Finite Group Databasebeta

← Group #13164477

Character table — Group #13164477

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111111122222233333333333366666666666666666666666666666666666666242424242424242424242424242424242424242424242424363636363636363636363636363636363636363636363636
order123344661212121224661212224466661212121223466666666666666666121212121212121212121212121212121212333666666666121212121212121212121212224444446666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1111111111111-11-1-1-1111111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-1
χ4111111111111-1-1-1-1-1-1111111111111-11-1-1-1111111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-11111
χ51111-1-111-1-1-1-11-111-1-111-1-11111-1-1-1-111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-111-1-1-1-11111-1-111-1-1
χ61111-1-111-1-1-1-11-111-1-111-1-11111-1-1-1-111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-1-11111-1-1-1-111-1-111
χ71111-1-111-1-1-1-1-11-1-11111-1-11111-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-11-1-111111-1-1-1-111-1-1-1-111
χ81111-1-111-1-1-1-1-11-1-11111-1-11111-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-111-111-1-1-1-1-11111-1-11111-1-1
χ922222222222222222222222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ102222222222222222222222222222222-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1000000000000000000000000
χ112222222222222222222222222222222-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-1000000000000000000000000
χ122222222222222222222222222222222-1222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-122000000000000000000000000
χ13222222222222-2-2-2-2-2-2222222222222-22-2-2-2222222-2-2-2-2-2-2-2-22-2-222222222-2-2-2-2-2-2-2-2-1-1-1111111-1-1-1-1-1-1-1-1-1111111000000000000000000000000
χ14222222222222-2-2-2-2-2-2222222222222-2-1-2-2-2-1-1-1-1-1-111111111-1-2-2-1-1-1-1-1-1-1-1111111112-1-1-2-211112-1-122-1-1-1-1-2-21111000000000000000000000000
χ15222222222222-2-2-2-2-2-2222222222222-2-1-2-2-2-1-1-1-1-1-111111111-1-2-2-1-1-1-1-1-1-1-111111111-12-111-2-211-12-1-1-122-1-111-2-211000000000000000000000000
χ16222222222222-2-2-2-2-2-2222222222222-2-1-2-2-2-1-1-1-1-1-111111111-1-2-2-1-1-1-1-1-1-1-111111111-1-121111-2-2-1-12-1-1-1-1221111-2-2000000000000000000000000
χ172222-2-222-2-2-2-22-222-2-222-2-22222-2-2-2-222-222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000
χ182222-2-222-2-2-2-22-222-2-222-2-22222-2-2-2-22-1-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-211111111111111112-1-122-1-1-1-12-1-1-2-21111-2-21111000000000000000000000000
χ192222-2-222-2-2-2-22-222-2-222-2-22222-2-2-2-22-1-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111111111111111-12-1-1-122-1-1-12-111-2-21111-2-211000000000000000000000000
χ202222-2-222-2-2-2-22-222-2-222-2-22222-2-2-2-22-1-222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111111111111111-1-12-1-1-1-122-1-121111-2-21111-2-2000000000000000000000000
χ212222-2-222-2-2-2-2-22-2-22222-2-22222-2-2-2-2-222-2-2222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-222222222-1-1-1111111-1-1-1111111-1-1-1-1-1-1000000000000000000000000
χ222222-2-222-2-2-2-2-22-2-22222-2-22222-2-2-2-2-2-12-2-2-1-1-1-1-1-111111111-12211111111-1-1-1-1-1-1-1-12-1-1-2-211112-1-1-2-2111122-1-1-1-1000000000000000000000000
χ232222-2-222-2-2-2-2-22-2-22222-2-22222-2-2-2-2-2-12-2-2-1-1-1-1-1-111111111-12211111111-1-1-1-1-1-1-1-1-12-111-2-211-12-111-2-211-1-122-1-1000000000000000000000000
