Finite Group Databasebeta

← Group #13166894

Character table — Group #13166894

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135
size111122444444444444881212121212121212121212121818242424242424363636363611112244444444444488121212121212121212121212181824242424242436363636361111224444444444448812121212121212121212121218182424242424243636363636
order12222233666666666666444412121212121212124444121212124888836666633666666666666121212121212121212121212121212121212121212242424243666663366666666666612121212121212121212121212121212121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111
χ51111-1-111111-1-1-1-1111-1-111-1-11111-1-1-1-1111-111-1-1-111-1-11111-1-111111-1-1-1-1111-1-111-1-11111-1-1-1-1111-111-1-1-111-1-11111-1-111111-1-1-1-1111-1-111-1-11111-1-1-1-1111-111-1-1-111-1-1
χ61111-1-111111-1-1-1-1111-1-111-1-11111-1-1-1-111-11-1-111-1-1-1111111-1-111111-1-1-1-1111-1-111-1-11111-1-1-1-111-11-1-111-1-1-1111111-1-111111-1-1-1-1111-1-111-1-11111-1-1-1-111-11-1-111-1-1-111
χ71111-1-111111-1-1-1-1111-1-1-1-111-1-1-1-11111111-111-1-1-1-1-1111111-1-111111-1-1-1-1111-1-1-1-111-1-1-1-11111111-111-1-1-1-1-1111111-1-111111-1-1-1-1111-1-1-1-111-1-1-1-11111111-111-1-1-1-1-111
χ81111-1-111111-1-1-1-1111-1-1-1-111-1-1-1-1111111-11-1-111-111-1-11111-1-111111-1-1-1-1111-1-1-1-111-1-1-1-1111111-11-1-111-111-1-11111-1-111111-1-1-1-1111-1-1-1-111-1-1-1-1111111-11-1-111-111-1-1
χ922222222222222222222000000000000-2-2000000-2000022222222222222222222000000000000-2-2000000-2000022222222222222222222000000000000-2-2000000-20000
χ102222-2-222222-2-2-2-2222-2-2000000000000-2-2000000200002222-2-222222-2-2-2-2222-2-2000000000000-2-2000000200002222-2-222222-2-2-2-2222-2-2000000000000-2-200000020000
χ1122-2-22-22222-222-2-2-2-2-22-20000000000000000000002−22−222-2-22-22222-222-2-2-2-2-22-20000000000000000000002−22−222-2-22-22222-222-2-2-2-2-22-20000000000000000000002−22−2
χ1222-2-22-22222-222-2-2-2-2-22-2000000000000000000000−22−2222-2-22-22222-222-2-2-2-2-22-2000000000000000000000−22−2222-2-22-22222-222-2-2-2-2-22-2000000000000000000000−22−22
χ1322-2-2-222222-2-2-222-2-2-2-220000000000000000000002−2−2222-2-2-222222-2-2-222-2-2-2-220000000000000000000002−2−2222-2-2-222222-2-2-222-2-2-2-220000000000000000000002−2−22
χ1422-2-2-222222-2-2-222-2-2-2-22000000000000000000000−222−222-2-2-222222-2-2-222-2-2-2-22000000000000000000000−222−222-2-2-222222-2-2-222-2-2-2-22000000000000000000000−222−2
χ152-2-220022-2-2-200002-2200002-2000022-2-22-2000000000002-2-220022-2-2-200002-2200002-2000022-2-22-2000000000002-2-220022-2-2-200002-2200002-2000022-2-22-200000000000
χ162-2-220022-2-2-200002-220000-220000-2-2222-2000000000002-2-220022-2-2-200002-220000-220000-2-2222-2000000000002-2-220022-2-2-200002-220000-220000-2-2222-200000000000
χ172-2-220022-2-2-200002-22002-20022-2-20000-22000000000002-2-220022-2-2-200002-22002-20022-2-20000-22000000000002-2-220022-2-2-200002-22002-20022-2-20000-2200000000000
χ182-2-220022-2-2-200002-2200-2200-2-2220000-22000000000002-2-220022-2-2-200002-2200-2200-2-2220000-22000000000002-2-220022-2-2-200002-2200-2200-2-2220000-2200000000000
χ194444441-21-211111-2-21-2-22222-1-1-1-1-1-1-1-100000000000004444441-21-211111-2-21-2-22222-1-1-1-1-1-1-1-100000000000004444441-21-211111-2-21-2-22222-1-1-1-1-1-1-1-10000000000000
