Finite Group Databasebeta

← Group #13154392

Character table — Group #13154392

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size11111122222222244444444444444444466666666121212121212121212121212181818181818181818181818181818181818242424242424242424242424242424242424242424242424363636363636363636363636363636
order123366244661212121224446688121212121212242424243333666666661212121212121212224466668812121212242424246666121212121212121212121212242424242424242424446681212121212122424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111111111111111111111111111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111
χ5111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-111-1-1
χ6111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-111111-1-111
χ7111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1-111
χ8111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1111111-1-1
χ9111111-1-11-1-1-1-1111-11-1111-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-111111-11-111-1-11111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-111-1-1-1-1-1-1
χ10111111-1-11-1-1-1-1111-11-1111-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11-1-1111111
χ11111111-1-11-1-1-1-1111-1-1111-11-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-111111-11-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1111-1-11111
χ12111111-1-11-1-1-1-1111-1-1111-11-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-11111-11-11-1-11111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1-111-1-1-1-1
χ13111111-1-11-1-1-1-111-111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111-11-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1111-1-111-1-111
χ14111111-1-11-1-1-1-111-111-1-1-1-111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-11-11-1-11111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-1-111-1-111-1-1
χ15111111-1-11-1-1-1-111-11-11-1-11-111-1-11111-1-111111111-1-1-1-1-1-1-1-111111-11-111-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-11111-1-1
χ16111111-1-11-1-1-1-111-11-11-1-11-111-1-11111-1-111111111-1-1-1-1-1-1-1-11111-11-11-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111111-1-1-1-111
χ172222222222222222222222222222222222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-10000000000000000002-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1000000000000000
χ18222222222222222222222222222222222-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1000000000000000000-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1000000000000000
χ19222222222222222222222222222222222-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1000000000000000000-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1000000000000000
χ20222222222222222222222222222222222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12000000000000000000-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12000000000000000
χ2122222222222222222-2-222-2-222-2-2-2-2-2-2-2-22-1-1-12-1-1-12-1-1-12-1-1-12-1-1-10000000000000000002-1-1-12-1-1-1-2111-2111-2111-2111000000000000000
χ2222222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-12-1-1-12-1-1-12-1-1-12-1-1-12-1-1000000000000000000-12-1-1-12-1-11-2111-2111-2111-211000000000000000
χ2322222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-1-12-1-1-12-1-1-12-1-1-12-1-1-12-1000000000000000000-1-12-1-1-12-111-2111-2111-2111-21000000000000000
χ2422222222222222222-2-222-2-222-2-2-2-2-2-2-2-2-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12000000000000000000-1-1-12-1-1-12111-2111-2111-2111-2000000000000000
χ25222222222222222-2-222-2-2-2-2-2-22222-2-2-2-22-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1000000000000000000-2111-21112-1-1-12-1-1-1-2111-2111000000000000000
χ26222222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-12-1-1-12-1-1-12-1-1-12-1-1-12-1-10000000000000000001-2111-211-12-1-1-12-1-11-2111-211000000000000000
