Finite Group Databasebeta

← Group #11723307

Character table — Group #11723307

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size111122222222224444444444441212121212121212121212121818181811112222222222444444444444121212121212121212121212181818181111222222222244444444444412121212121212121212121218181818
order1222223366666636666666666644441212121212121212444436666633666666366666666666121212121212121212121212121212123666663366666636666666666612121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-11-11111-1-1-1-1-1-1-1-1111111111111111111111111111-11-11111-1-1-1-1-1-1-1-1111111111111111111111111111-11-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-11-11-1-1-1-11111-1-1-1-111111111111111111111111111-11-11-1-1-1-11111-1-1-1-111111111111111111111111111-11-11-1-1-1-11111-1-1-1-1
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
χ51111-1-1111111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-111-1-11111-1-1111111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-111-1-11111-1-1111111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-111-1-1
χ61111-1-1111111111-1-1-1-1111-1-1-1-11-1-1111-1-1-1-111-1-1111111-1-1111111111-1-1-1-1111-1-1-1-11-1-1111-1-1-1-111-1-1111111-1-1111111111-1-1-1-1111-1-1-1-11-1-1111-1-1-1-111-1-111
χ71111-1-1111111111-1-1-1-1111-1-1-1-1-111-1-1-11111-1-1-1-1111111-1-1111111111-1-1-1-1111-1-1-1-1-111-1-1-11111-1-1-1-1111111-1-1111111111-1-1-1-1111-1-1-1-1-111-1-1-11111-1-1-1-111
χ81111-1-1111111111-1-1-1-1111-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1111111111-1-1-1-1111-1-1-1-1-1-111-1-111-1-11111-1-11111-1-1111111111-1-1-1-1111-1-1-1-1-1-111-1-111-1-11111-1-1
χ92222222-12-122-1-1-122-1-1-1-1-1-1-1-1-102020000-1-1-1-100002222222-12-122-1-1-122-1-1-1-1-1-1-1-1-102020000-1-1-1-100002222222-12-122-1-1-122-1-1-1-1-1-1-1-1-102020000-1-1-1-10000
χ102222222-12-122-1-1-122-1-1-1-1-1-1-1-1-10-20-20000111100002222222-12-122-1-1-122-1-1-1-1-1-1-1-1-10-20-20000111100002222222-12-122-1-1-122-1-1-1-1-1-1-1-1-10-20-2000011110000
χ11222222-12-12-1-122-1-1-122-1-1-1-1-1-1-12020-1-1-1-100000000222222-12-12-1-122-1-1-122-1-1-1-1-1-1-12020-1-1-1-100000000222222-12-12-1-122-1-1-122-1-1-1-1-1-1-12020-1-1-1-100000000
χ12222222-12-12-1-122-1-1-122-1-1-1-1-1-1-1-20-20111100000000222222-12-12-1-122-1-1-122-1-1-1-1-1-1-1-20-20111100000000222222-12-12-1-122-1-1-122-1-1-1-1-1-1-1-20-20111100000000
χ132222-2-22-12-122-1-1-1-2-211-1-1-11111020-20000-1-11100002222-2-22-12-122-1-1-1-2-211-1-1-11111020-20000-1-11100002222-2-22-12-122-1-1-1-2-211-1-1-11111020-20000-1-1110000
χ142222-2-22-12-122-1-1-1-2-211-1-1-111110-202000011-1-100002222-2-22-12-122-1-1-1-2-211-1-1-111110-202000011-1-100002222-2-22-12-122-1-1-1-2-211-1-1-111110-202000011-1-10000
χ152222-2-2-12-12-1-122-111-2-2-1-1-1111120-20-1-111000000002222-2-2-12-12-1-122-111-2-2-1-1-1111120-20-1-111000000002222-2-2-12-12-1-122-111-2-2-1-1-1111120-20-1-11100000000
χ162222-2-2-12-12-1-122-111-2-2-1-1-11111-202011-1-1000000002222-2-2-12-12-1-122-111-2-2-1-1-11111-202011-1-1000000002222-2-2-12-12-1-122-111-2-2-1-1-11111-202011-1-100000000
