Finite Group Databasebeta

← Group #13173332

Character table — Group #13173332

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size11112222222222222222222222444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444999918181818181818181818181818181818181818181818108108108108108108108108
order122234444446661212121212121212121212123333336666666666666666661212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212122222444444666612121212121212121212121244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−i−iii
χ81111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i
χ911111-1-111-1-1111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11-11-11-11-1
χ1011111-1-111-1-1111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-11-11
χ1111111-1-111-1-1111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111i−ii−i−ii−ii
χ1211111-1-111-1-1111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−ii−iii−ii−i
χ1311111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-111-1-11
χ1411111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-111-1
χ1511111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1i−i−ii−iii−i
χ1611111-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−iii−ii−i−ii
χ172222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ182222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2111111111111111100000000
χ192222-122-2-2-2-2-1-1-1-1-1-1-11111111122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-2-2-2-2-2-2-2-21111111111111111222222-2-2-2-2-1-1-1-1-1-1-1-11111111100000000
χ202222-122-2-2-2-2-1-1-1-1-1-1-11111111122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-2-2-2-2-2-2-2-21111111111111111-2-2-2-2-2-2222211111111-1-1-1-1-1-1-1-100000000
χ212222-1-2-222-2-2-1-1-11111-1-1-1-1111122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111112222-2-222-2-2-1-1-1-11111-1-1-1-1111100000000
χ222222-1-2-222-2-2-1-1-11111-1-1-1-1111122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-2-2-2-222-2-2221111-1-1-1-11111-1-1-1-100000000
χ232222-1-2-2-2-222-1-1-111111111-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-2-2-2-2-2-2-2-2111111111111111122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-222-1-1-1-111111111-1-1-1-100000000
χ242222-1-2-2-2-222-1-1-111111111-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-2-2-2-2-2-2-2-2111111111111111122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-21111-1-1-1-1-1-1-1-1111100000000
χ2522-2-2200002-22-2-20000000022-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002222-2-2-2-222222222-2-2-2-2-2-2-2-222-2-200002-222-2-20000000022-2-200000000
χ2622-2-2200002-22-2-20000000022-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2220000-22-2-22200000000-2-22200000000
χ2722-2-220000-222-2-200000000-2-22222222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000-2-2-2-22222-2-2-2-2-2-2-2-22222222222-2-20000-2222-2-200000000-2-22200000000
χ2822-2-220000-222-2-200000000-2-22222222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000-2-2-2-22222-2-2-2-2-2-2-2-222222222-2-22200002-2-2-2220000000022-2-200000000
χ2922-2-2-100002-2-11133−3−333−3−3-1-11122-1-1-1-122-2-2-2-2-1-1-1-1111111110000000033333333−3−3−3−3−3−3−3−30000000033333333−3−3−3−3−3−3−3−32222-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-200002-2-1-11133−3−333−3−3-1-11100000000
