Finite Group Databasebeta

← Group #11723244

Character table — Group #11723244

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size111122222222224444444444441212121212121212121212121818181811112222222222444444444444121212121212121212121212181818181111222222222244444444444412121212121212121212121218181818
order12223344666666366612121212121212124444121212121212121244443666331212666666366612121212121212121212121212121212121212121212121236663312126666663666121212121212121212121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1111111-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1111111-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1
χ6111111-1-11111111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-111111111-1-11111111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-111111111-1-11111111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-111
χ7111111-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111
χ8111111-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-1
χ922222-1222-12-12-1-1-1-1-122-1-1-1-1-1-100220000-1-1-1-1000022222-1222-12-12-1-1-1-1-122-1-1-1-1-1-100220000-1-1-1-1000022222-1222-12-12-1-1-1-1-122-1-1-1-1-1-100220000-1-1-1-10000
χ1022222-1222-12-12-1-1-1-1-122-1-1-1-1-1-100-2-200001111000022222-1222-12-12-1-1-1-1-122-1-1-1-1-1-100-2-200001111000022222-1222-12-12-1-1-1-1-122-1-1-1-1-1-100-2-2000011110000
χ1122222-1-2-22-12-12-1-1-1-1-1-2-2111111002-20000-1-111000022222-1-2-22-12-12-1-1-1-1-1-2-2111111002-20000-1-111000022222-1-2-22-12-12-1-1-1-1-1-2-2111111002-20000-1-1110000
χ1222222-1-2-22-12-12-1-1-1-1-1-2-211111100-22000011-1-1000022222-1-2-22-12-12-1-1-1-1-1-2-211111100-22000011-1-1000022222-1-2-22-12-12-1-1-1-1-1-2-211111100-22000011-1-10000
χ132222-1222-12-12-12-1-1-1-1-1-122-1-1-1-12200-1-1-1-1000000002222-1222-12-12-12-1-1-1-1-1-122-1-1-1-12200-1-1-1-1000000002222-1222-12-12-12-1-1-1-1-1-122-1-1-1-12200-1-1-1-100000000
χ142222-1222-12-12-12-1-1-1-1-1-122-1-1-1-1-2-2001111000000002222-1222-12-12-12-1-1-1-1-1-122-1-1-1-1-2-2001111000000002222-1222-12-12-12-1-1-1-1-1-122-1-1-1-1-2-200111100000000
χ152222-12-2-2-12-12-12-1-1-1-111-2-211112-200-1-111000000002222-12-2-2-12-12-12-1-1-1-111-2-211112-200-1-111000000002222-12-2-2-12-12-12-1-1-1-111-2-211112-200-1-11100000000
χ162222-12-2-2-12-12-12-1-1-1-111-2-21111-220011-1-1000000002222-12-2-2-12-12-12-1-1-1-111-2-21111-220011-1-1000000002222-12-2-2-12-12-12-1-1-1-111-2-21111-220011-1-100000000
χ1722-2-2222-2-2-222-2-22-2-222-22-222-2-2000000000000000022-2-2222-2-2-222-2-22-2-222-22-222-2-2000000000000000022-2-2222-2-2-222-2-22-2-222-22-222-2-20000000000000000
χ1822-2-222-22-2-222-2-22-2-22-22-22-2-222000000000000000022-2-222-22-2-222-2-22-2-22-22-22-2-222000000000000000022-2-222-22-2-222-2-22-2-22-22-22-2-2220000000000000000
χ1922-2-22-12-2-212-1-21-111-12-2-11-1-111000000003−33−3000022-2-22-12-2-212-1-21-111-12-2-11-1-111000000003−33−3000022-2-22-12-2-212-1-21-111-12-2-11-1-111000000003−33−30000
χ2022-2-22-12-2-212-1-21-111-12-2-11-1-11100000000−33−33000022-2-22-12-2-212-1-21-111-12-2-11-1-11100000000−33−33000022-2-22-12-2-212-1-21-111-12-2-11-1-11100000000−33−330000
χ2122-2-22-1-22-212-1-21-111-1-221-111-1-1000000003−3−33000022-2-22-1-22-212-1-21-111-1-221-111-1-1000000003−3−33000022-2-22-1-22-212-1-21-111-1-221-111-1-1000000003−3−330000
χ2222-2-22-1-22-212-1-21-111-1-221-111-1-100000000−333−3000022-2-22-1-22-212-1-21-111-1-221-111-1-100000000−333−3000022-2-22-1-22-212-1-21-111-1-221-111-1-100000000−333−30000
χ2322-2-2-122-21-2-121-2-111-1-112-2-1-11100003−33−30000000022-2-2-122-21-2-121-2-111-1-112-2-1-11100003−33−30000000022-2-2-122-21-2-121-2-111-1-112-2-1-11100003−33−300000000
χ2422-2-2-122-21-2-121-2-111-1-112-2-1-1110000−33−330000000022-2-2-122-21-2-121-2-111-1-112-2-1-1110000−33−330000000022-2-2-122-21-2-121-2-111-1-112-2-1-1110000−33−3300000000
χ2522-2-2-12-221-2-121-2-111-11-1-2211-1-100003−3−330000000022-2-2-12-221-2-121-2-111-11-1-2211-1-100003−3−330000000022-2-2-12-221-2-121-2-111-11-1-2211-1-100003−3−3300000000
χ2622-2-2-12-221-2-121-2-111-11-1-2211-1-10000−333−30000000022-2-2-12-221-2-121-2-111-11-1-2211-1-10000−333−30000000022-2-2-12-221-2-121-2-111-11-1-2211-1-10000−333−300000000
χ272-22-2220022-2-2-2-222-2-2000000000000000000002-2002-22-2220022-2-2-2-222-2-2000000000000000000002-2002-22-2220022-2-2-2-222-2-2000000000000000000002-200
χ282-22-2220022-2-2-2-222-2-200000000000000000000-22002-22-2220022-2-2-2-222-2-200000000000000000000-22002-22-2220022-2-2-2-222-2-200000000000000000000-2200
