Finite Group Databasebeta

← Group #13156565

Character table — Group #13156565

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212242424242424242424363636363636727272727272216
order12223334466666666612121212333666666666121212121212121212121212366612121212121288882424242424242424242424242424242424242424242424242424242424242424266666666441212121244121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-11-1-111-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-11
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000000000000002-222-2-20000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000000000000-22-2-2220000000
χ11222222-1222-122-1222-122222-1-122-1-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10000000200-1-10
χ12222222-1222-122-1222-122222-1-122-1-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111110000000-200110
χ13222222-1222-122-1222-122222-1-122-1-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-2000000000000111111111111222-1-1-1-1-1-10000000-200110
χ14222222-1222-122-1222-122222-1-122-1-1-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-2000000000000111111111111-2-2-21111110000000200-1-10
χ1522222-1222-122-1222-122222-12-1-1-122-1-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-122-1-1-1-100000020-1-1000
χ1622222-1222-122-1222-122222-12-1-1-122-1-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-211-2-21111000000-2011000
χ1722222-1222-122-1222-122222-12-1-1-122-1-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-200001111111111110000000000002-1-122-1-1-1-1000000-2011000
χ1822222-1222-122-1222-122222-12-1-1-122-1-1-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-20000111111111111000000000000-211-2-2111100000020-1-1000
χ192222-1222222-122-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000022-1-1-1-10000000
χ202222-1222222-122-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111000000000-2-211110000000
χ212222-1222222-122-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1000000000-2-211110000000
χ222222-1222222-122-1-122-1-1-1-1-1-12-1-1-1-122-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-21111111100000000022-1-1-1-10000000
χ232222-122-2-222-122-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−333−3−300003333−3−3−3−300003333−3−3−3−30000000002-2-1-1110000000
χ242222-122-2-222-122-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333000000000-2211-1-10000000
χ252222-122-2-222-122-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3000000000-2211-1-10000000
χ262222-122-2-222-122-1-1221111-1-12-1-1-1-122-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−333−3−3330000−3−3−3−333330000−3−3−3−333330000000002-2-1-1110000000
χ2722-2-22222-2-2-2222-2-2-2-222-2-2222-2-2-2-2-2-22222-222-2-2-22-2-2222-2-222-222-2-22i−2i002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000
χ2822-2-22222-2-2-2222-2-2-2-222-2-2222-2-2-2-2-2-22222-222-2-2-22-2-2222-2-222-222-2-2−2i2i00−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000
χ2922-2-2222-22-2-2222-2-2-2-2-2-222222-2-2-2-2-2-2222-22-2-2222-222-2-22-2-22-22-2-222002i−2i00002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ3022-2-2222-22-2-2222-2-2-2-2-2-222222-2-2-2-2-2-2222-22-2-2222-222-2-22-2-22-22-2-22200−2i2i0000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ3122-2-222-1-22-2122-1-2-2-21-2-2222-1-1-2-211112-1-1-2-1-2-2-1-1212211-111-11-111-1-1002i−2i00002i−2i2i−2i000000000000−i−iii−i−iii−i−iii000−i3i3−i3−i3i3i300000000003−30
χ3222-2-222-1-22-2122-1-2-2-21-2-2222-1-1-2-211112-1-1-2-1-2-2-1-1212211-111-11-111-1-1002i−2i00002i−2i2i−2i000000000000−i−iii−i−iii−i−iii000i3−i3i3i3−i3−i30000000000−330
χ3322-2-222-1-22-2122-1-2-2-21-2-2222-1-1-2-211112-1-1-2-1-2-2-1-1212211-111-11-111-1-100−2i2i0000−2i2i−2i2i000000000000ii−i−iii−i−iii−i−i000−i3i3−i3−i3i3i30000000000−330
χ3422-2-222-1-22-2122-1-2-2-21-2-2222-1-1-2-211112-1-1-2-1-2-2-1-1212211-111-11-111-1-100−2i2i0000−2i2i−2i2i000000000000ii−i−iii−i−iii−i−i000i3−i3i3i3−i3−i300000000003−30
χ3522-2-22-122-21-22-12-2-21-222-2-2-12-111-2-211-12-1-1-2-1-1-2-2121122-111-1-11-1-1112i−2i002i−2i2i−2i0000−i−iii−i−iii−i−iii0000000000000−i3i300−i3i3−i3i3000000003−3000
χ3622-2-22-122-21-22-12-2-21-222-2-2-12-111-2-211-12-1-1-2-1-1-2-2121122-111-1-11-1-1112i−2i002i−2i2i−2i0000−i−iii−i−iii−i−iii0000000000000i3−i300i3−i3i3−i300000000−33000
