Finite Group Databasebeta

← Group #72246516

Character table — Group #72246516

Order 3024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size112222446677771212121212121212141414141414141418282828284242424242424242424242424242424242425454126126112222446677771212121212121212141414141414141418282828284242424242424242424242424242424242425454126126
order123366367143366212121214242424233336666233662466666666121212121212121214146622666666141466664242424242424242666666662666624666666661212121212121212141466
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ3111111111111111111111111111111-111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-11111-11-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111111111111111111111-11111-11-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32
χ61111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32-1-1-1-11+i321−i321+i321+i321−i321−i32-1-11+i321−i321+i321+i321−i321−i3211−1−i32−1+i321111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32-1-1-1-11+i321−i321+i321+i321−i321−i32-1-11+i321−i321+i321+i321−i321−i3211−1−i32−1+i32
χ71111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1−1−i32−1+i32−1−i32−1+i321-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321+i321−i321−i32-1-11+i321−i321111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1−1−i32−1+i32−1−i32−1+i321-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321+i321−i321−i32-1-11+i321−i32
χ81111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1−1−i32−1+i32−1−i32−1+i32-11-1-11+i321−i321+i321+i321−i321−i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321111111111−1−i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1−1−i32−1+i32−1−i32−1+i32-11-1-11+i321−i321+i321+i321−i321−i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321−i32
χ91111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32
χ101111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32-1-1-1-11−i321+i321−i321−i321+i321+i32-1-11−i321+i321−i321−i321+i321+i3211−1+i32−1−i321111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32-1-1-1-11−i321+i321−i321−i321+i321+i32-1-11−i321+i321−i321−i321+i321+i3211−1+i32−1−i32
χ111111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1−1+i32−1−i32−1+i32−1−i321-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321−i321+i321+i32-1-11−i321+i321111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1−1+i32−1−i32−1+i32−1−i321-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321−i321+i321+i32-1-11−i321+i32
χ121111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1−1+i32−1−i32−1+i32−1−i32-11-1-11−i321+i321−i321−i321+i321+i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321111111111−1+i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1−1+i32−1−i32−1+i32−1−i32-11-1-11−i321+i321−i321−i321+i321+i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321+i32