χ242222-2-222-2-2-2-2-22-2-22222-2-22222-2-2-2-2-2-12-2-2-1-1-1-1-1-111111111-12211111111-1-1-1-1-1-1-1-1-1-121111-2-2-1-121111-2-2-1-1-1-122000000000000000000000000
χ252-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i02000222-2-2-200000000-2002i2i2i2i−2i−2i−2i−2i00000000222000000-2-2-22i−2i2i−2i2i−2i000000000000000000000000000000
χ262-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i02000222-2-2-200000000-2002i2i2i2i−2i−2i−2i−2i00000000-1-1-1−i3i3−i3i3−i3i3111−ii−ii−ii3−33−33−3000000000000000000000000
χ272-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i02000222-2-2-200000000-2002i2i2i2i−2i−2i−2i−2i00000000-1-1-1i3−i3i3−i3i3−i3111−ii−ii−ii−33−33−33000000000000000000000000
χ282-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i0-1000-1-1-1111−i3−i3−i3−i3i3i3i3i3100−i−i−i−iiiii3333−3−3−3−32-1-100−i3i3i3−i3-2112i−2i−ii−ii003−3−33000000000000000000000000
χ292-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i0-1000-1-1-1111−i3−i3−i3−i3i3i3i3i3100−i−i−i−iiiii3333−3−3−3−3-12-1i3−i300−i3i31-21−ii2i−2i−ii−33003−3000000000000000000000000
χ302-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i0-1000-1-1-1111−i3−i3−i3−i3i3i3i3i3100−i−i−i−iiiii3333−3−3−3−3-1-12−i3i3i3−i30011-2−ii−ii2i−2i3−3−3300000000000000000000000000
χ312-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i0-1000-1-1-1111i3i3i3i3−i3−i3−i3−i3100−i−i−i−iiiii−3−3−3−333332-1-100i3−i3−i3i3-2112i−2i−ii−ii00−333−3000000000000000000000000
χ322-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i0-1000-1-1-1111i3i3i3i3−i3−i3−i3−i3100−i−i−i−iiiii−3−3−3−33333-12-1−i3i300i3−i31-21−ii2i−2i−ii3−300−33000000000000000000000000
χ332-2222i−2i-2-22i2i−2i−2i0000002-22i−2i22-2-22i2i−2i−2i0-1000-1-1-1111i3i3i3i3−i3−i3−i3−i3100−i−i−i−iiiii−3−3−3−33333-1-12i3−i3−i3i30011-2−ii−ii2i−2i−333−300000000000000000000000000
χ342-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i02000222-2-2-200000000-200−2i−2i−2i−2i2i2i2i2i00000000222000000-2-2-2−2i2i−2i2i−2i2i000000000000000000000000000000
χ352-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i02000222-2-2-200000000-200−2i−2i−2i−2i2i2i2i2i00000000-1-1-1−i3i3−i3i3−i3i3111i−ii−ii−i−33−33−33000000000000000000000000
χ362-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i02000222-2-2-200000000-200−2i−2i−2i−2i2i2i2i2i00000000-1-1-1i3−i3i3−i3i3−i3111i−ii−ii−i3−33−33−3000000000000000000000000
χ372-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i0-1000-1-1-1111−i3−i3−i3−i3i3i3i3i3100iiii−i−i−i−i−3−3−3−333332-1-100−i3i3i3−i3-211−2i2ii−ii−i00−333−3000000000000000000000000
χ382-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i0-1000-1-1-1111−i3−i3−i3−i3i3i3i3i3100iiii−i−i−i−i−3−3−3−33333-12-1i3−i300−i3i31-21i−i−2i2ii−i3−300−33000000000000000000000000
χ392-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i0-1000-1-1-1111−i3−i3−i3−i3i3i3i3i3100iiii−i−i−i−i−3−3−3−33333-1-12−i3i3i3−i30011-2i−ii−i−2i2i−333−300000000000000000000000000
χ402-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i0-1000-1-1-1111i3i3i3i3−i3−i3−i3−i3100iiii−i−i−i−i3333−3−3−3−32-1-100i3−i3−i3i3-211−2i2ii−ii−i003−3−33000000000000000000000000
χ412-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i0-1000-1-1-1111i3i3i3i3−i3−i3−i3−i3100iiii−i−i−i−i3333−3−3−3−3-12-1−i3i300i3−i31-21i−i−2i2ii−i−33003−3000000000000000000000000
χ422-222−2i2i-2-2−2i−2i2i2i0000002-2−2i2i22-2-2−2i−2i2i2i0-1000-1-1-1111i3i3i3i3−i3−i3−i3−i3100iiii−i−i−i−i3333−3−3−3−3-1-12i3−i3−i3i30011-2i−ii−i−2i2i3−3−3300000000000000000000000000
