Finite Group Databasebeta

← Group #13144792

Character table — Group #13144792

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11111122222222244444466666666888888121212121212121212121212181818181818242424242424242424242424242424242424242424242424363636363636363636727272727272
order123366244661212121224661212333366664812122424666612121212121212128824242424666612121212121212121212121224242424242424248882424242424244812122424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111-1-1-1-1-1-1111111111-111-1-1111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-11-111-1-1
χ6111111111111111-1-1-1-1-1-1111111111-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-11-1-111
χ7111111111111111-1-1-1-1-1-111111111-11-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-11-1-111
χ8111111111111111-1-1-1-1-1-111111111-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-111111-111-1-1
χ92222222222222222222222-1-1-12-1-1-12222222-1-1-12-1-1-12-1-1-10000002-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000
χ102222222222222222222222-1-1-12-1-1-1-2-2-2-2-2-22-1-1-12-1-1-12-1-1-10000002-1-1-12-1-1-1-2-2111111-2-2111111000000000000000
χ11222222222222222222222-12-1-1-12-1-1222222-12-1-1-12-1-1-12-1-1000000-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000
χ12222222222222222222222-12-1-1-12-1-1-2-2-2-2-2-2-12-1-1-12-1-1-12-1-1000000-12-1-1-12-1-111-2-2111111-2-21111000000000000000
χ13222222222222222222222-1-12-1-1-12-1222222-1-12-1-1-12-1-1-12-1000000-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000
χ14222222222222222222222-1-12-1-1-12-1-2-2-2-2-2-2-1-12-1-1-12-1-1-12-1000000-1-12-1-1-12-11111-2-2111111-2-211000000000000000
χ15222222222222222222222-1-1-12-1-1-12222222-1-1-12-1-1-12-1-1-12000000-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122000000000000000
χ16222222222222222222222-1-1-12-1-1-12-2-2-2-2-2-2-1-1-12-1-1-12-1-1-12000000-1-1-12-1-1-12111111-2-2111111-2-2000000000000000
χ17222222222222222-2-2-2-2-2-22-1-1-12-1-1-12-222-2-22-1-1-12-1-1-12-1-1-1000000-2111-211122-1-1-1-1-1-1-2-2111111000000000000000
χ18222222222222222-2-2-2-2-2-22-1-1-12-1-1-1-22-2-2222-1-1-12-1-1-12-1-1-1000000-2111-2111-2-211111122-1-1-1-1-1-1000000000000000
χ19222222222222222-2-2-2-2-2-2-12-1-1-12-1-12-222-2-2-12-1-1-12-1-1-12-1-10000001-2111-211-1-122-1-1-1-111-2-21111000000000000000
χ20222222222222222-2-2-2-2-2-2-12-1-1-12-1-1-22-2-222-12-1-1-12-1-1-12-1-10000001-2111-21111-2-21111-1-122-1-1-1-1000000000000000
χ21222222222222222-2-2-2-2-2-2-1-12-1-1-12-12-222-2-2-1-12-1-1-12-1-1-12-100000011-2111-21-1-1-1-122-1-11111-2-211000000000000000
χ22222222222222222-2-2-2-2-2-2-1-12-1-1-12-1-22-2-222-1-12-1-1-12-1-1-12-100000011-2111-211111-2-211-1-1-1-122-1-1000000000000000
χ23222222222222222-2-2-2-2-2-2-1-1-12-1-1-122-222-2-2-1-1-12-1-1-12-1-1-12000000111-2111-2-1-1-1-1-1-122111111-2-2000000000000000
χ24222222222222222-2-2-2-2-2-2-1-1-12-1-1-12-22-2-222-1-1-12-1-1-12-1-1-12000000111-2111-2111111-2-2-1-1-1-1-1-122000000000000000
χ252222222-2-222-2-2-2-2000000222222220000002222-2-2-2-2-2-2-2-200000000000000000000000000000002i−2i002i2i−2i−2i000000
χ262222222-2-222-2-2-2-2000000222222220000002222-2-2-2-2-2-2-2-20000000000000000000000000000000−2i2i00−2i−2i2i2i000000
χ27222222-22-2-2-222-2-22-222-2-222222222000000-2-2-2-2-2-2-2-222220000002222-2-2-2-20000000000000000000000000000000
χ28222222-22-2-2-222-2-22-222-2-22-1-1-12-1-1-1000000-2111-21112-1-1-10000002-1-1-1-211100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3000000000000000