χ292-2-222200-2-2-2-2222-22-200000000000000000000002-22-2-222200-2-2-2-2222-22-200000000000000000000002-22-2-222200-2-2-2-2222-22-200000000000000000000002-2
χ302-2-222200-2-2-2-2222-22-20000000000000000000000-222-2-222200-2-2-2-2222-22-20000000000000000000000-222-2-222200-2-2-2-2222-22-20000000000000000000000-22
χ314444-2-244-2-2-2-2-2-21111-2-2-2-2111100000000000000004444-2-244-2-2-2-2-2-21111-2-2-2-2111100000000000000004444-2-244-2-2-2-2-2-21111-2-2-2-211110000000000000000
χ324444-2-2-4-4-2-2-2-2-2-211112222-1-1-1-100000000000000004444-2-2-4-4-2-2-2-2-2-211112222-1-1-1-100000000000000004444-2-2-4-4-2-2-2-2-2-211112222-1-1-1-10000000000000000
χ3344-4-4-2-24-422-2-2221-1-11-22-2211-1-1000000000000000044-4-4-2-24-422-2-2221-1-11-22-2211-1-1000000000000000044-4-4-2-24-422-2-2221-1-11-22-2211-1-10000000000000000
χ3444-4-4-2-2-4422-2-2221-1-112-22-2-1-111000000000000000044-4-4-2-2-4422-2-2221-1-112-22-2-1-111000000000000000044-4-4-2-2-4422-2-2221-1-112-22-2-1-1110000000000000000
χ354-44-44-2004-2-42-42-2-2220000000000000000000000004-44-44-2004-2-42-42-2-2220000000000000000000000004-44-44-2004-2-42-42-2-222000000000000000000000000
χ364-44-4-2400-242-42-4-2-2220000000000000000000000004-44-4-2400-242-42-4-2-2220000000000000000000000004-44-4-2400-242-42-4-2-222000000000000000000000000
χ374-44-4-2-200-2-2222211-1-100003i−3i3i−3i00000000000000004-44-4-2-200-2-2222211-1-100003i−3i3i−3i00000000000000004-44-4-2-200-2-2222211-1-100003i−3i3i−3i0000000000000000
χ384-44-4-2-200-2-2222211-1-10000−3i3i−3i3i00000000000000004-44-4-2-200-2-2222211-1-10000−3i3i−3i3i00000000000000004-44-4-2-200-2-2222211-1-10000−3i3i−3i3i0000000000000000
χ394-4-444-200-42-424-2-22-220000000000000000000000004-4-444-200-42-424-2-22-220000000000000000000000004-4-444-200-42-424-2-22-22000000000000000000000000
χ404-4-44-24002-42-4-24-22-220000000000000000000000004-4-44-24002-42-4-24-22-220000000000000000000000004-4-44-24002-42-4-24-22-22000000000000000000000000
χ414-4-44-2-2002222-2-21-11-100003i−3i−3i3i00000000000000004-4-44-2-2002222-2-21-11-100003i−3i−3i3i00000000000000004-4-44-2-2002222-2-21-11-100003i−3i−3i3i0000000000000000
χ424-4-44-2-2002222-2-21-11-10000−3i3i3i−3i00000000000000004-4-44-2-2002222-2-21-11-10000−3i3i3i−3i00000000000000004-4-44-2-2002222-2-21-11-10000−3i3i3i−3i0000000000000000
χ43111111111111111111111111111111111111111111−1+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+i32−1+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+i32−1+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−i32−1−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−i32−1−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−i32−1−i32−1−i32−1−i32−1−i32
χ441111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ4511111111111111111111111111-1-111-1-1-1-11111-1-1-1-1−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ4611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−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−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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ47111111-1-11111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ48111111-1-11111111111-1-1-1-1-1-1-1-11-1-1111-1-1-1-111-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ49111111-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ50111111-1-11111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ5122222-1222-12-12-1-1-1-1-122-1-1-1-1-1-100220000-1-1-1-10000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i31−i321−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i3200−1+i3−1+i300001−i321−i321−i321−i320000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i31+i321+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i3200−1−i3−1−i300001+i321+i321+i321+i320000
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χ1214-44-4-2-200-2-2222211-1-100003i−3i3i−3i0000000000000000−2−2i32+2i3−2−2i32+2i31+i31+i3001+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i32−1−i321+i321+i3200003ζ11−3ζ113ζ11−3ζ110000000000000000−2+2i32−2i3−2+2i32−2i31−i31−i3001−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i32−1+i321−i321−i3200003ζ7−3ζ73ζ7−3ζ70000000000000000
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χ1264-4-44-2-2002222-2-21-11-10000−3i3i3i−3i0000000000000000−2−2i32+2i32+2i3−2−2i31+i31+i300−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i321+i32−1−i321+i320000−3ζ113ζ113ζ11−3ζ110000000000000000−2+2i32−2i32−2i3−2+2i31−i31−i300−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i321−i32−1+i321−i320000−3ζ73ζ73ζ7−3ζ70000000000000000

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