Finite Group Databasebeta

← Group #13135805

Character table — Group #13135805

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111222222222222222444666666666666666688888812121212121212121212121212121212121212121212121224242424242424242424242424242424363636363636363636363636727272727272
order1233662446688121212122424242482424333366666666666644121212121212121212121212242424242424242424242424242424241212121212121212121212121212121216161616484848484848484824661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111-1-11-1-1-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1i−iii−i−i-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iiiii−i−i−i−i1-111-1-1
χ6111111-1-11-1-1-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1i−iii−i−i-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−i−i−iiiii-11-1-111
χ7111111-1-11-1-1-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1−ii−i−iii-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iiiii−i−i−i−i-11-1-111
χ8111111-1-11-1-1-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1−ii−i−iii-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−i−i−iiiii1-111-1-1
χ92222222222222222222222222-1-1-12-1-1-122-1-1-1-1-1-12222222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000
χ102222222222222222222222222-1-1-12-1-1-122-1-1-1-1-1-1-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111000000000000000000
χ11222222222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1222222-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000
χ12222222222222222222222222-12-1-1-12-1-1-1-122-1-1-1-1-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-111-2-2111111-2-21111000000000000000000
χ13222222222222222222222222-1-12-1-1-12-1-1-1-1-122-1-1222222-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000
χ14222222222222222222222222-1-12-1-1-12-1-1-1-1-122-1-1-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-11111-2-2111111-2-211000000000000000000
χ15222222222222222222222222-1-1-12-1-1-12-1-1-1-1-1-122222222-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000
χ16222222222222222222222222-1-1-12-1-1-12-1-1-1-1-1-122-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122111111-2-2111111-2-2000000000000000000
χ1722222222222-2-22222-2-2-2-2-2-2-2222222222222222200000022222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000
χ1822222222222-2-22222-2-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-10000002-1-1-12-1-1-1-2-2111111-2-211111100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000000
χ1922222222222-2-22222-2-2-2-2-2-2-22-1-1-12-1-1-122-1-1-1-1-1-10000002-1-1-12-1-1-1-2-2111111-2-211111100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000000
χ2022222222222-2-22222-2-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1000000-12-1-1-12-1-111-2-2111111-2-21111−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000000000
χ2122222222222-2-22222-2-2-2-2-2-2-2-12-1-1-12-1-1-1-122-1-1-1-1000000-12-1-1-12-1-111-2-2111111-2-21111i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000000000000000
χ2222222222222-2-22222-2-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1000000-1-12-1-1-12-11111-2-2111111-2-211−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000000000000000
χ2322222222222-2-22222-2-2-2-2-2-2-2-1-12-1-1-12-1-1-1-1-122-1-1000000-1-12-1-1-12-11111-2-2111111-2-211i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3000000000000000000
χ2422222222222-2-22222-2-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122000000-1-1-12-1-1-12111111-2-2111111-2-2−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000000000000000
χ2522222222222-2-22222-2-2-2-2-2-2-2-1-1-12-1-1-12-1-1-1-1-1-122000000-1-1-12-1-1-12111111-2-2111111-2-2i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300000000000000000000
χ262222222-2-22200-2-2-2-200000002222222222222222000000-2-2-2-2-2-2-2-2000000000000000000000000000000002−22−222−2−222−2−2000000