χ3722-2-22-122-21-22-12-2-21-222-2-2-12-111-2-211-12-1-1-2-1-1-2-2121122-111-1-11-1-111−2i2i00−2i2i−2i2i0000ii−i−iii−i−iii−i−i0000000000000−i3i300−i3i3−i3i300000000−33000
χ3822-2-22-122-21-22-12-2-21-222-2-2-12-111-2-211-12-1-1-2-1-1-2-2121122-111-1-11-1-111−2i2i00−2i2i−2i2i0000ii−i−iii−i−iii−i−i0000000000000i3−i300i3−i3i3−i3000000003−3000
χ3922-2-2-1222-2-2-2-12211-2-2-1-111-1-121111-2-2-1-122-2-1-111-2211-1-1-111-12-2-1-1112i−2i00−ii−ii−i3i3i3−i32i2i−2i−2i−i−iii−i−iii0000−i3−i3i3i3i3i3−i3−i3000000000003−33−30000000
χ4022-2-2-1222-2-2-2-12211-2-2-1-111-1-121111-2-2-1-122-2-1-111-2211-1-1-111-12-2-1-1112i−2i00−ii−iii3−i3−i3i32i2i−2i−2i−i−iii−i−iii0000i3i3−i3−i3−i3−i3i3i300000000000−33−330000000
χ4122-2-2-1222-2-2-2-12211-2-2-1-111-1-121111-2-2-1-122-2-1-111-2211-1-1-111-12-2-1-111−2i2i00i−ii−i−i3i3i3−i3−2i−2i2i2iii−i−iii−i−i0000−i3−i3i3i3i3i3−i3−i300000000000−33−330000000
χ4222-2-2-1222-2-2-2-12211-2-2-1-111-1-121111-2-2-1-122-2-1-111-2211-1-1-111-12-2-1-111−2i2i00i−ii−ii3−i3−i3i3−2i−2i2i2iii−i−iii−i−i0000i3i3−i3−i3−i3−i3i3i3000000000003−33−30000000
χ4322-2-2-122-22-2-2-12211-2-211-1-1-1-121111-2-2-1-12-2211-1-12-2-1-111-111-1-2211-1-1002i−2i−i3i3i3−i3−ii−ii0000−i3−i3i3i3i3i3−i3−i32i2i−2i−2i−i−iii−i−iii00000000000−333−30000000
χ4422-2-2-122-22-2-2-12211-2-211-1-1-1-121111-2-2-1-12-2211-1-12-2-1-111-111-1-2211-1-1002i−2ii3−i3−i3i3−ii−ii0000i3i3−i3−i3−i3−i3i3i32i2i−2i−2i−i−iii−i−iii000000000003−3−330000000
χ4522-2-2-122-22-2-2-12211-2-211-1-1-1-121111-2-2-1-12-2211-1-12-2-1-111-111-1-2211-1-100−2i2i−i3i3i3−i3i−ii−i0000−i3−i3i3i3i3i3−i3−i3−2i−2i2i2iii−i−iii−i−i000000000003−3−330000000
χ4622-2-2-122-22-2-2-12211-2-211-1-1-1-121111-2-2-1-12-2211-1-12-2-1-111-111-1-2211-1-100−2i2ii3−i3−i3i3i−ii−i0000i3i3−i3−i3−i3−i3i3i3−2i−2i2i2iii−i−iii−i−i00000000000−333−30000000
χ47444444-2-4-44-244-2444-2-4-4-4-44-2-244-2-2-2-24-2-2-42-4-422-42-4-422-2-2-2-22222220000000000000000000000000000000000000000000000000000000000
χ4844444-24-4-4-244-2444-24-4-4-4-4-24-2-2-244-2-2-24-22-422-4-42-422-4-4-2-2-2-22222220000000000000000000000000000000000000000000000000000000000
χ4944444-2-244-2-24-2-244-2-24444-2-21-2-2-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-211111111110000000000000000000000000000000000004-2-2-2-211110000000000000
χ5044444-2-244-2-24-2-244-2-24444-2-21-2-2-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000-42222-1-1-1-10000000000000
χ5144444-2-2-4-4-2-24-2-244-2-2-4-4-4-4-2-21-2-2-2-211-2-212222222222221111-1-1-1-1-1-1000000000000000000000000000000000000000003-3-330000000000000
χ5244444-2-2-4-4-2-24-2-244-2-2-4-4-4-4-2-21-2-2-2-211-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000-333-30000000000000
χ534444-24-2444-2-24-2-2-24-2-2-2-2-2-21-2-2-211-2-2-21-24-2-2-2114-2-2-2111111-2-2111100440000-2-2-2-2000000000000-2-2-2-2111111110000000000000000000000
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χ554444-24-2-4-44-2-24-2-2-24-22222-21-2-2-211-2-2-21-2-4222-1-1-4222-1-1111122-1-1-1-1000000002323−23−230000000000000000−3−3−3−333330000000000000000000000
χ564444-24-2-4-44-2-24-2-2-24-22222-21-2-2-211-2-2-21-2-4222-1-1-4222-1-1111122-1-1-1-100000000−23−23232300000000000000003333−3−3−3−30000000000000000000000
χ574444-2-2444-24-2-24-2-2-24-2-2-2-21-2-211-2-2-2-21-2-2-2411-2-2-2411-2-21111-2-211114400-2-2-2-20000-2-2-2-2111111110000000000000000000000000000000000
χ584444-2-2444-24-2-24-2-2-24-2-2-2-21-2-211-2-2-2-21-2-2-2411-2-2-2411-2-21111-2-21111-4-400222200002222-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ594444-2-24-4-4-24-2-24-2-2-2422221-2-211-2-2-2-21-2-22-4-1-1222-4-1-122111122-1-1-1-100002323−23−2300000000−3−3−3−333330000000000000000000000000000000000
χ604444-2-24-4-4-24-2-24-2-2-2422221-2-211-2-2-2-21-2-22-4-1-1222-4-1-122111122-1-1-1-10000−23−232323000000003333−3−3−3−30000000000000000000000000000000000
χ6144-4-444-24-4-4244-2-4-4-4244-4-44-2-2-4-422224-2-2424422-4-2-4-4-2-2-222-2-22-2-2220000000000000000000000000000000000000000000000000000000000
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χ7444-4-4-2-24-442-4-2-24222-422-2-21-2-2-1-122221-2-224-1-1-2-2-2-411221-1-112-2-1-11100002i3−2i3−2i32i300000000−i3−i3i3i3i3i3−i3−i30000000000000000000000000000000000
χ754-44-4444004-4-4-4-44-4-4400004444-44-44-4-4-4-400000000000044-4-40000000000000000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.