Finite Group Databasebeta

← Group #13167010

Character table — Group #13167010

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222224444444444444444444444444444888888888812121212121212121212121212121212121212121212121212121212121212121212121218183636363636727272727272108108108108
order1222344666121212123333666666666666121212121212121212121212366612121212121222446666666666666666121212121212121212121212121212124441212121244121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-111-1-111-1-1
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-11-1-111-1-111
χ711111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-111-1-11-111-1-1-1-111
χ811111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-111-1-1-11-1-11111-1-1
χ92222222222222222222222222222222222222222222222222222000000000000000000000000000000000000-2-2-2-2-2-2-20000000000
χ1022222-2-2222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000-2-22-2-2220000000000
χ112222-122-1-1-1-1-1-1-122-1-1222-1-1-1-122-1-122222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i3−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i3-2-2-211110000000000
χ122222-122-1-1-1-1-1-1-122-1-1222-1-1-1-122-1-122222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i3i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i3-2-2-211110000000000
χ132222-122-1-1-1-1-1-1-122-1-1222-1-1-1-122-1-122222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-10000000000
χ142222-122-1-1-1-1-1-1-122-1-1222-1-1-1-122-1-122222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-21111-2-2-2-2111111111111-2-2-2-211111111222-1-1-1-10000000000
χ152222-1-2-2-1-1-1111122-1-1222-1-1-1-122-1-12-2-2-2-211111111-1-1-1-1-2-211110000−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i3i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i3-2-2211-1-10000000000
χ162222-1-2-2-1-1-1111122-1-1222-1-1-1-122-1-12-2-2-2-211111111-1-1-1-1-2-211110000i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i3−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i3-2-2211-1-10000000000
χ172222-1-2-2-1-1-1111122-1-1222-1-1-1-122-1-12-2-2-2-211111111-1-1-1-1-2-2111122-2-2-1-1-1-12222-1-1-1-1-1-1-1-11111-2-2-2-21111111122-2-1-1110000000000
χ182222-1-2-2-1-1-1111122-1-1222-1-1-1-122-1-12-2-2-2-211111111-1-1-1-1-2-21111-2-2221111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-122-2-1-1110000000000
χ1922-2-222-22-2-222-2-22222-2-2-2-2-2-2-22222-222-2-22222-2-2-2-22-2-222-222-2-20000000000000000000000000000000000000000000000000−i2i2−i2i2
χ2022-2-222-22-2-222-2-22222-2-2-2-2-2-2-22222-222-2-22222-2-2-2-22-2-222-222-2-20000000000000000000000000000000000000000000000000i2−i2i2−i2
χ2122-2-22-222-2-2-2-2222222-2-2-2-2-2-2-22222-2-2-222-2-2-2-222222-2-22-22-2-2220000000000000000000000000000000000000000000000000−i2i2i2−i2
χ2222-2-22-222-2-2-2-2222222-2-2-2-2-2-2-22222-2-2-222-2-2-2-222222-2-22-22-2-2220000000000000000000000000000000000000000000000000i2−i2−i2i2
χ232-22-2200-22-20000222222-222-2-2-2-2-2-2-200000000000022-2-2000000002i−2i00000000000000002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i-2202-2000000000000
χ242-22-2200-22-20000222222-222-2-2-2-2-2-2-200000000000022-2-200000000−2i2i0000000000000000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i-2202-2000000000000
χ252-22-2200-22-20000222222-222-2-2-2-2-2-2-200000000000022-2-20000002-2002-22-222-2-222-2-222-2-200000000000000002-20-22000000000000
χ262-22-2200-22-20000222222-222-2-2-2-2-2-2-200000000000022-2-2000000-2200-22-22-2-222-2-222-2-22200000000000000002-20-22000000000000
χ272-22-2-1001-113−33−322-1-122-2-1-111-2-211-2000033−3−333−3−3-1-111003−33−3002i−2i−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i3−ii−ii2i2i−2i−2i−i−iii−i−iii-220-113−30000000000