χ29222222-22-2-2-222-2-22-222-2-22-1-1-12-1-1-1000000-2111-21112-1-1-10000002-1-1-1-211100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3000000000000000
χ30222222-22-2-2-222-2-22-222-2-2-12-1-1-12-1-10000001-2111-211-12-1-1000000-12-1-11-211−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3000000000000000
χ31222222-22-2-2-222-2-22-222-2-2-12-1-1-12-1-10000001-2111-211-12-1-1000000-12-1-11-211i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3000000000000000
χ32222222-22-2-2-222-2-22-222-2-2-1-12-1-1-12-100000011-2111-21-1-12-1000000-1-12-111-21−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3000000000000000
χ33222222-22-2-2-222-2-22-222-2-2-1-12-1-1-12-100000011-2111-21-1-12-1000000-1-12-111-21i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3000000000000000
χ34222222-22-2-2-222-2-22-222-2-2-1-1-12-1-1-12000000111-2111-2-1-1-12000000-1-1-12111-2−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300000000000000000
χ35222222-22-2-2-222-2-22-222-2-2-1-1-12-1-1-12000000111-2111-2-1-1-12000000-1-1-12111-2i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300000000000000000
χ36222222-22-2-2-222-2-2-22-2-22222222222000000-2-2-2-2-2-2-2-22222000000-2-2-2-222220000000000000000000000000000000
χ37222222-22-2-2-222-2-2-22-2-2222-1-1-12-1-1-1000000-2111-21112-1-1-1000000-21112-1-1-100−i3i3−i3i3−i3i300i3−i3i3−i3i3−i3000000000000000
χ38222222-22-2-2-222-2-2-22-2-2222-1-1-12-1-1-1000000-2111-21112-1-1-1000000-21112-1-1-100i3−i3i3−i3i3−i300−i3i3−i3i3−i3i3000000000000000
χ39222222-22-2-2-222-2-2-22-2-222-12-1-1-12-1-10000001-2111-211-12-1-10000001-211-12-1-1−i3i300−i3i3i3−i3i3−i300i3−i3−i3i3000000000000000
χ40222222-22-2-2-222-2-2-22-2-222-12-1-1-12-1-10000001-2111-211-12-1-10000001-211-12-1-1i3−i300i3−i3−i3i3−i3i300−i3i3i3−i3000000000000000
χ41222222-22-2-2-222-2-2-22-2-222-1-12-1-1-12-100000011-2111-21-1-12-100000011-21-1-12-1−i3i3i3−i300−i3i3i3−i3−i3i300i3−i3000000000000000
χ42222222-22-2-2-222-2-2-22-2-222-1-12-1-1-12-100000011-2111-21-1-12-100000011-21-1-12-1i3−i3−i3i300i3−i3−i3i3i3−i300−i3i3000000000000000
χ43222222-22-2-2-222-2-2-22-2-222-1-1-12-1-1-12000000111-2111-2-1-1-12000000111-2-1-1-12−i3i3−i3i3i3−i300i3−i3i3−i3−i3i300000000000000000
χ44222222-22-2-2-222-2-2-22-2-222-1-1-12-1-1-12000000111-2111-2-1-1-12000000111-2-1-1-12i3−i3i3−i3−i3i300−i3i3−i3i3i3−i300000000000000000
χ45222222-2-22-2-2-2-22200000022222222000000-2-2-2-22222-2-2-2-2222222000000000000000000000000-200-2-20000000000
χ46222222-2-22-2-2-2-22200000022222222000000-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000000000000000000000200220000000000
χ4733−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320000000033−3−3i32−3+3i32−3−3i32−3+3i3200000000000011−1−i32−1−i32−1+i32−1+i32000000000000000000000000111−1−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+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320000000033−3−3i32−3+3i32−3−3i32−3+3i32000000000000-1-11+i321+i321−i321−i32000000000000000000000000-1-1-11+i321−i321+i321−i321+i321−i32-1-11+i321−i321+i321−i32
χ4933−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000-3-33+3i323−3i323+3i323−3i3200000000000011−1−i32−1−i32−1+i32−1+i32000000000000000000000000111−1−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+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000-3-33+3i323−3i323+3i323−3i32000000000000-1-11+i321+i321−i321−i32000000000000000000000000-1-1-11+i321−i321+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i32
