Finite Group Databasebeta

← Group #72269127

Character table — Group #72269127

Order 3456.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160
size12333336666666666666666666669272727272748489696144144123333366666666666666666666692727272727484896961441441233333666666666666666666666927272727274848969614414412333336666666666666666666669272727272748489696144144
order132222236666666666666666666622222233336641244444121212121212121212121212121212121212121212444444121212121212262222266666666666666666666622222266666641244444121212121212121212121212121212121212121212444444121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ31111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ41111111111111111111111111111-1-1-1-1-1-11111-1-11111111111111111111111111111-1-1-1-1-1-11111-1-11111111111111111111111111111-1-1-1-1-1-11111-1-11111111111111111111111111111-1-1-1-1-1-11111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321111111111111111111111111111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321111111111111111111111111111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321111111111111111111111111111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i32
χ61111111111111111111111111111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321111111111111111111111111111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321111111111111111111111111111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321111111111111111111111111111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i32
χ72222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1002222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1002222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1002222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-100
χ82222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000−1+i3−1−i31−i321+i32002222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000−1+i3−1−i31−i321+i32002222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000−1+i3−1−i31−i321+i32002222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000−1+i3−1−i31−i321+i3200
χ92222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000−1−i3−1+i31+i321−i32002222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000−1−i3−1+i31+i321−i32002222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000−1−i3−1+i31+i321−i32002222222-122222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000−1−i3−1+i31+i321−i3200
χ10333-1-1-1-133-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1000000333-1-1-1-133-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1000000333-1-1-1-133-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1000000333-1-1-1-133-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-133-1-1-1-1000000
χ11333-1-1-1-133-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-3-31111000000333-1-1-1-133-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-3-31111000000333-1-1-1-133-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-3-31111000000333-1-1-1-133-1-1-1-1333-1-1-1-1-1-1-1-1-1-1-1-1-3-31111000000
χ1233-13-1-1-13-13-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-13-13-1-1-100000033-13-1-1-13-13-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-13-13-1-1-100000033-13-1-1-13-13-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-13-13-1-1-100000033-13-1-1-13-13-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-13-13-1-1-1000000
χ1333-13-1-1-13-13-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-31-311100000033-13-1-1-13-13-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-31-311100000033-13-1-1-13-13-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-31-311100000033-13-1-1-13-13-1-1-1-1-1-1333-1-1-1-1-1-1-1-1-1-31-3111000000
χ1433-1-13-1-13-1-13-1-1-1-1-1-1-1-1333-1-1-1-1-1-13-1-13-1-100000033-1-13-1-13-1-13-1-1-1-1-1-1-1-1333-1-1-1-1-1-13-1-13-1-100000033-1-13-1-13-1-13-1-1-1-1-1-1-1-1333-1-1-1-1-1-13-1-13-1-100000033-1-13-1-13-1-13-1-1-1-1-1-1-1-1333-1-1-1-1-1-13-1-13-1-1000000
