Finite Group Databasebeta

← Group #13173330

Character table — Group #13173330

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size111111112222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444499999999181818181818181818181818181818181818181854545454545454545454545454545454
order122244443444466612121212121212121212121233333366666666666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121222224444444466661212121212121212121212124444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ41111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ5111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ101111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ111111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-1111-1-1111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ141111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ151111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1711-1-111-1-11i−ii−i1-1-111-1-1ii−i−iii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i11-1-111-1-1i−ii−i11-1-111-1-1ii−i−iii−i−i1-11-1i−ii−i1-11-1i−ii−i
χ1811-1-111-1-11i−ii−i1-1-111-1-1ii−i−iii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i11-1-111-1-1i−ii−i11-1-111-1-1ii−i−iii−i−i-11-11−ii−ii-11-11−ii−ii
χ1911-1-111-1-11i−ii−i1-1-111-1-1ii−i−iii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-111-1-111−ii−ii-1-111-1-111−i−iii−i−iiii−ii−i-11-11−ii−ii1-11-1
χ2011-1-111-1-11i−ii−i1-1-111-1-1ii−i−iii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-111-1-111−ii−ii-1-111-1-111−i−iii−i−iii−ii−ii1-11-1i−ii−i-11-11
χ2111-1-111-1-11−ii−ii1-1-111-1-1−i−iii−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii11-1-111-1-1−ii−ii11-1-111-1-1−i−iii−i−iii1-11-1−ii−ii1-11-1−ii−ii
χ2211-1-111-1-11−ii−ii1-1-111-1-1−i−iii−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii11-1-111-1-1−ii−ii11-1-111-1-1−i−iii−i−iii-11-11i−ii−i-11-11i−ii−i
χ2311-1-111-1-11−ii−ii1-1-111-1-1−i−iii−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-111-1-111i−ii−i-1-111-1-111ii−i−iii−i−ii−ii−i1-11-1−ii−ii-11-11
χ2411-1-111-1-11−ii−ii1-1-111-1-1−i−iii−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-111-1-111i−ii−i-1-111-1-111ii−i−iii−i−i−ii−ii-11-11i−ii−i1-11-1
χ2511-1-1-1-1111i−i−ii1-1-1-1-111ii−i−i−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii11-1-1-1-111i−i−ii11-1-1-1-111ii−i−i−i−iii1-1-11i−i−ii1-1-11i−i−ii
χ2611-1-1-1-1111i−i−ii1-1-1-1-111ii−i−i−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii11-1-1-1-111i−i−ii11-1-1-1-111ii−i−i−i−iii-111-1−iii−i-111-1−iii−i
χ2711-1-1-1-1111i−i−ii1-1-1-1-111ii−i−i−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-11111-1-1−iii−i-1-11111-1-1−i−iiiii−i−ii−i−ii-111-1−iii−i1-1-11
χ2811-1-1-1-1111i−i−ii1-1-1-1-111ii−i−i−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-11111-1-1−iii−i-1-11111-1-1−i−iiiii−i−i−iii−i1-1-11i−i−ii-111-1
χ2911-1-1-1-1111−iii−i1-1-1-1-111−i−iiiii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i11-1-1-1-111−iii−i11-1-1-1-111−i−iiiii−i−i1-1-11−iii−i1-1-11−iii−i
χ3011-1-1-1-1111−iii−i1-1-1-1-111−i−iiiii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i11-1-1-1-111−iii−i11-1-1-1-111−i−iiiii−i−i-111-1i−i−ii-111-1i−i−ii
χ3111-1-1-1-1111−iii−i1-1-1-1-111−i−iiiii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-11111-1-1i−i−ii-1-11111-1-1ii−i−i−i−iiii−i−ii1-1-11−iii−i-111-1
χ3211-1-1-1-1111−iii−i1-1-1-1-111−i−iiiii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-11111-1-1i−i−ii-1-11111-1-1ii−i−i−i−iii−iii−i-111-1i−i−ii1-1-11
χ3322222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ3422222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-211111111111111110000000000000000
χ3522222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-211111111-2-2-2-21111111122222222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ3622222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-211111111-2-2-2-211111111-2-2-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ372222-2-2-2-2-122-2-2-1-1-11111-1-1-1-1111122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-2-2-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ382222-2-2-2-2-122-2-2-1-1-11111-1-1-1-1111122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-22222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ392222-2-2-2-2-1-2-222-1-1-111111111-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ402222-2-2-2-2-1-2-222-1-1-111111111-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2222222-2-21111-1-1-1-1-1-1-1-111110000000000000000
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χ1684-4-44−4i4i4i−4i-2000022-22i−2i−2i2i−232323−232i3−2i3−2i32i3-2111−1+3i32−1−3i322-1-1-11−3i321+3i322-1-21-1-11−3i321+3i3211−1+3i32−1−3i322i−i−2ii−i−i−2ζ7+ζ11ζ7−2ζ11ii2ζ7−ζ11−ζ7+2ζ11−2ii2i−iii2ζ7−ζ11−ζ7+2ζ11−i−i−2ζ7+ζ11ζ7−2ζ11003i−3i332ζ7+ζ11−ζ7−2ζ11−3−3−2ζ7−ζ11ζ7+2ζ1100−3i3i−3−3−2ζ7−ζ11ζ7+2ζ11332ζ7+ζ11−ζ7−2ζ11003-3−i3−i3−3+i323+i32i3i33−i32−3−i3200-33i3i33−i32−3−i32−i3−i3−3+i323+i3200000000000000000000000000000000000000000000

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