χ3022-2-2-100002-2-11133−3−333−3−3-1-11122-1-1-1-122-2-2-2-2-1-1-1-1111111110000000033333333−3−3−3−3−3−3−3−30000000033333333−3−3−3−3−3−3−3−32222-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2220000-2211-1-1−3−333−3−33311-1-100000000
χ3122-2-2-100002-2-111−3−333−3−333-1-11122-1-1-1-122-2-2-2-2-1-1-1-11111111100000000−3−3−3−3−3−3−3−33333333300000000−3−3−3−3−3−3−3−3333333332222-2-2-2-2-1-1-1-1-1-1-1-11111111122-2-200002-2-1-111−3−333−3−333-1-11100000000
χ3222-2-2-100002-2-111−3−333−3−333-1-11122-1-1-1-122-2-2-2-2-1-1-1-11111111100000000−3−3−3−3−3−3−3−33333333300000000−3−3−3−3−3−3−3−3333333332222-2-2-2-2-1-1-1-1-1-1-1-111111111-2-2220000-2211-1-133−3−333−3−311-1-100000000
χ3322-2-2-10000-22-11133−3−3−3−33311-1-122-1-1-1-122-2-2-2-2-1-1-1-1111111110000000033333333−3−3−3−3−3−3−3−300000000−3−3−3−3−3−3−3−333333333-2-2-2-2222211111111-1-1-1-1-1-1-1-122-2-20000-22-1-11133−3−3−3−33311-1-100000000
χ3422-2-2-10000-22-11133−3−3−3−33311-1-122-1-1-1-122-2-2-2-2-1-1-1-1111111110000000033333333−3−3−3−3−3−3−3−300000000−3−3−3−3−3−3−3−333333333-2-2-2-2222211111111-1-1-1-1-1-1-1-1-2-22200002-211-1-1−3−33333−3−3-1-11100000000
χ3522-2-2-10000-22-111−3−33333−3−311-1-122-1-1-1-122-2-2-2-2-1-1-1-11111111100000000−3−3−3−3−3−3−3−3333333330000000033333333−3−3−3−3−3−3−3−3-2-2-2-2222211111111-1-1-1-1-1-1-1-122-2-20000-22-1-111−3−33333−3−311-1-100000000
χ3622-2-2-10000-22-111−3−33333−3−311-1-122-1-1-1-122-2-2-2-2-1-1-1-11111111100000000−3−3−3−3−3−3−3−3333333330000000033333333−3−3−3−3−3−3−3−3-2-2-2-2222211111111-1-1-1-1-1-1-1-1-2-22200002-211-1-133−3−3−3−333-1-11100000000
χ372-22-22002-200-22-200002-22-20000222222-2-222-2-2-2-2-2-22222-2-2-2-20000000000000000000000002222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000002-22-2002-2002-22-200002-22-2000000000000
χ382-22-22002-200-22-200002-22-20000222222-2-222-2-2-2-2-2-22222-2-2-2-20000000000000000000000002222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000-22-2200-2200-22-220000-22-22000000000000
χ392-22-2200-2200-22-20000-22-220000222222-2-222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000-2-2-2-22222-2-2-2-22222-2-2-2-222220000000000000000000000002-22-200-22002-22-20000-22-22000000000000
χ402-22-2200-2200-22-20000-22-220000222222-2-222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000-2-2-2-22222-2-2-2-22222-2-2-2-22222000000000000000000000000-22-22002-200-22-2200002-22-2000000000000
χ412-22-2-1002-2001-113−33−3-11-113−33−322-1-1-1-1-2-222-2-21111-1-1-1-11111000000003333−3−3−3−33333−3−3−3−32222-2-2-2-2-1-1-1-11111-1-1-1-11111000000003333−3−3−3−33333−3−3−3−32-22-2002-200-11-113−33−3-11-113−33−300000000
χ422-22-2-1002-2001-113−33−3-11-113−33−322-1-1-1-1-2-222-2-21111-1-1-1-11111000000003333−3−3−3−33333−3−3−3−32222-2-2-2-2-1-1-1-11111-1-1-1-11111000000003333−3−3−3−33333−3−3−3−3-22-2200-22001-11-1−33−331-11-1−33−3300000000
χ432-22-2-1002-2001-11−33−33-11-11−33−3322-1-1-1-1-2-222-2-21111-1-1-1-1111100000000−3−3−3−33333−3−3−3−333332222-2-2-2-2-1-1-1-11111-1-1-1-1111100000000−3−3−3−33333−3−3−3−333332-22-2002-200-11-11−33−33-11-11−33−3300000000
χ442-22-2-1002-2001-11−33−33-11-11−33−3322-1-1-1-1-2-222-2-21111-1-1-1-1111100000000−3−3−3−33333−3−3−3−333332222-2-2-2-2-1-1-1-11111-1-1-1-1111100000000−3−3−3−33333−3−3−3−33333-22-2200-22001-11-13−33−31-11-13−33−300000000