χ27222222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-1-12-1-1-12-1-1-12-1-1-12-1-1-12-100000000000000000011-2111-21-1-12-1-1-12-111-2111-21000000000000000
χ28222222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12000000000000000000111-2111-2-1-1-12-1-1-12111-2111-2000000000000000
χ29222222222222222-2-2-2-2-2-222-2-2-2-2-2-222222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1000000000000000000-2111-2111-2111-21112-1-1-12-1-1-1000000000000000
χ30222222222222222-2-2-2-2-2-222-2-2-2-2-2-22222-12-1-1-12-1-1-12-1-1-12-1-1-12-1-10000000000000000001-2111-2111-2111-211-12-1-1-12-1-1000000000000000
χ31222222222222222-2-2-2-2-2-222-2-2-2-2-2-22222-1-12-1-1-12-1-1-12-1-1-12-1-1-12-100000000000000000011-2111-2111-2111-21-1-12-1-1-12-1000000000000000
χ32222222222222222-2-2-2-2-2-222-2-2-2-2-2-22222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-12000000000000000000111-2111-2111-2111-2-1-1-12-1-1-12000000000000000
χ332222222-2-222-2-2-2-2000000000000000000222222222222-2-2-2-2-2-2-2-22-2-2222-2-200-2-2220000000000000000000000000000000000000000000
χ342222222-2-222-2-2-2-2000000000000000000222222222222-2-2-2-2-2-2-2-2-222-2-2-2220022-2-20000000000000000000000000000000000000000000
χ35222222-22-2-2-222-2-200000000000000000022222222-2-2-2-22222-2-2-2-222-2-2222200-2-2-2-20000000000000000000000000000000000000000000
χ36222222-22-2-2-222-2-200000000000000000022222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-20022220000000000000000000000000000000000000000000
χ37222222-2-22-2-2-2-2222-22-2222-2-2-222-2-222-2-22-1-1-12-1-1-1-2111-21112-1-1-10000000000000000002-1-1-1-21112-1-1-1-21112-1-1-1-2111000000000000000
χ38222222-2-22-2-2-2-2222-22-2222-2-2-222-2-222-2-2-12-1-1-12-1-11-2111-211-12-1-1000000000000000000-12-1-11-211-12-1-11-211-12-1-11-211000000000000000
χ39222222-2-22-2-2-2-2222-22-2222-2-2-222-2-222-2-2-1-12-1-1-12-111-2111-21-1-12-1000000000000000000-1-12-111-21-1-12-111-21-1-12-111-21000000000000000
χ40222222-2-22-2-2-2-2222-22-2222-2-2-222-2-222-2-2-1-1-12-1-1-12111-2111-2-1-1-12000000000000000000-1-1-12111-2-1-1-12111-2-1-1-12111-2000000000000000
χ41222222-2-22-2-2-2-2222-2-2222-22-2-2-2-222-2-2222-1-1-12-1-1-1-2111-21112-1-1-10000000000000000002-1-1-1-2111-21112-1-1-1-21112-1-1-1000000000000000
χ42222222-2-22-2-2-2-2222-2-2222-22-2-2-2-222-2-222-12-1-1-12-1-11-2111-211-12-1-1000000000000000000-12-1-11-2111-211-12-1-11-211-12-1-1000000000000000
χ43222222-2-22-2-2-2-2222-2-2222-22-2-2-2-222-2-222-1-12-1-1-12-111-2111-21-1-12-1000000000000000000-1-12-111-2111-21-1-12-111-21-1-12-1000000000000000
χ44222222-2-22-2-2-2-2222-2-2222-22-2-2-2-222-2-222-1-1-12-1-1-12111-2111-2-1-1-12000000000000000000-1-1-12111-2111-2-1-1-12111-2-1-1-12000000000000000
χ45222222-2-22-2-2-2-222-222-2-2-2-222222-2-2-2-2222-1-1-12-1-1-1-2111-21112-1-1-1000000000000000000-21112-1-1-12-1-1-1-2111-21112-1-1-1000000000000000
χ46222222-2-22-2-2-2-222-222-2-2-2-222222-2-2-2-222-12-1-1-12-1-11-2111-211-12-1-10000000000000000001-211-12-1-1-12-1-11-2111-211-12-1-1000000000000000
χ47222222-2-22-2-2-2-222-222-2-2-2-222222-2-2-2-222-1-12-1-1-12-111-2111-21-1-12-100000000000000000011-21-1-12-1-1-12-111-2111-21-1-12-1000000000000000
χ48222222-2-22-2-2-2-222-222-2-2-2-222222-2-2-2-222-1-1-12-1-1-12111-2111-2-1-1-12000000000000000000111-2-1-1-12-1-1-12111-2111-2-1-1-12000000000000000
χ49222222-2-22-2-2-2-222-22-22-2-22-222-2-22222-2-22-1-1-12-1-1-1-2111-21112-1-1-1000000000000000000-21112-1-1-1-21112-1-1-12-1-1-1-2111000000000000000
χ50222222-2-22-2-2-2-222-22-22-2-22-222-2-22222-2-2-12-1-1-12-1-11-2111-211-12-1-10000000000000000001-211-12-1-11-211-12-1-1-12-1-11-211000000000000000
χ51222222-2-22-2-2-2-222-22-22-2-22-222-2-22222-2-2-1-12-1-1-12-111-2111-21-1-12-100000000000000000011-21-1-12-111-21-1-12-1-1-12-111-21000000000000000