χ204444441-21-211111-2-21-2-2-2-2-2-21111111100000000000004444441-21-211111-2-21-2-2-2-2-2-21111111100000000000004444441-21-211111-2-21-2-2-2-2-2-2111111110000000000000
χ21444444-21-21-2-2-2-2-211-2110000000000000022-1-1-1-100000444444-21-21-2-2-2-2-211-2110000000000000022-1-1-1-100000444444-21-21-2-2-2-2-211-2110000000000000022-1-1-1-100000
χ22444444-21-21-2-2-2-2-211-21100000000000000-2-2111100000444444-21-21-2-2-2-2-211-21100000000000000-2-2111100000444444-21-21-2-2-2-2-211-21100000000000000-2-2111100000
χ234444-4-41-21-21-1-1-1-1-2-212222-2-2-1-1-1-1111100000000000004444-4-41-21-21-1-1-1-1-2-212222-2-2-1-1-1-1111100000000000004444-4-41-21-21-1-1-1-1-2-212222-2-2-1-1-1-111110000000000000
χ244444-4-41-21-21-1-1-1-1-2-2122-2-2221111-1-1-1-100000000000004444-4-41-21-21-1-1-1-1-2-2122-2-2221111-1-1-1-100000000000004444-4-41-21-21-1-1-1-1-2-2122-2-2221111-1-1-1-10000000000000
χ254444-4-4-21-21-2222211-2-1-1000000000000002-2-1-111000004444-4-4-21-21-2222211-2-1-1000000000000002-2-1-111000004444-4-4-21-21-2222211-2-1-1000000000000002-2-1-11100000
χ264444-4-4-21-21-2222211-2-1-100000000000000-2211-1-1000004444-4-4-21-21-2222211-2-1-100000000000000-2211-1-1000004444-4-4-21-21-2222211-2-1-100000000000000-2211-1-100000
χ2744-4-44-41-21-2-111-1-122-1-2200003−33−33−33−3000000000000044-4-44-41-21-2-111-1-122-1-2200003−33−33−33−3000000000000044-4-44-41-21-2-111-1-122-1-2200003−33−33−33−30000000000000
χ2844-4-44-41-21-2-111-1-122-1-220000−33−33−33−33000000000000044-4-44-41-21-2-111-1-122-1-220000−33−33−33−33000000000000044-4-44-41-21-2-111-1-122-1-220000−33−33−33−330000000000000
χ2944-4-44-4-21-212-2-222-1-121-100000000000000003−33−30000044-4-44-4-21-212-2-222-1-121-100000000000000003−33−30000044-4-44-4-21-212-2-222-1-121-100000000000000003−33−300000
χ3044-4-44-4-21-212-2-222-1-121-10000000000000000−33−330000044-4-44-4-21-212-2-222-1-121-10000000000000000−33−330000044-4-44-4-21-212-2-222-1-121-10000000000000000−33−3300000
χ3144-4-4-441-21-2-1-1-11122-12-200003−33−3−33−33000000000000044-4-4-441-21-2-1-1-11122-12-200003−33−3−33−33000000000000044-4-4-441-21-2-1-1-11122-12-200003−33−3−33−330000000000000
χ3244-4-4-441-21-2-1-1-11122-12-20000−33−333−33−3000000000000044-4-4-441-21-2-1-1-11122-12-20000−33−333−33−3000000000000044-4-4-441-21-2-1-1-11122-12-20000−33−333−33−30000000000000
χ3344-4-4-44-21-21222-2-2-1-12-1100000000000000003−3−330000044-4-4-44-21-21222-2-2-1-12-1100000000000000003−3−330000044-4-4-44-21-21222-2-2-1-12-1100000000000000003−3−3300000
χ3444-4-4-44-21-21222-2-2-1-12-110000000000000000−333−30000044-4-4-44-21-21222-2-2-1-12-110000000000000000−333−30000044-4-4-44-21-21222-2-2-1-12-110000000000000000−333−300000
χ354-44-4001-2-1213-33-32-2-10000003−3−333−3−3300000000000004-44-4001-2-1213-33-32-2-10000003−3−333−3−3300000000000004-44-4001-2-1213-33-32-2-10000003−3−333−3−330000000000000
χ364-44-4001-2-1213-33-32-2-1000000−333−3−333−300000000000004-44-4001-2-1213-33-32-2-1000000−333−3−333−300000000000004-44-4001-2-1213-33-32-2-1000000−333−3−333−30000000000000
χ374-44-4001-2-121-33-332-2-10000003−3−33−333−300000000000004-44-4001-2-121-33-332-2-10000003−3−33−333−300000000000004-44-4001-2-121-33-332-2-10000003−3−33−333−30000000000000
