Finite Group Databasebeta

← Group #13144039

Character table — Group #13144039

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111222222222444444444444666666666666666688812121212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636363636727272727272
order12336624466121212122444661212121212123333666612121212121212128242466661212121212121212121212121212121212121212666612121212242424242424242424446612121212121226682424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-11111-1-1-1-11111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111-1-11111-1-1-1-11111111111111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111-1-111-1-1-1-111111111111111111111-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1111
χ6111111111111111-1-111-1-1-1-111111111111111111111-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1
χ7111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1111-1-1-1
χ8111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1111
χ92222222222222222222222222222-1-1-12-1-1-122-1-1-1-1-1-12222-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1000000000000000000
χ10222222222222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1222-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1000000000000000000
χ11222222222222222222222222222-1-12-1-1-12-1-1-1-1-122-1-1222-1-12-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-12-1-1-12-1-1-1-1-122-1-1000000000000000000
χ12222222222222222222222222222-1-1-12-1-1-12-1-1-1-1-1-122222-1-1-12-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-12-1-1-12-1-1-1-1-1-122000000000000000000
χ1322222222222222222-2-22222-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-1-2-2-22-1-1-12-1-1-1-2-2-2-21111111111112-1-1-12-1-1-1-2-2111111000000000000000000
χ1422222222222222222-2-22222-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-2-2-2-12-1-1-12-1-11111-2-2-2-211111111-12-1-1-12-1-111-2-21111000000000000000000
χ1522222222222222222-2-22222-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-2-2-2-1-12-1-1-12-111111111-2-2-2-21111-1-12-1-1-12-11111-2-211000000000000000000
χ1622222222222222222-2-22222-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122-2-2-2-1-1-12-1-1-12111111111111-2-2-2-2-1-1-12-1-1-12111111-2-2000000000000000000
χ17222222222222222-2-222-2-2-2-222222-1-1-12-1-1-122-1-1-1-1-1-1-2-2-22-1-1-12-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2111-2111-2-2111111000000000000000000
χ18222222222222222-2-222-2-2-2-22222-12-1-1-12-1-1-1-122-1-1-1-1-2-2-2-12-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-11-2111-21111-2-21111000000000000000000
χ19222222222222222-2-222-2-2-2-22222-1-12-1-1-12-1-1-1-1-122-1-1-2-2-2-1-12-1-1-12-1-1-1-1-1-1-1-1-12222-1-1-1-111-2111-211111-2-211000000000000000000
χ20222222222222222-2-222-2-2-2-22222-1-1-12-1-1-12-1-1-1-1-1-122-2-2-2-1-1-12-1-1-12-1-1-1-1-1-1-1-1-1-1-1-12222111-2111-2111111-2-2000000000000000000
χ21222222222222222-2-2-2-2-2-2-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-12222-1-1-12-1-1-1-2-2-2-2111111111111-2111-211122-1-1-1-1-1-1000000000000000000
χ22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1222-12-1-1-12-1-11111-2-2-2-2111111111-2111-211-1-122-1-1-1-1000000000000000000
χ23222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1222-1-12-1-1-12-111111111-2-2-2-2111111-2111-21-1-1-1-122-1-1000000000000000000
χ24222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122222-1-1-12-1-1-12111111111111-2-2-2-2111-2111-2-1-1-1-1-1-122000000000000000000
χ252222222-2-222-2-2-2-200000000000022222222-2-2-2-2-2-2-2-20002222-2-2-2-200000000000000000000000000000000002-2000022-2-2000000
χ262222222-2-222-2-2-2-200000000000022222222-2-2-2-2-2-2-2-20002222-2-2-2-20000000000000000000000000000000000-220000-2-222000000
χ27222222-22-2-2-222-2-20000000000002222222222222222000-2-2-2-2-2-2-2-2000000000000000000000000000000002-20022-2-20000000000
χ28222222-22-2-2-222-2-20000000000002222222222222222000-2-2-2-2-2-2-2-200000000000000000000000000000000-2200-2-2220000000000
χ29222222-2-22-2-2-2-2222-20022-2-2000022222222-2-2-2-2-2-2-2-2000-2-2-2-2222200000000000000002222-2-2-2-200000000000000000000000000
χ30222222-2-22-2-2-2-2222-20022-2-200002-1-1-12-1-1-1-2-2111111000-21112-1-1-1000033−3−333−3−333−3−32-1-1-1-2111003−33−33−3000000000000000000
χ31222222-2-22-2-2-2-2222-20022-2-200002-1-1-12-1-1-1-2-2111111000-21112-1-1-10000−3−333−3−333−3−3332-1-1-1-211100−33−33−33000000000000000000
χ32222222-2-22-2-2-2-2222-20022-2-20000-12-1-1-12-1-111-2-211110001-211-12-1-133−3−3000033−3−3−3−333-12-1-11-2113−3003−3−33000000000000000000
χ33222222-2-22-2-2-2-2222-20022-2-20000-12-1-1-12-1-111-2-211110001-211-12-1-1−3−3330000−3−33333−3−3-12-1-11-211−3300−333−3000000000000000000
χ34222222-2-22-2-2-2-2222-20022-2-20000-1-12-1-1-12-11111-2-21100011-21-1-12-133−3−3−3−333000033−3−3-1-12-111-213−3−33003−3000000000000000000
χ35222222-2-22-2-2-2-2222-20022-2-20000-1-12-1-1-12-11111-2-21100011-21-1-12-1−3−33333−3−30000−3−333-1-12-111-21−333−300−33000000000000000000
χ36222222-2-22-2-2-2-2222-20022-2-20000-1-1-12-1-1-12111111-2-2000111-2-1-1-1233−3−333−3−3−3−3330000-1-1-12111-23−33−3−3300000000000000000000
χ37222222-2-22-2-2-2-2222-20022-2-20000-1-1-12-1-1-12111111-2-2000111-2-1-1-12−3−333−3−33333−3−30000-1-1-12111-2−33−333−300000000000000000000