χ13222-1-12-1-12222222-1-1-12-1-1-122-1-1-1-1220-1-1-1-120-1-122-1-1-1-1000000000000222-1-12-1-12222222-1-1-12-1-1-122-1-1-1-1220-1-1-1-120-1-122-1-1-1-1000000000000
χ14222-1-12-1-12222222-1-1-12-1-1-122-1-1-1-1220-1-1-1-1-2011-2-21111000000000000222-1-12-1-12222222-1-1-12-1-1-122-1-1-1-1220-1-1-1-1-2011-2-21111000000000000
χ15222-1-12-1-122−1−i3−1+i3−1−i3−1+i32-1-1-12-1-1-1−1−i3−1+i31+i321−i321+i321−i32−1−i3−1+i301+i321−i321+i321−i3220-1-1−1−i3−1+i31+i321+i321−i321−i32000000000000222-1-12-1-122−1−i3−1+i3−1−i3−1+i32-1-1-12-1-1-1−1−i3−1+i31+i321−i321+i321−i32−1−i3−1+i301+i321−i321+i321−i3220-1-1−1−i3−1+i31+i321+i321−i321−i32000000000000
χ16222-1-12-1-122−1−i3−1+i3−1−i3−1+i32-1-1-12-1-1-1−1−i3−1+i31+i321−i321+i321−i32−1−i3−1+i301+i321−i321+i321−i32-20111+i31−i3−1−i32−1−i32−1+i32−1+i32000000000000222-1-12-1-122−1−i3−1+i3−1−i3−1+i32-1-1-12-1-1-1−1−i3−1+i31+i321−i321+i321−i32−1−i3−1+i301+i321−i321+i321−i32-20111+i31−i3−1−i32−1−i32−1+i32−1+i32000000000000
χ17222-1-12-1-122−1+i3−1−i3−1+i3−1−i32-1-1-12-1-1-1−1+i3−1−i31−i321+i321−i321+i32−1+i3−1−i301−i321+i321−i321+i3220-1-1−1+i3−1−i31−i321−i321+i321+i32000000000000222-1-12-1-122−1+i3−1−i3−1+i3−1−i32-1-1-12-1-1-1−1+i3−1−i31−i321+i321−i321+i32−1+i3−1−i301−i321+i321−i321+i3220-1-1−1+i3−1−i31−i321−i321+i321+i32000000000000
χ18222-1-12-1-122−1+i3−1−i3−1+i3−1−i32-1-1-12-1-1-1−1+i3−1−i31−i321+i321−i321+i32−1+i3−1−i301−i321+i321−i321+i32-20111−i31+i3−1+i32−1+i32−1−i32−1−i32000000000000222-1-12-1-122−1+i3−1−i3−1+i3−1−i32-1-1-12-1-1-1−1+i3−1−i31−i321+i321−i321+i32−1+i3−1−i301−i321+i321−i321+i32-20111−i31+i3−1+i32−1+i32−1−i32−1−i32000000000000
χ1922-122-1-1-1222222-12-1-1-12-1-1-1-12222-1-10-1-1-1-10200000000-1-122-1-1-1-1000022-122-1-1-1222222-12-1-1-12-1-1-1-12222-1-10-1-1-1-10200000000-1-122-1-1-1-10000
χ2022-122-1-1-1222222-12-1-1-12-1-1-1-12222-1-10-1-1-1-10-20000000011-2-21111000022-122-1-1-1222222-12-1-1-12-1-1-1-12222-1-10-1-1-1-10-20000000011-2-211110000
χ2122-122-1-1-122−1−i3−1+i3−1−i3−1+i3-12-1-1-12-1-11+i321−i32−1−i3−1+i3−1−i3−1+i31+i321−i3201+i321−i321+i321−i320200000000-1-1−1−i3−1+i31+i321+i321−i321−i32000022-122-1-1-122−1−i3−1+i3−1−i3−1+i3-12-1-1-12-1-11+i321−i32−1−i3−1+i3−1−i3−1+i31+i321−i3201+i321−i321+i321−i320200000000-1-1−1−i3−1+i31+i321+i321−i321−i320000
χ2222-122-1-1-122−1−i3−1+i3−1−i3−1+i3-12-1-1-12-1-11+i321−i32−1−i3−1+i3−1−i3−1+i31+i321−i3201+i321−i321+i321−i320-200000000111+i31−i3−1−i32−1−i32−1+i32−1+i32000022-122-1-1-122−1−i3−1+i3−1−i3−1+i3-12-1-1-12-1-11+i321−i32−1−i3−1+i3−1−i3−1+i31+i321−i3201+i321−i321+i321−i320-200000000111+i31−i3−1−i32−1−i32−1+i32−1+i320000
χ2322-122-1-1-122−1+i3−1−i3−1+i3−1−i3-12-1-1-12-1-11−i321+i32−1+i3−1−i3−1+i3−1−i31−i321+i3201−i321+i321−i321+i320200000000-1-1−1+i3−1−i31−i321−i321+i321+i32000022-122-1-1-122−1+i3−1−i3−1+i3−1−i3-12-1-1-12-1-11−i321+i32−1+i3−1−i3−1+i3−1−i31−i321+i3201−i321+i321−i321+i320200000000-1-1−1+i3−1−i31−i321−i321+i321+i320000