χ52222222-2-22-2-2-2-222-22-22-2-22-222-2-22222-2-2-1-1-12-1-1-12111-2111-2-1-1-12000000000000000000111-2-1-1-12111-2-1-1-12-1-1-12111-2000000000000000
χ5333−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000001111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i320000000000000000000000001111−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ5433−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000-1-1-1-11+i321−i321+i321−i32-1-11+i321−i321+i321−i321+i321+i321−i321−i32000000000000000000000000-1-1-1-11+i321−i32-11+i321−i321+i321−i321+i321−i321+i321−i32
χ5533−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233-3-3−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32000000000000000000001111−1−i32−1+i32−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32000000000000000000000000-111-11+i321−i32-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ5633−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233-3-3−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i3200000000000000000000-1-1-1-11+i321−i321+i321−i32111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i320000000000000000000000001-1-11−1−i32−1+i3211+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ5733−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3333+3i323−3i32-3-33+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32000000000000000000001111−1−i32−1+i32−1−i32−1+i32-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i320000000000000000000000001-1-11−1−i32−1+i32-11+i321−i321+i321−i32−1−i32−1+i321+i321−i32
χ5833−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3333+3i323−3i32-3-33+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i3200000000000000000000-1-1-1-11+i321−i321+i321−i32111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32000000000000000000000000-111-11+i321−i321−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ5933−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-33+3i323−3i32333+3i323−3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000001111−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32000000000000000000000000-1-1-1-11+i321−i3211+i321−i321+i321−i321+i321−i32−1−i32−1+i32
χ6033−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-3-3-33+3i323−3i32333+3i323−3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000-1-1-1-11+i321−i321+i321−i32-1-11+i321−i321+i321−i321+i321+i321−i321−i320000000000000000000000001111−1−i32−1+i32-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i32
χ6133−3−3i32−3+3i32−3−3i32−3+3i32-3-333+3i323−3i323+3i323−3i32−3−3i32−3+3i323-33-3−3−3i32−3+3i323-33+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32000000000000000000001-11-1−1−i32−1+i321+i321−i3211−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i3200000000000000000000000011-1-1−1−i32−1+i32-1−1−i32−1+i321+i321−i321+i321−i321+i321−i32
χ6233−3−3i32−3+3i32−3−3i32−3+3i32-3-333+3i323−3i323+3i323−3i32−3−3i32−3+3i323-33-3−3−3i32−3+3i323-33+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i3200000000000000000000-11-111+i321−i32−1−i32−1+i32-1-11+i321−i32−1−i32−1+i321+i321+i321−i321−i32000000000000000000000000-1-1111+i321−i3211+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ6333−3−3i32−3+3i32−3−3i32−3+3i32-3-333+3i323−3i323+3i323−3i32−3−3i32−3+3i323-3-33−3−3i32−3+3i32-333+3i323−3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i32000000000000000000001-11-1−1−i32−1+i321+i321−i32-1-1−1−i32−1+i321+i321−i321+i321+i321−i321−i32000000000000000000000000-11-111+i321−i321−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ6433−3−3i32−3+3i32−3−3i32−3+3i32-3-333+3i323−3i323+3i323−3i32−3−3i32−3+3i323-3-33−3−3i32−3+3i32-333+3i323−3i323+3i323−3i32−3−3i32−3+3i323+3i323−3i32−3−3i32−3+3i3200000000000000000000-11-111+i321−i32−1−i32−1+i32111+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i320000000000000000000000001-11-1−1−i32−1+i32-11+i321−i32−1−i32−1+i321+i321−i321+i321−i32
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.