χ38222222-2-22-2-2-2-222-2200-2-222000022222222-2-2-2-2-2-2-2-2000-2-2-2-222220000000000000000-2-2-2-2222200000000000000000000000000
χ39222222-2-22-2-2-2-222-2200-2-22200002-1-1-12-1-1-1-2-2111111000-21112-1-1-1000033−3−333−3−333−3−3-21112-1-1-100−33−33−33000000000000000000
χ40222222-2-22-2-2-2-222-2200-2-22200002-1-1-12-1-1-1-2-2111111000-21112-1-1-10000−3−333−3−333−3−333-21112-1-1-1003−33−33−3000000000000000000
χ41222222-2-22-2-2-2-222-2200-2-2220000-12-1-1-12-1-111-2-211110001-211-12-1-133−3−3000033−3−3−3−3331-211-12-1-1−3300−333−3000000000000000000
χ42222222-2-22-2-2-2-222-2200-2-2220000-12-1-1-12-1-111-2-211110001-211-12-1-1−3−3330000−3−33333−3−31-211-12-1-13−3003−3−33000000000000000000
χ43222222-2-22-2-2-2-222-2200-2-2220000-1-12-1-1-12-11111-2-21100011-21-1-12-133−3−3−3−333000033−3−311-21-1-12-1−333−300−33000000000000000000
χ44222222-2-22-2-2-2-222-2200-2-2220000-1-12-1-1-12-11111-2-21100011-21-1-12-1−3−33333−3−30000−3−33311-21-1-12-13−3−33003−3000000000000000000
χ45222222-2-22-2-2-2-222-2200-2-2220000-1-1-12-1-1-12111111-2-2000111-2-1-1-1233−3−333−3−3−3−3330000111-2-1-1-12−33−333−300000000000000000000
χ46222222-2-22-2-2-2-222-2200-2-2220000-1-1-12-1-1-12111111-2-2000111-2-1-1-12−3−333−3−33333−3−30000111-2-1-1-123−33−3−3300000000000000000000
χ4733−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3200000000000000003−3−3i32−3+3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ4833−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3200000000000000003−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-11+i321−i32-11+i321−i32
χ4933−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i320000000000000000-33+3i323−3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11+i321−i32-11+i321−i32
χ5033−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i320000000000000000-33+3i323−3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321−1−i32−1+i321−1−i32−1+i32
χ5133−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3333+3i323−3i323+3i323−3i32−3−3i32−3−3i32−3+3i32−3+3i320000000000000000-33+3i323−3i32000000000000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32-11+i321−i321−1−i32−1+i32
χ5233−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3333+3i323−3i323+3i323−3i32−3−3i32−3−3i32−3+3i32−3+3i320000000000000000-33+3i323−3i320000000000000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32-11+i321−i32
χ5333−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-33+3i323−3i323+3i323−3i323+3i323+3i323−3i323−3i3200000000000000003−3−3i32−3+3i32000000000000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321−1−i32−1+i32-11+i321−i32
χ5433−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-33+3i323−3i323+3i323−3i323+3i323+3i323−3i323−3i3200000000000000003−3−3i32−3+3i320000000000000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32-11+i321−i321−1−i32−1+i32
χ5533−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3200000000000000003−3+3i32−3−3i3200000000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ5633−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i323333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3200000000000000003−3+3i32−3−3i320000000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-11−i321+i32-11−i321+i32
χ5733−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323−3i323+3i323+3i320000000000000000-33−3i323+3i3200000000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11−i321+i32-11−i321+i32
χ5833−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323−3i323+3i323+3i320000000000000000-33−3i323+3i320000000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−1+i32−1−i321−1+i32−1−i32
χ5933−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-3333−3i323+3i323−3i323+3i32−3+3i32−3+3i32−3−3i32−3−3i320000000000000000-33−3i323+3i32000000000000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32-11−i321+i321−1+i32−1−i32
χ6033−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-3333−3i323+3i323−3i323+3i32−3+3i32−3+3i32−3−3i32−3−3i320000000000000000-33−3i323+3i320000000000000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32-11−i321+i32
χ6133−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-3-3-33−3i323+3i323−3i323+3i323−3i323−3i323+3i323+3i3200000000000000003−3+3i32−3−3i32000000000000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−1+i32−1−i32-11−i321+i32
χ6233−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-3-3-33−3i323+3i323−3i323+3i323−3i323−3i323+3i323+3i3200000000000000003−3+3i32−3−3i320000000000000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32-11−i321+i321−1+i32−1−i32
χ634444444-4-444-4-4-4-40000000000004-2-2-24-2-2-2-4-42222220004-2-2-2-422200000000000000000000000000000000000000000000000000
χ644444444-4-444-4-4-4-4000000000000-24-2-2-24-2-222-4-42222000-24-2-22-42200000000000000000000000000000000000000000000000000
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χ664444444-4-444-4-4-4-4000000000000-2-2-24-2-2-24222222-4-4000-2-2-24222-400000000000000000000000000000000000000000000000000
χ67444444-44-4-4-444-4-40000000000004-2-2-24-2-2-244-2-2-2-2-2-2000-4222-422200000000000000000000000000000000000000000000000000
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χ714-444-4-4000000000002i−2i00002i−2i2i−2i4444-4-4-4-400000000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.