χ272222222-2-22200-2-2-2-200000002222222222222222000000-2-2-2-2-2-2-2-200000000000000000000000000000000−22−22−2−222−2−222000000
χ28222222-22-2-2-20022-2-2000000022222222-2-2-2-2-2-2-2-20000002222-2-2-2-200000000000000000000000000000000−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2000000
χ29222222-22-2-2-20022-2-2000000022222222-2-2-2-2-2-2-2-20000002222-2-2-2-200000000000000000000000000000000i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2000000
χ30222222-2-22-2-222-2-2222222-2-2-222222222-2-2-2-2-2-2-2-2000000-2-2-2-22222-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000
χ31222222-2-22-2-222-2-2222222-2-2-22-1-1-12-1-1-1-2-2111111000000-21112-1-1-1-2-211111122-1-1-1-1-1-1003−33−33−300−33−33−33000000000000000000
χ32222222-2-22-2-222-2-2222222-2-2-22-1-1-12-1-1-1-2-2111111000000-21112-1-1-1-2-211111122-1-1-1-1-1-100−33−33−33003−33−33−3000000000000000000
χ33222222-2-22-2-222-2-2222222-2-2-2-12-1-1-12-1-111-2-211110000001-211-12-1-111-2-21111-1-122-1-1-1-13−3003−3−33−3300−333−3000000000000000000
χ34222222-2-22-2-222-2-2222222-2-2-2-12-1-1-12-1-111-2-211110000001-211-12-1-111-2-21111-1-122-1-1-1-1−3300−333−33−3003−3−33000000000000000000
χ35222222-2-22-2-222-2-2222222-2-2-2-1-12-1-1-12-11111-2-21100000011-21-1-12-11111-2-211-1-1-1-122-1-13−3−33003−3−333−300−33000000000000000000
χ36222222-2-22-2-222-2-2222222-2-2-2-1-12-1-1-12-11111-2-21100000011-21-1-12-11111-2-211-1-1-1-122-1-1−333−300−333−3−33003−3000000000000000000
χ37222222-2-22-2-222-2-2222222-2-2-2-1-1-12-1-1-12111111-2-2000000111-2-1-1-12111111-2-2-1-1-1-1-1-1223−33−3−3300−33−333−300000000000000000000
χ38222222-2-22-2-222-2-2222222-2-2-2-1-1-12-1-1-12111111-2-2000000111-2-1-1-12111111-2-2-1-1-1-1-1-122−33−333−3003−33−3−3300000000000000000000
χ39222222-2-22-2-2-2-2-2-222-2-2-2-22222-1-1-12-1-1-1-2-21111112i−2i2i2i−2i−2i-21112-1-1-122-1-1-1-1-1-1-2-21111112i2i−i−i−i−i−i−i−2i−2iiiiiii000000000000000000
χ40222222-2-22-2-2-2-2-2-222-2-2-2-22222-1-1-12-1-1-1-2-2111111−2i2i−2i−2i2i2i-21112-1-1-122-1-1-1-1-1-1-2-2111111−2i−2iiiiiii2i2i−i−i−i−i−i−i000000000000000000
χ41222222-2-22-2-2-2-2-2-222-2-2-2-2222-12-1-1-12-1-111-2-211112i−2i2i2i−2i−2i1-211-12-1-1-1-122-1-1-1-111-2-21111−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000000000
χ42222222-2-22-2-2-2-2-2-222-2-2-2-2222-12-1-1-12-1-111-2-21111−2i2i−2i−2i2i2i1-211-12-1-1-1-122-1-1-1-111-2-21111ii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000000000
χ43222222-2-22-2-2-2-2-2-222-2-2-2-2222-1-12-1-1-12-11111-2-2112i−2i2i2i−2i−2i11-21-1-12-1-1-1-1-122-1-11111-2-211−i−i−i−i2i2i−i−iiiii−2i−2iii000000000000000000
χ44222222-2-22-2-2-2-2-2-222-2-2-2-2222-1-12-1-1-12-11111-2-211−2i2i−2i−2i2i2i11-21-1-12-1-1-1-1-122-1-11111-2-211iiii−2i−2iii−i−i−i−i2i2i−i−i000000000000000000
χ45222222-2-22-2-2-2-2-2-222-2-2-2-2222-1-1-12-1-1-12111111-2-22i−2i2i2i−2i−2i111-2-1-1-12-1-1-1-1-1-122111111-2-2−i−i−i−i−i−i2i2iiiiiii−2i−2i000000000000000000
χ46222222-2-22-2-2-2-2-2-222-2-2-2-2222-1-1-12-1-1-12111111-2-2−2i2i−2i−2i2i2i111-2-1-1-12-1-1-1-1-1-122111111-2-2iiiiii−2i−2i−i−i−i−i−i−i2i2i000000000000000000
χ4733−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i323−3−3i32−3+3i32000000000000000033−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ4833−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i323−3−3i32−3+3i32000000000000000033−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321−i321+i321−i32
χ4933−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i323−3−3i32−3+3i320000000000000000-3-33+3i323−3i323+3i323−3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i32
χ5033−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i323−3−3i32−3+3i320000000000000000-3-33+3i323−3i323+3i323−3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i32
χ5133−3−3i32−3+3i32−3−3i32−3+3i32-3-333+3i323−3i32-3-33+3i323−3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i323−3−3i32−3+3i3200000000000000003i−3i3ζ223ζ14−3ζ22−3ζ140000000000000000000000000000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ141-1−1−i32−1+i321+i321−i32