χ1533-1-13-1-13-1-13-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-311-31100000033-1-13-1-13-1-13-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-311-31100000033-1-13-1-13-1-13-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-311-31100000033-1-13-1-13-1-13-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-311-311000000
χ1633-1-1-13-13-1-1-13-1-1-1-1-1-1-1-1-1-1333-1-1-13-1-1-13-100000033-1-1-13-13-1-1-13-1-1-1-1-1-1-1-1-1-1333-1-1-13-1-1-13-100000033-1-1-13-13-1-1-13-1-1-1-1-1-1-1-1-1-1333-1-1-13-1-1-13-100000033-1-1-13-13-1-1-13-1-1-1-1-1-1-1-1-1-1333-1-1-13-1-1-13-1000000
χ1733-1-1-13-13-1-1-13-1-1-1-1-1-1-1-1-1-1333-1-1-1-3111-3100000033-1-1-13-13-1-1-13-1-1-1-1-1-1-1-1-1-1333-1-1-1-3111-3100000033-1-1-13-13-1-1-13-1-1-1-1-1-1-1-1-1-1333-1-1-1-3111-3100000033-1-1-13-13-1-1-13-1-1-1-1-1-1-1-1-1-1333-1-1-1-3111-31000000
χ1833-1-1-1-133-1-1-1-13-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1300000033-1-1-1-133-1-1-1-13-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1300000033-1-1-1-133-1-1-1-13-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1300000033-1-1-1-133-1-1-1-13-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-13000000
χ1933-1-1-1-133-1-1-1-13-1-1-1-1-1-1-1-1-1-1-1-1333-31111-300000033-1-1-1-133-1-1-1-13-1-1-1-1-1-1-1-1-1-1-1-1333-31111-300000033-1-1-1-133-1-1-1-13-1-1-1-1-1-1-1-1-1-1-1-1333-31111-300000033-1-1-1-133-1-1-1-13-1-1-1-1-1-1-1-1-1-1-1-1333-31111-3000000
χ20666-2-2-2-2-36-2-2-2-2-3-3-3111111111111000000000000666-2-2-2-2-36-2-2-2-2-3-3-3111111111111000000000000666-2-2-2-2-36-2-2-2-2-3-3-3111111111111000000000000666-2-2-2-2-36-2-2-2-2-3-3-3111111111111000000000000
χ2166-26-2-2-2-3-26-2-2-2111-3-3-311111111100000000000066-26-2-2-2-3-26-2-2-2111-3-3-311111111100000000000066-26-2-2-2-3-26-2-2-2111-3-3-311111111100000000000066-26-2-2-2-3-26-2-2-2111-3-3-3111111111000000000000
χ2266-2-26-2-2-3-2-26-2-2111111-3-3-311111100000000000066-2-26-2-2-3-2-26-2-2111111-3-3-311111100000000000066-2-26-2-2-3-2-26-2-2111111-3-3-311111100000000000066-2-26-2-2-3-2-26-2-2111111-3-3-3111111000000000000
χ2366-2-2-26-2-3-2-2-26-2111111111-3-3-311100000000000066-2-2-26-2-3-2-2-26-2111111111-3-3-311100000000000066-2-2-26-2-3-2-2-26-2111111111-3-3-311100000000000066-2-2-26-2-3-2-2-26-2111111111-3-3-3111000000000000
χ2466-2-2-2-26-3-2-2-2-26111111111111-3-3-300000000000066-2-2-2-26-3-2-2-2-26111111111111-3-3-300000000000066-2-2-2-26-3-2-2-2-26111111111111-3-3-300000000000066-2-2-2-26-3-2-2-2-26111111111111-3-3-3000000000000
χ256-3666660-3-3-3-3-30000000000000000000000000006-3666660-3-3-3-3-30000000000000000000000000006-3666660-3-3-3-3-30000000000000000000000000006-3666660-3-3-3-3-3000000000000000000000000000
χ266-36-2-2-2-20-311110004-2-24-2-24-2-24-2-20000000000006-36-2-2-2-20-311110004-2-24-2-24-2-24-2-20000000000006-36-2-2-2-20-311110004-2-24-2-24-2-24-2-20000000000006-36-2-2-2-20-311110004-2-24-2-24-2-24-2-2000000000000
χ276-36-2-2-2-20-31111000-24-2-24-2-24-2-24-20000000000006-36-2-2-2-20-31111000-24-2-24-2-24-2-24-20000000000006-36-2-2-2-20-31111000-24-2-24-2-24-2-24-20000000000006-36-2-2-2-20-31111000-24-2-24-2-24-2-24-2000000000000
χ286-36-2-2-2-20-31111000-2-24-2-24-2-24-2-240000000000006-36-2-2-2-20-31111000-2-24-2-24-2-24-2-240000000000006-36-2-2-2-20-31111000-2-24-2-24-2-24-2-240000000000006-36-2-2-2-20-31111000-2-24-2-24-2-24-2-24000000000000
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χ316-3-26-2-2-201-3111-2-24000-2-244-2-2-24-20000000000006-3-26-2-2-201-3111-2-24000-2-244-2-2-24-20000000000006-3-26-2-2-201-3111-2-24000-2-244-2-2-24-20000000000006-3-26-2-2-201-3111-2-24000-2-244-2-2-24-2000000000000
χ326-3-2-26-2-2011-3114-2-24-2-2000-2-24-24-20000000000006-3-2-26-2-2011-3114-2-24-2-2000-2-24-24-20000000000006-3-2-26-2-2011-3114-2-24-2-2000-2-24-24-20000000000006-3-2-26-2-2011-3114-2-24-2-2000-2-24-24-2000000000000