χ282-22-2-1001-113−33−322-1-122-2-1-111-2-211-2000033−3−333−3−3-1-111003−33−300−2i2ii3−i3−i3i30000i3i3−i3−i3−i3−i3i3i3i−ii−i−2i−2i2i2iii−i−iii−i−i-220-113−30000000000
χ292-22-2-1001-113−33−322-1-122-2-1-111-2-211-2000033−3−333−3−3-1-111003−33−32-200-11-1122-2-2-1-111-1-1113−3−33000033−3−3−3−3332-201-1−330000000000
χ302-22-2-1001-113−33−322-1-122-2-1-111-2-211-2000033−3−333−3−3-1-111003−33−3-22001-11-1-2-22211-1-111-1-1−333−30000−3−33333−3−32-201-1−330000000000
χ312-22-2-1001-11−33−3322-1-122-2-1-111-2-211-20000−3−333−3−333-1-11100−33−33002i−2ii3−i3−i3i30000i3i3−i3−i3−i3−i3i3i3−ii−ii2i2i−2i−2i−i−iii−i−iii-220-11−330000000000
χ322-22-2-1001-11−33−3322-1-122-2-1-111-2-211-20000−3−333−3−333-1-11100−33−3300−2i2i−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i3i−ii−i−2i−2i2i2iii−i−iii−i−i-220-11−330000000000
χ332-22-2-1001-11−33−3322-1-122-2-1-111-2-211-20000−3−333−3−333-1-11100−33−332-200-11-1122-2-2-1-111-1-111−333−30000−3−33333−3−32-201-13−30000000000
χ342-22-2-1001-11−33−3322-1-122-2-1-111-2-211-20000−3−333−3−333-1-11100−33−33-22001-11-1-2-22211-1-111-1-13−3−33000033−3−3−3−3332-201-13−30000000000
χ35444444444444441-2-2-21-2-2-2-2-2-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000000000022-1-1-1-10000
χ36444444444444441-2-2-21-2-2-2-2-2-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-211111111110000000000000000000000000000000000000000000-2-211110000
χ3744444444444444-2111-2111111-2111-2111111111111-2-2-2-2-2-2-2-2-2-222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000
χ3844444444444444-2111-2111111-2111-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111-2-2-2-211111111111100000000000000000
χ3944444-4-4444-4-4-4-41-2-2-21-2-2-2-2-2-21-2-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000002-2-1-1110000
χ4044444-4-4444-4-4-4-41-2-2-21-2-2-2-2-2-21-2-2-212222222222221111-1-1-1-1-1-10000000000000000000000000000000000000000000-2211-1-10000
χ4144444-4-4444-4-4-4-4-2111-2111111-2111-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222222222-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000000000000
χ4244444-4-4444-4-4-4-4-2111-2111111-2111-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222222-2-222-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000
χ434444-244-2-2-2-2-2-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32−1−3i32−1+3i32-21−1−3i32−1+3i32-21111−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i321111-2-211112222−1−i3−1−i3−1+i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i3−1−i3−1+i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3200000000000000000
χ444444-244-2-2-2-2-2-2-2-21−1−3i32−1+3i32-211−1−3i32−1+3i32−1−3i32−1+3i32-21−1−3i32−1+3i32-21111−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i321111-2-21111-2-2-2-21+i31+i31−i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i31+i31−i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200000000000000000
χ454444-244-2-2-2-2-2-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32−1+3i32−1−3i32-21−1+3i32−1−3i32-21111−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i321111-2-211112222−1+i3−1+i3−1−i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i3−1+i3−1−i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3200000000000000000
χ464444-244-2-2-2-2-2-2-2-21−1+3i32−1−3i32-211−1+3i32−1−3i32−1+3i32−1−3i32-21−1+3i32−1−3i32-21111−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i321111-2-21111-2-2-2-21−i31−i31+i31+i31111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i31−i31+i31+i31111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3200000000000000000
χ474444-2-4-4-2-2-22222-21−1−3i32−1+3i32-211−1−3i32−1+3i32−1−3i32−1+3i32-21−1−3i32−1+3i32-2-1-1-1-11+3i321−3i321+3i321−3i321+3i321−3i321+3i321−3i32111122-1-1-1-122-2-2−1−i3−1−i3−1+i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i31+i31−i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200000000000000000
