Finite Group Databasebeta

← Group #13136913

Character table — Group #13136913

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111111111112222224444441212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order1233446612121212246612128824242424336666661212121212121212242424242424242424242424242424248888242424242424242424661212161616161616161648484848484848484848484848484848
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii
χ5111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-111-1-1-1-11-111-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iiiii−i−i−i−i1-111-1-1ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ101111-1-111-1-1-1-11-111-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−iiiii−i−i−i−i1-111-1-1−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ111111-1-111-1-1-1-11-111-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−i−i−iiiii-11-1-111−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ121111-1-111-1-1-1-11-111-1-1i−iii−i−i11111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii−i−i−i−iiiii-11-1-111ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ131111-1-111-1-1-1-11-111-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iiiii−i−i−i−i-11-1-111ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ141111-1-111-1-1-1-11-111-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−iiiii−i−i−i−i-11-1-111−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ151111-1-111-1-1-1-11-111-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−i−i−iiiii1-111-1-1−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ161111-1-111-1-1-1-11-111-1-1−ii−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii−i−i−i−iiiii1-111-1-1ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ17222222222222-2-2-2-2-2-200000022-2-2-2-222-2-2-2-2222200000000000000002-22-222-2-222-2-2000000000000000000000000000000
χ18222222222222-2-2-2-2-2-200000022-2-2-2-222-2-2-2-222220000000000000000-22-22-2-222-2-222000000000000000000000000000000
χ192222-2-222-2-2-2-2-22-2-22200000022-2-2-2-2222222-2-2-2-200000000000000002i−2i−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ202222-2-222-2-2-2-2-22-2-22200000022-2-2-2-2222222-2-2-2-20000000000000000−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ2133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32iiii−i−i−i−iζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22
χ2233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32−i−i−i−iiiii−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22
χ2333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321−i321+i321−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ2433−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321−i321+i321−i32-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32
χ2533−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i32ii−i−i−i−iiiζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22
χ2633−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i32−i−iiiii−i−i−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22
χ2733−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i3200000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i3211-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ2833−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i3200000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i32-1-111-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ2933−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ1400000000000000000000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ141-1−1−i32−1+i321+i321−i32−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13ζ5ζ13−ζ5−ζ13ζ23ζ7−ζ23−ζ7−ζ23−ζ7ζ23ζ7−ζ5−ζ13ζ5ζ13
χ3033−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ1400000000000000000000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ141-1−1−i32−1+i321+i321−i32ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5ζ13−ζ23−ζ7ζ23ζ7ζ23ζ7−ζ23−ζ7ζ5ζ13−ζ5−ζ13
χ3133−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ1400000000000000000000000000000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14-111+i321−i32−1−i32−1+i32ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ23−ζ7ζ23ζ7ζ5ζ13−ζ5−ζ13ζ5ζ13−ζ5−ζ13−ζ23−ζ7ζ23ζ7
χ3233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ1400000000000000000000000000000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14-111+i321−i32−1−i32−1+i32−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ23ζ7−ζ23−ζ7−ζ5−ζ13ζ5ζ13−ζ5−ζ13ζ5ζ13ζ23ζ7−ζ23−ζ7
χ3333−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ22−3ζ143ζ223ζ1400000000000000000000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14-111+i321−i32−1−i32−1+i32−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ5ζ13−ζ5−ζ13−ζ23−ζ7ζ23ζ7−ζ23−ζ7ζ23ζ7ζ5ζ13−ζ5−ζ13
χ3433−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ22−3ζ143ζ223ζ1400000000000000000000000000000000ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14-111+i321−i32−1−i32−1+i32ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5ζ13ζ23ζ7−ζ23−ζ7ζ23ζ7−ζ23−ζ7−ζ5−ζ13ζ5ζ13
χ3533−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ22−3ζ143ζ223ζ1400000000000000000000000000000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ141-1−1−i32−1+i321+i321−i32ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23−ζ23−ζ7ζ23ζ7−ζ5−ζ13ζ5ζ13ζ5ζ13−ζ5−ζ13ζ23ζ7−ζ23−ζ7
χ3633−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32−3i3i−3ζ22−3ζ143ζ223ζ1400000000000000000000000000000000−i−iii−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ141-1−1−i32−1+i321+i321−i32−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23ζ23ζ7−ζ23−ζ7ζ5ζ13−ζ5−ζ13−ζ5−ζ13ζ5ζ13−ζ23−ζ7ζ23ζ7
χ3733−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32iiii−i−i−i−iζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14
χ3833−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32−i−i−i−iiiii−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14
χ3933−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-11−i321+i321−i321+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ4033−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-11−i321+i321−i321+i32-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ4133−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32ii−i−i−i−iiiζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14
χ4233−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32−i−iiiii−i−i−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14
χ4333−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i3200000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i3211-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+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.