χ1722-2-22-22222-2-2-2-222-22-22-2-222-2-2000000000000000022-2-22-22222-2-2-2-222-22-22-2-222-2-2000000000000000022-2-22-22222-2-2-2-222-22-22-2-222-2-20000000000000000
χ1822-2-22-22-12-1-2-211-12-2-11-111-1-111000000003−33−3000022-2-22-22-12-1-2-211-12-2-11-111-1-111000000003−33−3000022-2-22-22-12-1-2-211-12-2-11-111-1-111000000003−33−30000
χ1922-2-22-22-12-1-2-211-12-2-11-111-1-11100000000−33−33000022-2-22-22-12-1-2-211-12-2-11-111-1-11100000000−33−33000022-2-22-22-12-1-2-211-12-2-11-111-1-11100000000−33−330000
χ2022-2-22-2-12-1211-2-2-1-112-2-111-1-11100003−33−30000000022-2-22-2-12-1211-2-2-1-112-2-111-1-11100003−33−30000000022-2-22-2-12-1211-2-2-1-112-2-111-1-11100003−33−300000000
χ2122-2-22-2-12-1211-2-2-1-112-2-111-1-1110000−33−330000000022-2-22-2-12-1211-2-2-1-112-2-111-1-1110000−33−330000000022-2-22-2-12-1211-2-2-1-112-2-111-1-1110000−33−3300000000
χ2222-2-2-222222-2-2-2-22-22-222-2-2-2-222000000000000000022-2-2-222222-2-2-2-22-22-222-2-2-2-222000000000000000022-2-2-222222-2-2-2-22-22-222-2-2-2-2220000000000000000
χ2322-2-2-222-12-1-2-211-1-221-1-11111-1-1000000003−3−33000022-2-2-222-12-1-2-211-1-221-1-11111-1-1000000003−3−33000022-2-2-222-12-1-2-211-1-221-1-11111-1-1000000003−3−330000
χ2422-2-2-222-12-1-2-211-1-221-1-11111-1-100000000−333−3000022-2-2-222-12-1-2-211-1-221-1-11111-1-100000000−333−3000022-2-2-222-12-1-2-211-1-221-1-11111-1-100000000−333−30000
χ2522-2-2-22-12-1211-2-2-11-1-22-11111-1-100003−3−330000000022-2-2-22-12-1211-2-2-11-1-22-11111-1-100003−3−330000000022-2-2-22-12-1211-2-2-11-1-22-11111-1-100003−3−3300000000
χ2622-2-2-22-12-1211-2-2-11-1-22-11111-1-10000−333−30000000022-2-2-22-12-1211-2-2-11-1-22-11111-1-10000−333−30000000022-2-2-22-12-1211-2-2-11-1-22-11111-1-10000−333−300000000
χ272-22-20022-2-22-22-220000-22-20000000000000000002i−2i2-22-20022-2-22-22-220000-22-20000000000000000002i−2i2-22-20022-2-22-22-220000-22-20000000000000000002i−2i
χ282-22-20022-2-22-22-220000-22-2000000000000000000−2i2i2-22-20022-2-22-22-220000-22-2000000000000000000−2i2i2-22-20022-2-22-22-220000-22-2000000000000000000−2i2i
χ292-2-220022-2-2-22-2220000-2-2200000000000000002-2002-2-220022-2-2-22-2220000-2-2200000000000000002-2002-2-220022-2-2-22-2220000-2-2200000000000000002-200
χ302-2-220022-2-2-22-2220000-2-220000000000000000-22002-2-220022-2-2-22-2220000-2-220000000000000000-22002-2-220022-2-2-22-2220000-2-220000000000000000-2200
χ31444444-2-2-2-2-2-2-2-21-2-2-2-211111110000000000000000444444-2-2-2-2-2-2-2-21-2-2-2-211111110000000000000000444444-2-2-2-2-2-2-2-21-2-2-2-211111110000000000000000
χ324444-4-4-2-2-2-2-2-2-2-212222111-1-1-1-100000000000000004444-4-4-2-2-2-2-2-2-2-212222111-1-1-1-100000000000000004444-4-4-2-2-2-2-2-2-2-212222111-1-1-1-10000000000000000
χ3344-4-44-4-2-2-2-222221-22-221-1-111-1-1000000000000000044-4-44-4-2-2-2-222221-22-221-1-111-1-1000000000000000044-4-44-4-2-2-2-222221-22-221-1-111-1-10000000000000000
χ3444-4-4-44-2-2-2-2222212-22-21-1-1-1-111000000000000000044-4-4-44-2-2-2-2222212-22-21-1-1-1-111000000000000000044-4-4-44-2-2-2-2222212-22-21-1-1-1-1110000000000000000