χ5133−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32000000003-3−3−3i32−3+3i323+3i323−3i3200000000000011−1−i32−1−i32−1+i32−1+i320000000000000000000000001-1-1−1−i32−1+i321+i321−i321+i321−i321-1−1−i32−1+i321+i321−i32
χ5233−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32000000003-3−3−3i32−3+3i323+3i323−3i32000000000000-1-11+i321+i321−i321−i32000000000000000000000000-1111+i321−i32−1−i32−1+i32−1−i32−1+i32-111+i321−i32−1−i32−1+i32
χ5333−3−3i32−3+3i32−3−3i32−3+3i32333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i3200000000-333+3i323−3i32−3−3i32−3+3i3200000000000011−1−i32−1−i32−1+i32−1+i320000000000000000000000001-1-1−1−i32−1+i321+i321−i321+i321−i32-111+i321−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+3i32-3-33+3i323−3i323+3i323−3i3200000000-333+3i323−3i32−3−3i32−3+3i32000000000000-1-11+i321+i321−i321−i32000000000000000000000000-1111+i321−i32−1−i32−1+i32−1−i32−1+i321-1−1−i32−1+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+3i32−3−3i32−3+3i32−3−3i320000000033−3+3i32−3−3i32−3+3i32−3−3i3200000000000011−1+i32−1+i32−1−i32−1−i32000000000000000000000000111−1+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+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320000000033−3+3i32−3−3i32−3+3i32−3−3i32000000000000-1-11−i321−i321+i321+i32000000000000000000000000-1-1-11−i321+i321−i321+i321−i321+i32-1-11−i321+i321−i321+i32
χ5733−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000-3-33−3i323+3i323−3i323+3i3200000000000011−1+i32−1+i32−1−i32−1−i32000000000000000000000000111−1+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+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000-3-33−3i323+3i323−3i323+3i32000000000000-1-11−i321−i321+i321+i32000000000000000000000000-1-1-11−i321+i321−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ5933−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32000000003-3−3+3i32−3−3i323−3i323+3i3200000000000011−1+i32−1+i32−1−i32−1−i320000000000000000000000001-1-1−1+i32−1−i321−i321+i321−i321+i321-1−1+i32−1−i321−i321+i32
χ6033−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32000000003-3−3+3i32−3−3i323−3i323+3i32000000000000-1-11−i321−i321+i321+i32000000000000000000000000-1111−i321+i32−1+i32−1−i32−1+i32−1−i32-111−i321+i32−1+i32−1−i32
χ6133−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i3200000000-333−3i323+3i32−3+3i32−3−3i3200000000000011−1+i32−1+i32−1−i32−1−i320000000000000000000000001-1-1−1+i32−1−i321−i321+i321−i321+i32-111−i321+i32−1+i32−1−i32
χ6233−3+3i32−3−3i32−3+3i32−3−3i32333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i3200000000-333−3i323+3i32−3+3i32−3−3i32000000000000-1-11−i321−i321+i321+i32000000000000000000000000-1111−i321+i32−1+i32−1−i32−1+i32−1−i321-1−1+i32−1−i321−i321+i32
χ634444444-4-444-4-4-4-40000004-2-2-24-2-2-20000004-2-2-2-4222-4222000000000000000000000000000000000000000000000
χ644444444-4-444-4-4-4-4000000-24-2-2-24-2-2000000-24-2-22-4222-422000000000000000000000000000000000000000000000
χ654444444-4-444-4-4-4-4000000-2-24-2-2-24-2000000-2-24-222-4222-42000000000000000000000000000000000000000000000
χ664444444-4-444-4-4-4-4000000-2-2-24-2-2-24000000-2-2-24222-4222-4000000000000000000000000000000000000000000000
χ67444444-4-44-4-4-4-4440000004-2-2-24-2-2-2000000-42224-2-2-2-4222000000000000000000000000000000000000000000000
χ68444444-4-44-4-4-4-444000000-24-2-2-24-2-20000002-422-24-2-22-422000000000000000000000000000000000000000000000