χ336-3-2-26-2-2011-311-24-2-24-20004-2-2-2-240000000000006-3-2-26-2-2011-311-24-2-24-20004-2-2-2-240000000000006-3-2-26-2-2011-311-24-2-24-20004-2-2-2-240000000000006-3-2-26-2-2011-311-24-2-24-20004-2-2-2-24000000000000
χ346-3-2-26-2-2011-311-2-24-2-24000-24-24-2-20000000000006-3-2-26-2-2011-311-2-24-2-24000-24-24-2-20000000000006-3-2-26-2-2011-311-2-24-2-24000-24-24-2-20000000000006-3-2-26-2-2011-311-2-24-2-24000-24-24-2-2000000000000
χ356-3-2-2-26-20111-314-2-2-24-2-2-240004-2-20000000000006-3-2-2-26-20111-314-2-2-24-2-2-240004-2-20000000000006-3-2-2-26-20111-314-2-2-24-2-2-240004-2-20000000000006-3-2-2-26-20111-314-2-2-24-2-2-240004-2-2000000000000
χ366-3-2-2-26-20111-31-24-2-2-244-2-2000-24-20000000000006-3-2-2-26-20111-31-24-2-2-244-2-2000-24-20000000000006-3-2-2-26-20111-31-24-2-2-244-2-2000-24-20000000000006-3-2-2-26-20111-31-24-2-2-244-2-2000-24-2000000000000
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χ386-3-2-2-2-2601111-34-2-2-2-24-24-24-2-20000000000000006-3-2-2-2-2601111-34-2-2-2-24-24-24-2-20000000000000006-3-2-2-2-2601111-34-2-2-2-24-24-24-2-20000000000000006-3-2-2-2-2601111-34-2-2-2-24-24-24-2-2000000000000000
χ396-3-2-2-2-2601111-3-24-24-2-2-2-24-24-20000000000000006-3-2-2-2-2601111-3-24-24-2-2-2-24-24-20000000000000006-3-2-2-2-2601111-3-24-24-2-2-2-24-24-20000000000000006-3-2-2-2-2601111-3-24-24-2-2-2-24-24-2000000000000000
χ406-3-2-2-2-2601111-3-2-24-24-24-2-2-2-240000000000000006-3-2-2-2-2601111-3-2-24-24-24-2-2-2-240000000000000006-3-2-2-2-2601111-3-2-24-24-24-2-2-2-240000000000000006-3-2-2-2-2601111-3-2-24-24-24-2-2-2-24000000000000000
χ411111111111111111111111111111111111111111iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ421111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiζ7ζ11ζ7ζ11ζ7ζ11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i32−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11
χ431111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiζ11ζ7ζ11ζ7ζ11ζ7-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i32−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7
χ441111111111111111111111111111-1-1-1-1-1-11111-1-1iiiiiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−iiiii−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ451111111111111111111111111111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i32iiiiiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−iζ7ζ11ζ7ζ11−ζ7−ζ11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111−i321+i321−i321+i32−1+i32−1−i32−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiii−ζ7−ζ11−ζ7−ζ11ζ7ζ11
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χ14266-2-26-2-2-3-2-26-2-2111111-3-3-3111111000000000000−6i−6i2i2i−6i2i2i3i2i2i−6i2i2i−i−i−i−i−i−i3i3i3i−i−i−i−i−i−i000000000000-6-622-622322-622-1-1-1-1-1-1333-1-1-1-1-1-10000000000006i6i−2i−2i6i−2i−2i−3i−2i−2i6i−2i−2iiiiiii−3i−3i−3iiiiiii000000000000
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χ1566-3-2-2-26-20111-31-24-2-2-244-2-2000-24-2000000000000−6i3i2i2i2i−6i2i0−i−i−i3i−i2i−4i2i2i2i−4i−4i2i2i0002i−4i2i000000000000-63222-620-1-1-13-12-4222-4-4220002-420000000000006i−3i−2i−2i−2i6i−2i0iii−3ii−2i4i−2i−2i−2i4i4i−2i−2i000−2i4i−2i000000000000
χ1576-3-2-2-26-20111-31-2-244-2-2-24-2000-2-24000000000000−6i3i2i2i2i−6i2i0−i−i−i3i−i2i2i−4i−4i2i2i2i−4i2i0002i2i−4i000000000000-63222-620-1-1-13-122-4-4222-4200022-40000000000006i−3i−2i−2i−2i6i−2i0iii−3ii−2i−2i4i4i−2i−2i−2i4i−2i000−2i−2i4i000000000000
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χ1596-3-2-2-2-2601111-3-24-24-2-2-2-24-24-2000000000000000−6i3i2i2i2i2i−6i0−i−i−i−i3i2i−4i2i−4i2i2i2i2i−4i2i−4i2i000000000000000-632222-60-1-1-1-132-42-42222-42-420000000000000006i−3i−2i−2i−2i−2i6i0iiii−3i−2i4i−2i4i−2i−2i−2i−2i4i−2i4i−2i000000000000000
χ1606-3-2-2-2-2601111-3-2-24-24-24-2-2-2-24000000000000000−6i3i2i2i2i2i−6i0−i−i−i−i3i2i2i−4i2i−4i2i−4i2i2i2i2i−4i000000000000000-632222-60-1-1-1-1322-42-42-42222-40000000000000006i−3i−2i−2i−2i−2i6i0iiii−3i−2i−2i4i−2i4i−2i4i−2i−2i−2i−2i4i000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.