χ5233−3−3i32−3+3i32−3−3i32−3+3i32-3-333+3i323−3i32-3-33+3i323−3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i323−3−3i32−3+3i3200000000000000003i−3i3ζ223ζ14−3ζ22−3ζ140000000000000000000000000000000000000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14-111+i321−i32−1−i32−1+i32
χ5333−3−3i32−3+3i32−3−3i32−3+3i32-3-333+3i323−3i32-3-33+3i323−3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i323−3−3i32−3+3i320000000000000000−3i3i−3ζ22−3ζ143ζ223ζ140000000000000000000000000000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14-111+i321−i32−1−i32−1+i32
χ5433−3−3i32−3+3i32−3−3i32−3+3i32-3-333+3i323−3i32-3-33+3i323−3i32−3−3i32−3+3i323+3i323+3i323−3i323−3i323−3−3i32−3+3i320000000000000000−3i3i−3ζ22−3ζ143ζ223ζ140000000000000000000000000000000000000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ141-1−1−i32−1+i321+i321−i32
χ5533−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i323−3+3i32−3−3i32000000000000000033−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ5633−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i323−3+3i32−3−3i32000000000000000033−3+3i32−3−3i32−3+3i32−3−3i320000000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-11−i321+i321−i321+i32
χ5733−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i323−3+3i32−3−3i320000000000000000-3-33−3i323+3i323−3i323+3i3200000000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32
χ5833−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i323−3+3i32−3−3i320000000000000000-3-33−3i323+3i323−3i323+3i320000000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ5933−3+3i32−3−3i32−3+3i32−3−3i32-3-333−3i323+3i32-3-33−3i323+3i32−3+3i32−3−3i323−3i323−3i323+3i323+3i323−3+3i32−3−3i3200000000000000003i−3i3ζ143ζ22−3ζ14−3ζ220000000000000000000000000000000000000000ii−i−iζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ221-1−1+i32−1−i321−i321+i32
χ6033−3+3i32−3−3i32−3+3i32−3−3i32-3-333−3i323+3i32-3-33−3i323+3i32−3+3i32−3−3i323−3i323−3i323+3i323+3i323−3+3i32−3−3i3200000000000000003i−3i3ζ143ζ22−3ζ14−3ζ220000000000000000000000000000000000000000−i−iii−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22-111−i321+i32−1+i32−1−i32
χ6133−3+3i32−3−3i32−3+3i32−3−3i32-3-333−3i323+3i32-3-33−3i323+3i32−3+3i32−3−3i323−3i323−3i323+3i323+3i323−3+3i32−3−3i320000000000000000−3i3i−3ζ14−3ζ223ζ143ζ220000000000000000000000000000000000000000ii−i−iζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22-111−i321+i32−1+i32−1−i32
χ6233−3+3i32−3−3i32−3+3i32−3−3i32-3-333−3i323+3i32-3-33−3i323+3i32−3+3i32−3−3i323−3i323−3i323+3i323+3i323−3+3i32−3−3i320000000000000000−3i3i−3ζ14−3ζ223ζ143ζ220000000000000000000000000000000000000000−i−iii−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ221-1−1+i32−1−i321−i321+i32
χ634444444-4-44400-4-4-4-400000004-2-2-24-2-2-244-2-2-2-2-2-2000000-4222-422200000000000000000000000000000000000000000000000000
χ644444444-4-44400-4-4-4-40000000-24-2-2-24-2-2-2-244-2-2-2-20000002-4222-42200000000000000000000000000000000000000000000000000
χ654444444-4-44400-4-4-4-40000000-2-24-2-2-24-2-2-2-2-244-2-200000022-4222-4200000000000000000000000000000000000000000000000000
χ664444444-4-44400-4-4-4-40000000-2-2-24-2-2-24-2-2-2-2-2-244000000222-4222-400000000000000000000000000000000000000000000000000
χ67444444-44-4-4-40044-4-400000004-2-2-24-2-2-2-4-42222220000004-2-2-2-422200000000000000000000000000000000000000000000000000
χ68444444-44-4-4-40044-4-40000000-24-2-2-24-2-222-4-42222000000-24-2-22-42200000000000000000000000000000000000000000000000000
χ69444444-44-4-4-40044-4-40000000-2-24-2-2-24-22222-4-422000000-2-24-222-4200000000000000000000000000000000000000000000000000
χ70444444-44-4-4-40044-4-40000000-2-2-24-2-2-24222222-4-4000000-2-2-24222-400000000000000000000000000000000000000000000000000
χ714-444-4-400000−2i22i20000−2i22i2−2i22i20004444-4-4-4-4000000000000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.