Finite Group Databasebeta

← Group #13161842

Character table — Group #13161842

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204C205C206C207C208C209C210C211C212C213C214C215C216
size111122222222222244444444444444444444181818181818181818181818181818181818111122222222222244444444444444444444181818181818181818181818181818181818111122222222222244444444444444444444181818181818181818181818181818181818111122222222222244444444444444444444181818181818181818181818181818181818
order12223336666666663333366666666666666622444466661212121212121212444412121212121212121212121212121212121212121212121212121212121212124444441212121212121212121212122222666666666666666666666666666666662244446666121212121212121244441212121212121212121212121212121212121212121212121212121212121212444444121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ511-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1i−ii−i11-1-1ii−i−iii−i−i11-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1i−ii−i11-1-1ii−i−iii−i−i11-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1i−ii−i11-1-1ii−i−iii−i−i11-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1i−ii−i11-1-1ii−i−iii−i−i
χ611-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1−ii−ii11-1-1−i−iii−i−iii11-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1−ii−ii11-1-1−i−iii−i−iii11-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1−ii−ii11-1-1−i−iii−i−iii11-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1−ii−ii11-1-1−i−iii−i−iii
χ711-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11i−i−ii-1-111ii−i−i−i−iii11-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11i−i−ii-1-111ii−i−i−i−iii11-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11i−i−ii-1-111ii−i−i−i−iii11-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11i−i−ii-1-111ii−i−i−i−iii
χ811-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11−iii−i-1-111−i−iiiii−i−i11-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11−iii−i-1-111−i−iiiii−i−i11-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11−iii−i-1-111−i−iiiii−i−i11-1-111111-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11−iii−i-1-111−i−iiiii−i−i
χ9222222-12222-1-1-1222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1220000-1-1-1-100000000222222-12222-1-1-1222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1220000-1-1-1-100000000222222-12222-1-1-1222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1220000-1-1-1-100000000222222-12222-1-1-1222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1220000-1-1-1-100000000
χ10222222-12222-1-1-1222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-20000111100000000222222-12222-1-1-1222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-20000111100000000222222-12222-1-1-1222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-20000111100000000222222-12222-1-1-1222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-20000111100000000
χ1122222-122-12-12222-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-100002200000000-1-1-1-122222-122-12-12222-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-100002200000000-1-1-1-122222-122-12-12222-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-100002200000000-1-1-1-122222-122-12-12222-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-100002200000000-1-1-1-1
χ1222222-122-12-12222-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-10000-2-200000000111122222-122-12-12222-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-10000-2-200000000111122222-122-12-12222-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-10000-2-200000000111122222-122-12-12222-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-10000-2-2000000001111
