #13155995

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212181824242424242424242436363636363636363672727272216
order12223334466666666612121212333666666666121212121212121212121212366612121212121288882424242424242424242424242424242424242424242424242424242424242424442666666664444412121212121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11
χ511111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111111111-1-1-111-1-1-1-111-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-11111-1-1-1-11
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111111111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000002200000000000-20022-2-200000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000-2-200000000000200-2-22200000
χ11222222-12222-12-122-1222222-1-122-1-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100222-1-1-1-1-1-1000220000-1-1000
χ12222222-12222-12-122-1222222-1-122-1-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2111111000-2-2000011000
χ13222222-12222-12-122-1222222-1-122-1-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-200000000000011111111111100222-1-1-1-1-1-1000-2-2000011000
χ14222222-12222-12-122-1222222-1-122-1-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-200000000000011111111111100-2-2-2111111000220000-1-1000
χ1522222-1222-1-1222222-12222-12-1-1-122-1-1-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000002-1-122-1-1-1-122000000000-1-10
χ1622222-1222-1-1222222-12222-12-1-1-122-1-1-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000-211-2-21111-2-2000000000110
χ1722222-1222-1-1222222-12222-12-1-1-122-1-1-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-20000111111111111000000000000002-1-122-1-1-1-1-2-2000000000110
χ1822222-1222-1-1222222-12222-12-1-1-122-1-1-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2000011111111111100000000000000-211-2-2111122000000000-1-10
χ192222-12222222-12-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12200000000000200-1-1-1-100000
χ202222-12222222-12-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-200000000000-200111100000
χ212222-12222222-12-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-200000000000-200111100000
χ222222-12222222-12-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2111111112200000000000200-1-1-1-100000
χ232222-122-2-2222-12-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−333−3−300003333−3−3−3−300003333−3−3−3−32200000000000-200-1-11100000
χ242222-122-2-2222-12-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333-2-20000000000020011-1-100000
χ252222-122-2-2222-12-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3-2-20000000000020011-1-100000
χ262222-122-2-2222-12-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−333−3−3330000−3−3−3−333330000−3−3−3−333332200000000000-200-1-11100000
χ2722-2-2222002-22-2-22-2-2-200002222-22-22-2-2-2-200000000000022-2-2000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22-2000000000000002-20000000
χ2822-2-2222002-22-2-22-2-2-200002222-22-22-2-2-2-200000000000022-2-2000000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2-2200000000000000-220000000
χ2922-2-2222002-22-2-22-2-2-200002222-22-22-2-2-2-200000000000022-2-2000000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2-2200000000000000-220000000
χ3022-2-2222002-22-2-22-2-2-200002222-22-22-2-2-2-200000000000022-2-2000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22-2000000000000002-20000000
χ3122-2-2-122002-221-2-11-2-23−33−3-1-12-11-112-211-2003−33−3003−33−3-1-1110033−3−3−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−i2−i2i2i2ζ5+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−ζ232-200000000000000-113−300000
χ3222-2-2-122002-221-2-11-2-23−33−3-1-12-11-112-211-2003−33−3003−33−3-1-1110033−3−3−i2i2i2−i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−i2−i2i2i2ζ5+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+ζ23-22000000000000001-1−3300000
χ3322-2-2-122002-221-2-11-2-23−33−3-1-12-11-112-211-2003−33−3003−33−3-1-1110033−3−3i2−i2−i2i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23i2i2−i2−i2−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−ζ23-22000000000000001-1−3300000