χ354-44-4004-2-424-4-22-200002-22000000000000000000004-44-4004-2-424-4-22-200002-22000000000000000000004-44-4004-2-424-4-22-200002-2200000000000000000000
χ364-44-400-242-4-224-4-200002-22000000000000000000004-44-400-242-4-224-4-200002-22000000000000000000004-44-400-242-4-224-4-200002-2200000000000000000000
χ374-44-400-2-222-22-2210000-11-13-33-300000000000000004-44-400-2-222-22-2210000-11-13-33-300000000000000004-44-400-2-222-22-2210000-11-13-33-30000000000000000
χ384-44-400-2-222-22-2210000-11-1-33-3300000000000000004-44-400-2-222-22-2210000-11-1-33-3300000000000000004-44-400-2-222-22-2210000-11-1-33-330000000000000000
χ394-4-44004-2-42-442-2-2000022-2000000000000000000004-4-44004-2-42-442-2-2000022-2000000000000000000004-4-44004-2-42-442-2-2000022-200000000000000000000
χ404-4-4400-242-42-2-44-2000022-2000000000000000000004-4-4400-242-42-2-44-2000022-2000000000000000000004-4-4400-242-42-2-44-2000022-200000000000000000000
χ414-4-4400-2-2222-22-210000-1-113-3-3300000000000000004-4-4400-2-2222-22-210000-1-113-3-3300000000000000004-4-4400-2-2222-22-210000-1-113-3-330000000000000000
χ424-4-4400-2-2222-22-210000-1-11-333-300000000000000004-4-4400-2-2222-22-210000-1-11-333-300000000000000004-4-4400-2-2222-22-210000-1-11-333-30000000000000000
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
χ44111111111111111111111111111-11-11111-1-1-1-1-1-1-1-1−1+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+i321−i32−1+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−i321+i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ4511111111111111111111111111-11-11-1-1-1-11111-1-1-1-1−1+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−i32−1+i321−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+i32−1−i321+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
χ471111-1-1111111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-111-1-1−1+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ481111-1-1111111111-1-1-1-1111-1-1-1-11-1-1111-1-1-1-111-1-111−1+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−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
χ491111-1-1111111111-1-1-1-1111-1-1-1-1-111-1-1-11111-1-1-1-111−1+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−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
χ501111-1-1111111111-1-1-1-1111-1-1-1-1-1-111-1-111-1-11111-1-1−1+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ512222222-12-122-1-1-122-1-1-1-1-1-1-1-1-102020000-1-1-1-10000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i320−1+i30−1+i300001−i321−i321−i321−i320000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i320−1−i30−1−i300001+i321+i321+i321+i320000
χ522222222-12-122-1-1-122-1-1-1-1-1-1-1-1-10-20-2000011110000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i3201−i301−i30000−1+i32−1+i32−1+i32−1+i320000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i3201+i301+i30000−1−i32−1−i32−1−i32−1−i320000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.