χ69444444-4-44-4-4-4-444000000-2-24-2-2-24-200000022-42-2-24-222-42000000000000000000000000000000000000000000000
χ70444444-4-44-4-4-4-444000000-2-2-24-2-2-24000000222-4-2-2-24222-4000000000000000000000000000000000000000000000
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χ724-444-4-40000000000000004444-4-4-4-4000000000000000000−2222−2222−2222000000000000000000000000000000000000000
χ7366−3−3i3−3+3i3−3−3i3−3+3i36-6-6−3−3i3−3+3i33+3i33−3i33+3i33−3i30000000000000000000000000000000000000000000000000000000000000002i−2i002ζ222ζ14−2ζ22−2ζ14000000
χ7466−3−3i3−3+3i3−3−3i3−3+3i36-6-6−3−3i3−3+3i33+3i33−3i33+3i33−3i3000000000000000000000000000000000000000000000000000000000000000−2i2i00−2ζ22−2ζ142ζ222ζ14000000
χ7566−3−3i3−3+3i3−3−3i3−3+3i3-66-63+3i33−3i3−3−3i3−3+3i33+3i33−3i36-6−3−3i3−3+3i33+3i33−3i300000000000000000000000000000000000000000000000000000000000000000000000
χ7666−3−3i3−3+3i3−3−3i3−3+3i3-66-63+3i33−3i3−3−3i3−3+3i33+3i33−3i3-663+3i33−3i3−3−3i3−3+3i300000000000000000000000000000000000000000000000000000000000000000000000
χ7766−3−3i3−3+3i3−3−3i3−3+3i3-6-663+3i33−3i33+3i33−3i3−3−3i3−3+3i30000000000000000000000000000000022−1−i3−1−i3−1+i3−1+i3000000000000000000000000-2001+i31−i30000000000
χ7866−3−3i3−3+3i3−3−3i3−3+3i3-6-663+3i33−3i33+3i33−3i3−3−3i3−3+3i300000000000000000000000000000000-2-21+i31+i31−i31−i3000000000000000000000000200−1−i3−1+i30000000000
χ7966−3+3i3−3−3i3−3+3i3−3−3i36-6-6−3+3i3−3−3i33−3i33+3i33−3i33+3i30000000000000000000000000000000000000000000000000000000000000002i−2i002ζ142ζ22−2ζ14−2ζ22000000
χ8066−3+3i3−3−3i3−3+3i3−3−3i36-6-6−3+3i3−3−3i33−3i33+3i33−3i33+3i3000000000000000000000000000000000000000000000000000000000000000−2i2i00−2ζ14−2ζ222ζ142ζ22000000
χ8166−3+3i3−3−3i3−3+3i3−3−3i3-66-63−3i33+3i3−3+3i3−3−3i33−3i33+3i36-6−3+3i3−3−3i33−3i33+3i300000000000000000000000000000000000000000000000000000000000000000000000
χ8266−3+3i3−3−3i3−3+3i3−3−3i3-66-63−3i33+3i3−3+3i3−3−3i33−3i33+3i3-663−3i33+3i3−3+3i3−3−3i300000000000000000000000000000000000000000000000000000000000000000000000
χ8366−3+3i3−3−3i3−3+3i3−3−3i3-6-663−3i33+3i33−3i33+3i3−3+3i3−3−3i30000000000000000000000000000000022−1+i3−1+i3−1−i3−1−i3000000000000000000000000-2001−i31+i30000000000
χ8466−3+3i3−3−3i3−3+3i3−3−3i3-6-663−3i33+3i33−3i33+3i3−3+3i3−3−3i300000000000000000000000000000000-2-21−i31−i31+i31+i3000000000000000000000000200−1+i3−1−i30000000000
χ858-888-8-80000000000000008-4-4-4-8444000000000000000000000000000000000000000000000000000000000000000
χ868-888-8-8000000000000000-48-4-44-844000000000000000000000000000000000000000000000000000000000000000
χ878-888-8-8000000000000000-4-48-444-84000000000000000000000000000000000000000000000000000000000000000
χ888-888-8-8000000000000000-4-4-48444-8000000000000000000000000000000000000000000000000000000000000000
χ8912-12−6−6i3−6+6i36+6i36−6i30000000000000000000000000000000000000000022−22−2ζ7+2ζ132ζ7−2ζ132ζ5−2ζ23−2ζ5+2ζ23000000000000000000000000000000000000000
χ9012-12−6−6i3−6+6i36+6i36−6i300000000000000000000000000000000000000000−22222ζ7−2ζ13−2ζ7+2ζ13−2ζ5+2ζ232ζ5−2ζ23000000000000000000000000000000000000000
χ9112-12−6+6i3−6−6i36−6i36+6i30000000000000000000000000000000000000000022−222ζ5−2ζ23−2ζ5+2ζ23−2ζ7+2ζ132ζ7−2ζ13000000000000000000000000000000000000000
χ9212-12−6+6i3−6−6i36−6i36+6i300000000000000000000000000000000000000000−2222−2ζ5+2ζ232ζ5−2ζ232ζ7−2ζ13−2ζ7+2ζ13000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.