χ3422-2-2-122002-221-2-11-2-23−33−3-1-12-11-112-211-2003−33−3003−33−3-1-1110033−3−3i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23i2i2−i2−i2−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+ζ232-200000000000000-113−300000
χ3522-2-2-122002-221-2-11-2-2−33−33-1-12-11-112-211-200−33−3300−33−33-1-11100−3−333−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−i2−i2i2i2ζ13+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−ζ72-200000000000000-11−3300000
χ3622-2-2-122002-221-2-11-2-2−33−33-1-12-11-112-211-200−33−3300−33−33-1-11100−3−333−i2i2i2−i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−i2−i2i2i2ζ13+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+ζ7-22000000000000001-13−300000
χ3722-2-2-122002-221-2-11-2-2−33−33-1-12-11-112-211-200−33−3300−33−33-1-11100−3−333i2−i2−i2i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7i2i2−i2−i2−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−ζ7-22000000000000001-13−300000
χ3822-2-2-122002-221-2-11-2-2−33−33-1-12-11-112-211-200−33−3300−33−33-1-11100−3−333i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7i2i2−i2−i2−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+ζ72-200000000000000-11−3300000
χ392-22-22222-2-2-2-222-2-2-2222-2-2222-2-2-2-2-2-2222222222-2-2-2-2-2-22-2-222-22-22-2000000000000000000000000000000000000000000000000002i−2i00002i−2i000
χ402-22-22222-2-2-2-222-2-2-2222-2-2222-2-2-2-2-2-2222222222-2-2-2-2-2-22-2-222-22-22-200000000000000000000000000000000000000000000000000−2i2i0000−2i2i000
χ412-22-2222-22-2-2-222-2-2-22-2-222222-2-2-2-2-2-2222-2-2-2-2-2-22222222-2-22-22-22-22000000000000000000000000000000000000000000000002-20000000002-20
χ422-22-2222-22-2-2-222-2-2-22-2-222222-2-2-2-2-2-2222-2-2-2-2-2-22222222-2-22-22-22-2200000000000000000000000000000000000000000000000-22000000000-220
χ432-22-222-12-2-2-212-1-2-21222-2-22-1-1-2-211112-1-1-1222-1-11-2-2-211-111-1-11-11-110000000000000000000000003−33−33−33−33−33−300000−i3i3−i3−i3i3i30002i−2i0000−ii000
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χ462-22-222-12-2-2-212-1-2-21222-2-22-1-1-2-211112-1-1-1222-1-11-2-2-211-111-1-11-11-11000000000000000000000000−33−33−33−33−33−3300000i3−i3i3i3−i3−i30002i−2i0000−ii000
χ472-22-22-12-2211-222-2-2-2-1-2-222-12-111-2-211-12-1-2111-2-22-1-1-122-111-11-11-11-1000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000−i3i300−i3i3−i3i32-2000000000-110
χ482-22-22-12-2211-222-2-2-2-1-2-222-12-111-2-211-12-1-2111-2-22-1-1-122-111-11-11-11-1000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000000i3−i300i3−i3i3−i3-220000000001-10
χ492-22-22-12-2211-222-2-2-2-1-2-222-12-111-2-211-12-1-2111-2-22-1-1-122-111-11-11-11-1000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000−i3i300−i3i3−i3i3-220000000001-10
χ502-22-22-12-2211-222-2-2-2-1-2-222-12-111-2-211-12-1-2111-2-22-1-1-122-111-11-11-11-1000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000000i3−i300i3−i3i3−i32-2000000000-110
χ51444444-2-4-444-24-244-24-4-4-4-44-2-244-2-2-2-24-2-22-4-4-4222-4-4-422-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
χ5244444-24-4-4-2-2444444-2-4-4-4-4-24-2-2-244-2-2-24-2-4222-4-4-4222-4-4-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
χ5344444-2-244-2-2-24-244-2-24444-2-21-2-2-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000004-2-2-2-2111100000000000000
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χ5544444-2-2-4-4-2-2-24-244-2-2-4-4-4-4-2-21-2-2-2-211-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000003-3-3300000000000000
χ5644444-2-2-4-4-2-2-24-244-2-2-4-4-4-4-2-21-2-2-2-211-2-212222222222221111-1-1-1-1-1-10000000000000000000000000000000000000000000-333-300000000000000
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χ594444-24-2-4-444-2-2-2-2-2-242222-21-2-2-211-2-2-21-22-422-1-12-422-1-1111122-1-1-1-1000000002323−23−230000000000000000−3−3−3−333330000000000000000000000000
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χ634444-2-24-4-4-2-24-24-2-24-222221-2-211-2-2-2-21-2-2-42-1-122-42-1-122111122-1-1-1-100002323−23−2300000000−3−3−3−333330000000000000000000000000000000000000
χ644444-2-24-4-4-2-24-24-2-24-222221-2-211-2-2-2-21-2-2-42-1-122-42-1-122111122-1-1-1-10000−23−232323000000003333−3−3−3−30000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.