χ384-44-4001-2-121-33-332-2-1000000−333−33−3−3300000000000004-44-4001-2-121-33-332-2-1000000−333−33−3−3300000000000004-44-4001-2-121-33-332-2-1000000−333−33−3−330000000000000
χ394-44-40044-4-440000-44-40000000000000000000000000004-44-40044-4-440000-44-40000000000000000000000000004-44-40044-4-440000-44-4000000000000000000000000000
χ404-4-44001-2-12-13-3-33-221002-22-2-1-111-1-11100000000000004-4-44001-2-12-13-3-33-221002-22-2-1-111-1-11100000000000004-4-44001-2-12-13-3-33-221002-22-2-1-111-1-1110000000000000
χ414-4-44001-2-12-13-3-33-22100-22-2211-1-111-1-100000000000004-4-44001-2-12-13-3-33-22100-22-2211-1-111-1-100000000000004-4-44001-2-12-13-3-33-22100-22-2211-1-111-1-10000000000000
χ424-4-44001-2-12-1-333-3-221002-2-22-1-11111-1-100000000000004-4-44001-2-12-1-333-3-221002-2-22-1-11111-1-100000000000004-4-44001-2-12-1-333-3-221002-2-22-1-11111-1-10000000000000
χ434-4-44001-2-12-1-333-3-22100-222-211-1-1-1-11100000000000004-4-44001-2-12-1-333-3-22100-222-211-1-1-1-11100000000000004-4-44001-2-12-1-333-3-22100-222-211-1-1-1-1110000000000000
χ448-88-800-424-2-40000-2240000000000000000000000000008-88-800-424-2-40000-2240000000000000000000000000008-88-800-424-2-40000-224000000000000000000000000000
χ458-8-8800-424-2400002-2-40000000000000000000000000008-8-8800-424-2400002-2-40000000000000000000000000008-8-8800-424-2400002-2-4000000000000000000000000000
χ46111111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ471111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i321+i321+i321+i32
χ4811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1−1+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+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+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−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−i321+i321+i321+i321+i32
χ4911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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+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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ501111-1-111111-1-1-1-1111-1-111-1-11111-1-1-1-1111-111-1-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ511111-1-111111-1-1-1-1111-1-111-1-11111-1-1-1-111-11-1-111-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32
χ521111-1-111111-1-1-1-1111-1-1-1-111-1-1-1-11111111-111-1-1-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−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−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ531111-1-111111-1-1-1-1111-1-1-1-111-1-1-1-1111111-11-1-111-111-1-1−1+i32−1+i32−1+i32−1+i321−i321−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−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32
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χ1348-88-800-424-2-40000-224000000000000000000000000000−4−4i34+4i3−4−4i34+4i3002+2i3−1−i3−2−2i31+i32+2i300001+i3−1−i3−2−2i3000000000000000000000000000−4+4i34−4i3−4+4i34−4i3002−2i3−1+i3−2+2i31−i32−2i300001−i3−1+i3−2+2i3000000000000000000000000000
χ1358-8-8800-424-2400002-2-4000000000000000000000000000−4−4i34+4i34+4i3−4−4i3002+2i3−1−i3−2−2i31+i3−2−2i30000−1−i31+i32+2i3000000000000000000000000000−4+4i34−4i34−4i3−4+4i3002−2i3−1+i3−2+2i31−i3−2+2i30000−1+i31−i32−2i3000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.