χ132222-122-12-12222-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-10022000000-1-1-1-100002222-122-12-12222-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-10022000000-1-1-1-100002222-122-12-12222-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-10022000000-1-1-1-100002222-122-12-12222-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-10022000000-1-1-1-10000
χ142222-122-12-12222-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-100-2-2000000111100002222-122-12-12222-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-100-2-2000000111100002222-122-12-12222-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-100-2-2000000111100002222-122-12-12222-12-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-100-2-200000011110000
χ1522-2-222-122-2-2-111-2-22-1-1-1-12-1-1-1-1-2-2111111112-20000-1-1110000000022-2-222-122-2-2-111-2-22-1-1-1-12-1-1-1-1-2-2111111112-20000-1-1110000000022-2-222-122-2-2-111-2-22-1-1-1-12-1-1-1-1-2-2111111112-20000-1-1110000000022-2-222-122-2-2-111-2-22-1-1-1-12-1-1-1-1-2-2111111112-20000-1-11100000000
χ1622-2-222-122-2-2-111-2-22-1-1-1-12-1-1-1-1-2-211111111-22000011-1-10000000022-2-222-122-2-2-111-2-22-1-1-1-12-1-1-1-1-2-211111111-22000011-1-10000000022-2-222-122-2-2-111-2-22-1-1-1-12-1-1-1-1-2-211111111-22000011-1-10000000022-2-222-122-2-2-111-2-22-1-1-1-12-1-1-1-1-2-211111111-22000011-1-100000000
χ1722-2-22-122-1-212-2-2-21-12-1-1-1-12-1-1-111-2-211111100002i−2i00000000−i−iii22-2-22-122-1-212-2-2-21-12-1-1-1-12-1-1-111-2-211111100002i−2i00000000−i−iii22-2-22-122-1-212-2-2-21-12-1-1-1-12-1-1-111-2-211111100002i−2i00000000−i−iii22-2-22-122-1-212-2-2-21-12-1-1-1-12-1-1-111-2-211111100002i−2i00000000−i−iii
χ1822-2-22-122-1-212-2-2-21-12-1-1-1-12-1-1-111-2-21111110000−2i2i00000000ii−i−i22-2-22-122-1-212-2-2-21-12-1-1-1-12-1-1-111-2-21111110000−2i2i00000000ii−i−i22-2-22-122-1-212-2-2-21-12-1-1-1-12-1-1-111-2-21111110000−2i2i00000000ii−i−i22-2-22-122-1-212-2-2-21-12-1-1-1-12-1-1-111-2-21111110000−2i2i00000000ii−i−i
χ1922-2-2-122-121-22-2-21-2-1-12-1-1-1-12-1-11111-2-21111002i−2i000000−i−iii000022-2-2-122-121-22-2-21-2-1-12-1-1-1-12-1-11111-2-21111002i−2i000000−i−iii000022-2-2-122-121-22-2-21-2-1-12-1-1-1-12-1-11111-2-21111002i−2i000000−i−iii000022-2-2-122-121-22-2-21-2-1-12-1-1-1-12-1-11111-2-21111002i−2i000000−i−iii0000
χ2022-2-2-122-121-22-2-21-2-1-12-1-1-1-12-1-11111-2-2111100−2i2i000000ii−i−i000022-2-2-122-121-22-2-21-2-1-12-1-1-1-12-1-11111-2-2111100−2i2i000000ii−i−i000022-2-2-122-121-22-2-21-2-1-12-1-1-1-12-1-11111-2-2111100−2i2i000000ii−i−i000022-2-2-122-121-22-2-21-2-1-12-1-1-1-12-1-11111-2-2111100−2i2i000000ii−i−i0000
χ212-22-2222-2-22-2-22-2-2222222-2-2-2-2-22-22-22-222-2-20000000000000000002-22-2222-2-22-2-22-2-2222222-2-2-2-2-22-22-22-222-2-20000000000000000002-22-2222-2-22-2-22-2-2222222-2-2-2-2-22-22-22-222-2-20000000000000000002-22-2222-2-22-2-22-2-2222222-2-2-2-2-22-22-22-222-2-2000000000000000000
χ222-22-222-1-2-22-21-11-222-1-1-1-1-211112-2-11-11-1-111000000−i3i3−i3i3000000002-22-222-1-2-22-21-11-222-1-1-1-1-211112-2-11-11-1-111000000−i3i3−i3i3000000002-22-222-1-2-22-21-11-222-1-1-1-1-211112-2-11-11-1-111000000−i3i3−i3i3000000002-22-222-1-2-22-21-11-222-1-1-1-1-211112-2-11-11-1-111000000−i3i3−i3i300000000
χ232-22-222-1-2-22-21-11-222-1-1-1-1-211112-2-11-11-1-111000000i3−i3i3−i3000000002-22-222-1-2-22-21-11-222-1-1-1-1-211112-2-11-11-1-111000000i3−i3i3−i3000000002-22-222-1-2-22-21-11-222-1-1-1-1-211112-2-11-11-1-111000000i3−i3i3−i3000000002-22-222-1-2-22-21-11-222-1-1-1-1-211112-2-11-11-1-111000000i3−i3i3−i300000000