χ484444-2-4-4-2-2-22222-21−1−3i32−1+3i32-211−1−3i32−1+3i32−1−3i32−1+3i32-21−1−3i32−1+3i32-2-1-1-1-11+3i321−3i321+3i321−3i321+3i321−3i321+3i321−3i32111122-1-1-1-1-2-2221+i31+i31−i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i3−1−i3−1+i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3200000000000000000
χ494444-2-4-4-2-2-22222-21−1+3i32−1−3i32-211−1+3i32−1−3i32−1+3i32−1−3i32-21−1+3i32−1−3i32-2-1-1-1-11−3i321+3i321−3i321+3i321−3i321+3i321−3i321+3i32111122-1-1-1-122-2-2−1+i3−1+i3−1−i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i31−i31+i31+i31111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3200000000000000000
χ504444-2-4-4-2-2-22222-21−1+3i32−1−3i32-211−1+3i32−1−3i32−1+3i32−1−3i32-21−1+3i32−1−3i32-2-1-1-1-11−3i321+3i321−3i321+3i321−3i321+3i321−3i321+3i32111122-1-1-1-1-2-2221−i31−i31+i31+i31111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i3−1+i3−1−i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3200000000000000000
χ5144-4-444-44-4-444-4-41-2-2-2-12222221-2-2-2-1-2-222-2-2-2-222221-1-111-111-1-10000000000000000000000000000000000000000000003−33−30000
χ5244-4-444-44-4-444-4-41-2-2-2-12222221-2-2-2-1-2-222-2-2-2-222221-1-111-111-1-1000000000000000000000000000000000000000000000−33−330000
χ5344-4-444-44-4-444-4-4-21112-1-1-1-1-1-1-2111211-1-11111-1-1-1-1-222-2-22-2-22200000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300000000000000000
χ5444-4-444-44-4-444-4-4-21112-1-1-1-1-1-1-2111211-1-11111-1-1-1-1-222-2-22-2-22200000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300000000000000000
χ5544-4-44-444-4-4-4-4441-2-2-2-12222221-2-2-2-122-2-22222-2-2-2-21-1-11-11-1-1110000000000000000000000000000000000000000000003−3−330000
χ5644-4-44-444-4-4-4-4441-2-2-2-12222221-2-2-2-122-2-22222-2-2-2-21-1-11-11-1-111000000000000000000000000000000000000000000000−333−30000
χ5744-4-44-444-4-4-4-444-21112-1-1-1-1-1-1-21112-1-111-1-1-1-11111-222-22-222-2-200000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300000000000000000
χ5844-4-44-444-4-4-4-444-21112-1-1-1-1-1-1-21112-1-111-1-1-1-11111-222-22-222-2-200000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300000000000000000
χ5944-4-4-24-4-222-2-22244-2-2-4-4-4222244-2-2-444-4-4-2-2-2-22222-222-24-4-2-22200000000000000000000000000000000000000000000000000000
χ6044-4-4-24-4-222-2-222-21−1−3i32−1+3i322-1-11+3i321−3i321+3i321−3i32-21−1−3i32−1+3i32211-1-1−1−3i32−1+3i32−1−3i32−1+3i321+3i321−3i321+3i321−3i321-1-11-2211-1-100000000−i3i3−i3i3−3+i323−i32−3+i323−i323+i32−3−i323+i32−3−i320000−i3i3−i3i3−3+i323−i32−3+i323−i323+i32−3−i323+i32−3−i3200000000000000000
χ6144-4-4-24-4-222-2-222-21−1−3i32−1+3i322-1-11+3i321−3i321+3i321−3i32-21−1−3i32−1+3i32211-1-1−1−3i32−1+3i32−1−3i32−1+3i321+3i321−3i321+3i321−3i321-1-11-2211-1-100000000i3−i3i3−i33−i32−3+i323−i32−3+i32−3−i323+i32−3−i323+i320000i3−i3i3−i33−i32−3+i323−i32−3+i32−3−i323+i32−3−i323+i3200000000000000000
χ6244-4-4-24-4-222-2-222-21−1+3i32−1−3i322-1-11−3i321+3i321−3i321+3i32-21−1+3i32−1−3i32211-1-1−1+3i32−1−3i32−1+3i32−1−3i321−3i321+3i321−3i321+3i321-1-11-2211-1-100000000−i3i3−i3i33+i32−3−i323+i32−3−i32−3+i323−i32−3+i323−i320000−i3i3−i3i33+i32−3−i323+i32−3−i32−3+i323−i32−3+i323−i3200000000000000000
χ6344-4-4-24-4-222-2-222-21−1+3i32−1−3i322-1-11−3i321+3i321−3i321+3i32-21−1+3i32−1−3i32211-1-1−1+3i32−1−3i32−1+3i32−1−3i321−3i321+3i321−3i321+3i321-1-11-2211-1-100000000i3−i3i3−i3−3−i323+i32−3−i323+i323−i32−3+i323−i32−3+i320000i3−i3i3−i3−3−i323+i32−3−i323+i323−i32−3+i323−i32−3+i3200000000000000000
χ6444-4-4-2-44-22222-2-244-2-2-4-4-4222244-2-2-4-4-4442222-2-2-2-2-222-2-4422-2-200000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.