χ43333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1-13-1-1-13-1-1-13-1-1-13-1-1-10000000000000000000000001111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ44333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1-13-1-1-13-1-1-13-1-1-13-1-1-1000000000000000000000000-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ45333333333333-3-3-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-113111-1-1-1-1-1-1-3111-31113113-1-1-13-1-1-1-3111-31110000000000000000000000001-11-1-1-11111-1-111-1-1-1-1-1-11111
χ46333333333333-3-3-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-113111-1-1-1-1-1-1-3111-31113113-1-1-13-1-1-1-3111-3111000000000000000000000000-11-1111-1-1-1-111-1-1111111-1-1-1-1
χ473333-3-333-3-3-3-33-333-3-3-1-111-1-1-1-11111-131-1-1-1-1-1-1-1-13-1-1-13-1-1-1311-3111-3111-3111-31110000000000000000000000001-1-11-11-1111-1-1-1-111-1-111-1-111
χ483333-3-333-3-3-3-33-333-3-3-1-111-1-1-1-11111-131-1-1-1-1-1-1-1-13-1-1-13-1-1-1311-3111-3111-3111-3111000000000000000000000000-111-11-11-1-1-11111-1-111-1-111-1-1
χ493333-3-333-3-3-3-3-33-3-333-1-111-1-1-1-1111113-111-1-1-1-1-1-1-3111-31113-1-1-3111-31113-1-1-13-1-1-100000000000000000000000011-1-1-111-11111-1-1-1-1-1-11111-1-1
χ503333-3-333-3-3-3-3-33-3-333-1-111-1-1-1-1111113-111-1-1-1-1-1-1-3111-31113-1-1-3111-31113-1-1-13-1-1-1000000000000000000000000-1-1111-1-11-1-1-1-1111111-1-1-1-111
χ5133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32303−3−3i32−3+3i32000000000000000−3−3i32−3+3i32000000000000000000000000000000000000000011111111−1−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
χ5233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32303−3−3i32−3+3i32000000000000000−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ5333−3−3i32−3+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−i32-10-11+i321−i322−1−i3−1+i32−1−i3−1+i302−1−i3−1+i302−1−i3−1+i301+i321−i3202−1−i3−1+i302−1−i3−1+i302−1−i3−1+i302−1−i3−1+i30000000000000000000000001111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ5433−3−3i32−3+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−i32-10-11+i321−i322−1−i3−1+i32−1−i3−1+i302−1−i3−1+i302−1−i3−1+i301+i321−i3202−1−i3−1+i302−1−i3−1+i302−1−i3−1+i302−1−i3−1+i3000000000000000000000000-1-1-1-111111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ5533−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-30-33+3i323−3i320000000000000003+3i323−3i3200000000000000000000000000000000000000001-11-111-1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ5633−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-30-33+3i323−3i320000000000000003+3i323−3i320000000000000000000000000000000000000000-11-11-1-1111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ5733−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32101−1−i32−1+i322−1−i3−1+i32−1−i3−1+i30-21+i31−i30-21+i31−i30−1−i32−1+i3202−1−i3−1+i302−1−i3−1+i30-21+i31−i30-21+i31−i30000000000000000000000001-11-1-1-111−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ5833−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32101−1−i32−1+i322−1−i3−1+i32−1−i3−1+i30-21+i31−i30-21+i31−i30−1−i32−1+i3202−1−i3−1+i302−1−i3−1+i30-21+i31−i30-21+i31−i3000000000000000000000000-11-1111-1-11+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+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 12 (ζ12 = 1); i = ζ3.