χ242-22-22-12-2121-22-2-2-1-12-1-1-11-2111-112-2-11-1-11100000000000000−i3i3−i3i32-22-22-12-2121-22-2-2-1-12-1-1-11-2111-112-2-11-1-11100000000000000−i3i3−i3i32-22-22-12-2121-22-2-2-1-12-1-1-11-2111-112-2-11-1-11100000000000000−i3i3−i3i32-22-22-12-2121-22-2-2-1-12-1-1-11-2111-112-2-11-1-11100000000000000−i3i3−i3i3
χ252-22-22-12-2121-22-2-2-1-12-1-1-11-2111-112-2-11-1-11100000000000000i3−i3i3−i32-22-22-12-2121-22-2-2-1-12-1-1-11-2111-112-2-11-1-11100000000000000i3−i3i3−i32-22-22-12-2121-22-2-2-1-12-1-1-11-2111-112-2-11-1-11100000000000000i3−i3i3−i32-22-22-12-2121-22-2-2-1-12-1-1-11-2111-112-2-11-1-11100000000000000i3−i3i3−i3
χ262-22-2-1221-2-1-2-22-212-1-12-1-111-211-11-112-2-1-11100000000003−33−300002-22-2-1221-2-1-2-22-212-1-12-1-111-211-11-112-2-1-11100000000003−33−300002-22-2-1221-2-1-2-22-212-1-12-1-111-211-11-112-2-1-11100000000003−33−300002-22-2-1221-2-1-2-22-212-1-12-1-111-211-11-112-2-1-11100000000003−33−30000
χ272-22-2-1221-2-1-2-22-212-1-12-1-111-211-11-112-2-1-1110000000000−33−3300002-22-2-1221-2-1-2-22-212-1-12-1-111-211-11-112-2-1-1110000000000−33−3300002-22-2-1221-2-1-2-22-212-1-12-1-111-211-11-112-2-1-1110000000000−33−3300002-22-2-1221-2-1-2-22-212-1-12-1-111-211-11-112-2-1-1110000000000−33−330000
χ282-2-22222-2-2-22-2-222-222222-2-2-2-2-2-22-22-22-2-2220000000000000000002-2-22222-2-2-22-2-222-222222-2-2-2-2-2-22-22-22-2-2220000000000000000002-2-22222-2-2-22-2-222-222222-2-2-2-2-2-22-22-22-2-2220000000000000000002-2-22222-2-2-22-2-222-222222-2-2-2-2-2-22-22-22-2-222000000000000000000
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χ302-2-2222-1-2-2-2211-12-22-1-1-1-1-21111-221-11-111-1-1000000i3−i3−i3i3000000002-2-2222-1-2-2-2211-12-22-1-1-1-1-21111-221-11-111-1-1000000i3−i3−i3i3000000002-2-2222-1-2-2-2211-12-22-1-1-1-1-21111-221-11-111-1-1000000i3−i3−i3i3000000002-2-2222-1-2-2-2211-12-22-1-1-1-1-21111-221-11-111-1-1000000i3−i3−i3i300000000
χ312-2-222-12-21-2-1-2-2221-12-1-1-11-21111-1-221-111-1-1000000000000003−3−332-2-222-12-21-2-1-2-2221-12-1-1-11-21111-1-221-111-1-1000000000000003−3−332-2-222-12-21-2-1-2-2221-12-1-1-11-21111-1-221-111-1-1000000000000003−3−332-2-222-12-21-2-1-2-2221-12-1-1-11-21111-1-221-111-1-1000000000000003−3−33
χ322-2-222-12-21-2-1-2-2221-12-1-1-11-21111-1-221-111-1-100000000000000−333−32-2-222-12-21-2-1-2-2221-12-1-1-11-21111-1-221-111-1-100000000000000−333−32-2-222-12-21-2-1-2-2221-12-1-1-11-21111-1-221-111-1-100000000000000−333−32-2-222-12-21-2-1-2-2221-12-1-1-11-21111-1-221-111-1-100000000000000−333−3
χ332-2-22-1221-212-2-22-1-2-1-12-1-111-2111-11-1-2211-1-10000000000−i3i3i3−i300002-2-22-1221-212-2-22-1-2-1-12-1-111-2111-11-1-2211-1-10000000000−i3i3i3−i300002-2-22-1221-212-2-22-1-2-1-12-1-111-2111-11-1-2211-1-10000000000−i3i3i3−i300002-2-22-1221-212-2-22-1-2-1-12-1-111-2111-11-1-2211-1-10000000000−i3i3i3−i30000
χ342-2-22-1221-212-2-22-1-2-1-12-1-111-2111-11-1-2211-1-10000000000i3−i3−i3i300002-2-22-1221-212-2-22-1-2-1-12-1-111-2111-11-1-2211-1-10000000000i3−i3−i3i300002-2-22-1221-212-2-22-1-2-1-12-1-111-2111-11-1-2211-1-10000000000i3−i3−i3i300002-2-22-1221-212-2-22-1-2-1-12-1-111-2111-11-1-2211-1-10000000000i3−i3−i3i30000
χ3544444-2-24-24-2-2-2-24-2-2-2111-2-2111-2-2-2-211111100000000000000000044444-2-24-24-2-2-2-24-2-2-2111-2-2111-2-2-2-211111100000000000000000044444-2-24-24-2-2-2-24-2-2-2111-2-2111-2-2-2-211111100000000000000000044444-2-24-24-2-2-2-24-2-2-2111-2-2111-2-2-2-2111111000000000000000000
χ364444-24-2-24-24-2-2-2-24-21-211-21-211-2-211-2-211110000000000000000004444-24-2-24-24-2-2-2-24-21-211-21-211-2-211-2-211110000000000000000004444-24-2-24-24-2-2-2-24-21-211-21-211-2-211-2-211110000000000000000004444-24-2-24-24-2-2-2-24-21-211-21-211-2-211-2-21111000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.