Finite Group Databasebeta

← Group #13136732

Character table — Group #13136732

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111112222229999999999991818181818181818181818181818181818181818181818181818181818182424242424242424363636363636363636363636363636363636363636363636
order12334466121212122466121222446666121212122444444444661212121212121212121212121212121212123666121212124444888812121212121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1111-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i
χ6111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-1111-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1111-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1111-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-111-1-1-1-11-111-1-1-1-111-1-1-1-11111-11ii−i−iii−i−i-1-111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1i−ii−i1-11-1ii−i−iii−i−i11-1-111-1-1
χ101111-1-111-1-1-1-11-111-1-1-1-111-1-1-1-11111-11ii−i−iii−i−i-1-111iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−ii−ii-11-11−i−iii−i−iii-1-111-1-111
χ111111-1-111-1-1-1-11-111-1-1-1-111-1-1-1-11111-11−i−iii−i−iii-1-111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1i−ii−i-11-11ii−i−iii−i−i-1-111-1-111
χ121111-1-111-1-1-1-11-111-1-1-1-111-1-1-1-11111-11−i−iii−i−iii-1-111−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−ii−ii1-11-1−i−iii−i−iii11-1-111-1-1
χ131111-1-111-1-1-1-1-11-1-11111-1-11111-1-1-1-1-11ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11-1-1111-1-11−iii−i11-1-1-1-111−i−iiiii−i−i
χ141111-1-111-1-1-1-1-11-1-11111-1-11111-1-1-1-1-11ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii1-1-11-1-111-111-1i−i−ii-1-11111-1-1ii−i−i−i−iii
χ151111-1-111-1-1-1-1-11-1-11111-1-11111-1-1-1-1-11−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11-1-1111-1-11i−i−ii11-1-1-1-111ii−i−i−i−iii
χ161111-1-111-1-1-1-1-11-1-11111-1-11111-1-1-1-1-11−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i1-1-11-1-111-111-1−iii−i-1-11111-1-1−i−iiiii−i−i
χ17222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2000000000000000022222222000000000000000000000000
χ18222222222222-2-2-2-2-2-2222222222222-2-200000000-2-2-2-200000000000000002-2-2222-2-2000000000000000000000000
χ192222-2-222-2-2-2-22-222-2-222-2-22222-2-2-2-22-20000000022-2-200000000000000002222-2-2-2-2000000000000000000000000
χ202222-2-222-2-2-2-2-22-2-222-2-222-2-2-2-222222-20000000022-2-200000000000000002-2-22-2-222000000000000000000000000
χ212-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i200-22i−2i00000000000000000000000000
χ222-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i200-22i−2i00000000000000000000000000
χ232-2222i−2i-2-22i2i−2i−2i000000-22−2i2i-2-222−2i−2i2i2i001+i−1−i1−i−1+i−1+i1−i−1−i1+i00001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i200-22i−2i00000000000000000000000000
χ242-2222i−2i-2-22i2i−2i−2i000000-22−2i2i-2-222−2i−2i2i2i00−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i200-22i−2i00000000000000000000000000
χ252-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i200-2−2i2i00000000000000000000000000
χ262-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i200-2−2i2i00000000000000000000000000
χ272-222−2i2i-2-2−2i−2i2i2i000000-222i−2i-2-2222i2i−2i−2i001−i−1+i1+i−1−i−1−i1+i−1+i1−i00001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i200-2−2i2i00000000000000000000000000
χ282-222−2i2i-2-2−2i−2i2i2i000000-222i−2i-2-2222i2i−2i−2i00−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i200-2−2i2i00000000000000000000000000
χ2933−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-1111111111+i321−i321+i321−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−i32−1+i320000000011111111−1−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
χ3033−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-1111111111+i321−i321+i321−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−i32−1+i3200000000-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ3133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32000000001111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-1-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i3200000000-1-1-1-111111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ3333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-1-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i3200000000ii−i−iii−i−iζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7
χ3433−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-1-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i3200000000−i−iii−i−iii−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7
χ3533−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-111111+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000ii−i−i−i−iiiζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7
χ3633−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-111111+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000−i−iiiii−i−i−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7
χ3733−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1ii−i−iii−i−i−1−i32−1+i321+i321−i32ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ700000000i−ii−i1-11-1ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ3833−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1ii−i−iii−i−i−1−i32−1+i321+i321−i32ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ700000000−ii−ii-11-11−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ71+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ3933−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1−i−iii−i−iii−1−i32−1+i321+i321−i32−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ700000000i−ii−i-11-11ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ71+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ4033−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i3211-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1−i−iii−i−iii−1−i32−1+i321+i321−i32−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ700000000−ii−ii1-11-1−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ4133−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i32-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321-1ii−i−i−i−iii−1−i32−1+i321+i321−i32ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7000000001-1-11−iii−i−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
χ4233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i32-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321-1ii−i−i−i−iii−1−i32−1+i321+i321−i32ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ700000000-111-1i−i−ii1+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7
χ4333−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i32-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321-1−i−iiiii−i−i−1−i32−1+i321+i321−i32−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7000000001-1-11i−i−ii−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7
χ4433−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i32-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321-1−i−iiiii−i−i−1−i32−1+i321+i321−i32−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ700000000-111-1−iii−i1+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
χ4533−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-1111111111−i321+i321−i321+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+i32−1−i320000000011111111−1+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
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χ898-8888i−8i-8-88i8i−8i−8i000000000000000000000000000000000000000000000000-13-31−ii3i−3i000000000000000000000000
χ908-8888i−8i-8-88i8i−8i−8i000000000000000000000000000000000000000000000000-1-331−ii−3i3i000000000000000000000000
χ918-888−8i8i-8-8−8i−8i8i8i000000000000000000000000000000000000000000000000-13-31i−i−3i3i000000000000000000000000
χ928-888−8i8i-8-8−8i−8i8i8i000000000000000000000000000000000000000000000000-1-331i−i3i−3i000000000000000000000000

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