χ452-22-2-100-22001-113−33−31-11-1−33−3322-1-1-1-1-2-222-2-21111-1-1-1-11111000000003333−3−3−3−33333−3−3−3−3-2-2-2-222221111-1-1-1-11111-1-1-1-100000000−3−3−3−33333−3−3−3−333332-22-200-2200-11-113−33−31-11-1−33−3300000000
χ462-22-2-100-22001-113−33−31-11-1−33−3322-1-1-1-1-2-222-2-21111-1-1-1-11111000000003333−3−3−3−33333−3−3−3−3-2-2-2-222221111-1-1-1-11111-1-1-1-100000000−3−3−3−33333−3−3−3−33333-22-22002-2001-11-1−33−33-11-113−33−300000000
χ472-22-2-100-22001-11−33−331-11-13−33−322-1-1-1-1-2-222-2-21111-1-1-1-1111100000000−3−3−3−33333−3−3−3−33333-2-2-2-222221111-1-1-1-11111-1-1-1-1000000003333−3−3−3−33333−3−3−3−32-22-200-2200-11-11−33−331-11-13−33−300000000
χ482-22-2-100-22001-11−33−331-11-13−33−322-1-1-1-1-2-222-2-21111-1-1-1-1111100000000−3−3−3−33333−3−3−3−33333-2-2-2-222221111-1-1-1-11111-1-1-1-1000000003333−3−3−3−33333−3−3−3−3-22-22002-2001-11-13−33−3-11-11−33−3300000000
χ492-2-2222-20000-2-222-2-2200000000222222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000000000002-2-222-200002-2-222-2-220000000000000000
χ502-2-2222-20000-2-222-2-2200000000222222-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000-222-2-220000-222-2-222-20000000000000000
χ512-2-222-220000-2-22-222-200000000222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000000000002-2-22-2200002-2-22-222-20000000000000000
χ522-2-222-220000-2-22-222-200000000222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000-222-22-20000-222-22-2-220000000000000000
χ532-2-22-12-2000011-1-111-13−3−33−333−322-1-1-1-1-2-2-2-22211111111-1-1-1-12222-2-2-2-2-1-1-1-111111111-1-1-1-1000000003333−3−3−3−3−3−3−3−3333300000000−3−3−3−333333333−3−3−3−32-2-222-20000-111-1-111-13−3−33−333−300000000
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χ1534-4-44-2-44000022-22-2-22−232323−23−232323−231-2−1−3i32−1+3i3211-12-121-21+3i321−3i32-1-11+3i321−3i32-1-1−1−3i32−1+3i3211-1-12211-2-21+3i321−3i32-1-1−1−3i32−1+3i3211−1−3i32−1+3i32111+3i321−3i32-1-1−3i3i003i−3i00−ζ7−2ζ112ζ7+ζ1133ζ7+2ζ11−2ζ7−ζ11−3−3ζ7+2ζ11−2ζ7−ζ11−3−3−ζ7−2ζ112ζ7+ζ1133−3i3i003i−3i00−ζ7−2ζ112ζ7+ζ1133ζ7+2ζ11−2ζ7−ζ11−3−3ζ7+2ζ11−2ζ7−ζ11−3−3−ζ7−2ζ112ζ7+ζ11330000000000000000000000000000000000
χ1544-4-44-2-44000022-22-2-22−232323−23−232323−231-2−1+3i32−1−3i3211-12-121-21−3i321+3i32-1-11−3i321+3i32-1-1−1+3i32−1−3i3211-1-12211-2-21−3i321+3i32-1-1−1+3i32−1−3i3211−1+3i32−1−3i32111−3i321+3i32-1-13i−3i00−3i3i002ζ7+ζ11−ζ7−2ζ1133−2ζ7−ζ11ζ7+2ζ11−3−3−2ζ7−ζ11ζ7+2ζ11−3−32ζ7+ζ11−ζ7−2ζ11333i−3i00−3i3i002ζ7+ζ11−ζ7−2ζ1133−2ζ7−ζ11ζ7+2ζ11−3−3−2ζ7−ζ11ζ7+2ζ11−3−32ζ7+ζ11−ζ7−2ζ11330000000000000000000000000000000000
χ1554-4-44-2-44000022-22-2-22−232323−23−232323−23-2111−1−3i32−1+3i322-12-1-21-1-11+3i321−3i32-1-11+3i321−3i3211−1−3i32−1+3i3222-1-1-2-211-1-11+3i321−3i3211−1−3i32−1+3i3211−1−3i32−1+3i32-1-11+3i321−3i3200−3i3i003i−3i33−ζ7−2ζ112ζ7+ζ11−3−3ζ7+2ζ11−2ζ7−ζ11−3−3ζ7+2ζ11−2ζ7−ζ1133−ζ7−2ζ112ζ7+ζ1100−3i3i003i−3i33−ζ7−2ζ112ζ7+ζ11−3−3ζ7+2ζ11−2ζ7−ζ11−3−3ζ7+2ζ11−2ζ7−ζ1133−ζ7−2ζ112ζ7+ζ110000000000000000000000000000000000
χ1564-4-44-2-44000022-22-2-22−232323−23−232323−23-2111−1+3i32−1−3i322-12-1-21-1-11−3i321+3i32-1-11−3i321+3i3211−1+3i32−1−3i3222-1-1-2-211-1-11−3i321+3i3211−1+3i32−1−3i3211−1+3i32−1−3i32-1-11−3i321+3i32003i−3i00−3i3i332ζ7+ζ11−ζ7−2ζ11−3−3−2ζ7−ζ11ζ7+2ζ11−3−3−2ζ7−ζ11ζ7+2ζ11332ζ7+ζ11−ζ7−2ζ11003i−3i00−3i3i332ζ7+ζ11−ζ7−2ζ11−3−3−2ζ7−ζ11ζ7+2ζ11−3−3−2ζ7−ζ11ζ7+2ζ11332ζ7+ζ11−ζ7−2ζ110000000000000000000000000000000000

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