χ2422-122-1-1-122−1+i3−1−i3−1+i3−1−i3-12-1-1-12-1-11−i321+i32−1+i3−1−i3−1+i3−1−i31−i321+i3201−i321+i321−i321+i320-200000000111−i31+i3−1+i32−1+i32−1−i32−1−i32000022-122-1-1-122−1+i3−1−i3−1+i3−1−i3-12-1-1-12-1-11−i321+i32−1+i3−1−i3−1+i3−1−i31−i321+i3201−i321+i321−i321+i320-200000000111−i31+i3−1+i32−1+i32−1−i32−1−i320000
χ252-222-2-22-22-222-2-22222-2-2-2-22222-2-2-2-2022-2-200000000000000000000002-222-2-22-22-222-2-22222-2-2-2-22222-2-2-2-2022-2-20000000000000000000000
χ262-222-2-22-22-2−1−i3−1+i31+i31−i32222-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30−1−i3−1+i31+i31−i300000000000000000000002-222-2-22-22-2−1−i3−1+i31+i31−i32222-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i30−1−i3−1+i31+i31−i30000000000000000000000
χ272-222-2-22-22-2−1+i3−1−i31−i31+i32222-2-2-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i30−1+i3−1−i31−i31+i300000000000000000000002-222-2-22-22-2−1+i3−1−i31−i31+i32222-2-2-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i30−1+i3−1−i31−i31+i30000000000000000000000
χ282-22-11-2-112-222-2-22-1-1-1-211122-1-111-2-20-1-11100−i3i300−i3i3−i3i30000000000002-22-11-2-112-222-2-22-1-1-1-211122-1-111-2-20-1-11100−i3i300−i3i3−i3i3000000000000
χ292-22-11-2-112-222-2-22-1-1-1-211122-1-111-2-20-1-11100i3−i300i3−i3i3−i30000000000002-22-11-2-112-222-2-22-1-1-1-211122-1-111-2-20-1-11100i3−i300i3−i3i3−i3000000000000
χ302-22-11-2-112-2−1−i3−1+i31+i31−i32-1-1-1-2111−1−i3−1+i31+i321−i32−1−i32−1+i321+i31−i301+i321−i32−1−i32−1+i3200−i3i300−3+i323−i323+i32−3−i320000000000002-22-11-2-112-2−1−i3−1+i31+i31−i32-1-1-1-2111−1−i3−1+i31+i321−i32−1−i32−1+i321+i31−i301+i321−i32−1−i32−1+i3200−i3i300−3+i323−i323+i32−3−i32000000000000
χ312-22-11-2-112-2−1−i3−1+i31+i31−i32-1-1-1-2111−1−i3−1+i31+i321−i32−1−i32−1+i321+i31−i301+i321−i32−1−i32−1+i3200i3−i3003−i32−3+i32−3−i323+i320000000000002-22-11-2-112-2−1−i3−1+i31+i31−i32-1-1-1-2111−1−i3−1+i31+i321−i32−1−i32−1+i321+i31−i301+i321−i32−1−i32−1+i3200i3−i3003−i32−3+i32−3−i323+i32000000000000
χ322-22-11-2-112-2−1+i3−1−i31−i31+i32-1-1-1-2111−1+i3−1−i31−i321+i32−1+i32−1−i321−i31+i301−i321+i32−1+i32−1−i3200−i3i3003+i32−3−i32−3+i323−i320000000000002-22-11-2-112-2−1+i3−1−i31−i31+i32-1-1-1-2111−1+i3−1−i31−i321+i32−1+i32−1−i321−i31+i301−i321+i32−1+i32−1−i3200−i3i3003+i32−3−i32−3+i323−i32000000000000
χ332-22-11-2-112-2−1+i3−1−i31−i31+i32-1-1-1-2111−1+i3−1−i31−i321+i32−1+i32−1−i321−i31+i301−i321+i32−1+i32−1−i3200i3−i300−3−i323+i323−i32−3+i320000000000002-22-11-2-112-2−1+i3−1−i31−i31+i32-1-1-1-2111−1+i3−1−i31−i321+i32−1+i32−1−i321−i31+i301−i321+i32−1+i32−1−i3200i3−i300−3−i323+i323−i32−3+i32000000000000
χ342-2-12-21-112-222-2-2-12-1-11-211-1-122-2-2110-1-11100000000003−3003−33−300002-2-12-21-112-222-2-2-12-1-11-211-1-122-2-2110-1-11100000000003−3003−33−30000
χ352-2-12-21-112-222-2-2-12-1-11-211-1-122-2-2110-1-1110000000000−3300−33−3300002-2-12-21-112-222-2-2-12-1-11-211-1-122-2-2110-1-1110000000000−3300−33−330000
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.