Finite Group Databasebeta

← Group #13140060

Character table — Group #13140060

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order1222222236666666441212121233666666666666663666666612121212121212121212121212121212444444444444444444121212121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91-1111-1-1-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-111-1-1i−ii−ii−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i
χ101-1111-1-1-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111-1-111i−i−ii−ii11-1-1ii−i−i-1-111−i−iii-1-111−i−iii
χ111-1111-1-1-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1-1-111−iii−i−ii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii
χ121-1111-1-1-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-11111-1-1−ii−iii−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i
χ131-1111-1-1-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-1−ii−ii−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii
χ141-1111-1-1-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111-1-111−iii−ii−i11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i
χ151-1111-1-1-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1-1-111i−i−iii−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i
χ161-1111-1-1-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-11111-1-1i−ii−i−ii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii
χ1722222222222222222222222-122-1-122-1-12-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ1822222222222222222222222-122-1-122-1-12-12-12-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
χ192222222222222222222222-12-1-122-1-122-12-12-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100002222000000220000000000-1-1-1-1-1-1-1-100000000
χ202222222222222222222222-12-1-122-1-122-12-12-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000-2-2-2-2000000-2-200000000001111111100000000
χ212222222222222222-2-2-2-2-2-22-122-1-122-1-12-12-12-1-1-1-1-1-1-1-1-1-2-211-2-211111111110000000022220000-2-20000000000000000-1-1-1-11111
χ222222222222222222-2-2-2-2-2-22-122-1-122-1-12-12-12-1-1-1-1-1-1-1-1-1-2-211-2-2111111111100000000-2-2-2-200002200000000000000001111-1-1-1-1
χ232222222222222222-2-2-2-2-2-2-12-1-122-1-122-12-12-12-1-1-1-1-1-1-1-111-2-211-2-21111111100002222000000-2-20000000000-1-1-1-1111100000000
χ242222222222222222-2-2-2-2-2-2-12-1-122-1-122-12-12-12-1-1-1-1-1-1-1-111-2-211-2-2111111110000-2-2-2-20000002200000000001111-1-1-1-100000000
χ25222-2-22-2-222-22-22-2-2000000222-2-2-2-2-22-222-222-222-2-22-2-2200000000000000002i−2i2i−2i000000000000002i−2i2i−2i00000000000000000000
χ26222-2-22-2-222-22-22-2-2000000222-2-2-2-2-22-222-222-222-2-22-2-220000000000000000−2i2i−2i2i00000000000000−2i2i−2i2i00000000000000000000
χ2722-22-2-22-22-22-2-22-2200000022-2-22-22-2-22222-2-2-22-22-2-22-220000000000000000000000002i−2i2i−2i00000000000000000000002i−2i2i−2i0000
χ2822-22-2-22-22-22-2-22-2200000022-2-22-22-2-22222-2-2-22-22-2-22-22000000000000000000000000−2i2i−2i2i0000000000000000000000−2i2i−2i2i0000
χ2922-22-2-22-22-22-2-22-220000002-1-2-2-112-21-12-121-21-11-111-11-100−i3i300−i3i3−i3−i3i3i3−i3−i3i3i3000000002i−2i2i−2i0000000000000000000000−ii−ii3−33−3
χ3022-22-2-22-22-22-2-22-220000002-1-2-2-112-21-12-121-21-11-111-11-100−i3i300−i3i3−i3−i3i3i3−i3−i3i3i300000000−2i2i−2i2i0000000000000000000000i−ii−i−33−33
χ3122-22-2-22-22-22-2-22-220000002-1-2-2-112-21-12-121-21-11-111-11-100i3−i300i3−i3i3i3−i3−i3i3i3−i3−i3000000002i−2i2i−2i0000000000000000000000−ii−ii−33−33
χ3222-22-2-22-22-22-2-22-220000002-1-2-2-112-21-12-121-21-11-111-11-100i3−i300i3−i3i3i3−i3−i3i3i3−i3−i300000000−2i2i−2i2i0000000000000000000000i−ii−i3−33−3
χ3322-2-22-2-222-2-2-2222-200000022-22-22-22-2-222-2-2-222-2-22-2-222000000000000000000002i−2i2i−2i0000000000000000002i−2i2i−2i000000000000
χ3422-2-22-2-222-2-2-2222-200000022-22-22-22-2-222-2-2-222-2-22-2-22200000000000000000000−2i2i−2i2i000000000000000000−2i2i−2i2i000000000000
χ3522-2-22-2-222-2-2-2222-2000000-121-1-221-1-2-2-121-212-111-111-1-1−i3i300−i3i300−i3i3−i3i3−i3i3−i3i300002i−2i2i−2i000000000000000000−ii−ii3−33−300000000
χ3622-2-22-2-222-2-2-2222-2000000-121-1-221-1-2-2-121-212-111-111-1-1−i3i300−i3i300−i3i3−i3i3−i3i3−i3i30000−2i2i−2i2i000000000000000000i−ii−i−33−3300000000
χ3722-2-22-2-222-2-2-2222-2000000-121-1-221-1-2-2-121-212-111-111-1-1i3−i300i3−i300i3−i3i3−i3i3−i3i3−i300002i−2i2i−2i000000000000000000−ii−ii−33−3300000000
χ3822-2-22-2-222-2-2-2222-2000000-121-1-221-1-2-2-121-212-111-111-1-1i3−i300i3−i300i3−i3i3−i3i3−i3i3−i30000−2i2i−2i2i000000000000000000i−ii−i3−33−300000000
χ392-2222-2-2-2222-2-2-22-22i−2i2i2i−2i−2i2-122-1-1-2-211-212-1-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii0000000022-2-200002i−2i0000000000000000-1-111−i−iii
χ402-2222-2-2-2222-2-2-22-22i−2i2i2i−2i−2i2-122-1-1-2-211-212-1-21-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii00000000-2-2220000−2i2i000000000000000011-1-1ii−i−i
χ412-2222-2-2-2222-2-2-22-22i−2i2i2i−2i−2i-12-1-12211-2-21-2-121-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii000022-2-20000002i−2i0000000000-1-111−i−iii00000000
χ422-2222-2-2-2222-2-2-22-22i−2i2i2i−2i−2i-12-1-12211-2-21-2-121-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii0000-2-222000000−2i2i000000000011-1-1ii−i−i00000000
χ432-2222-2-2-2222-2-2-22-2−2i2i−2i−2i2i2i2-122-1-1-2-211-212-1-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i0000000022-2-20000−2i2i0000000000000000-1-111ii−i−i
χ442-2222-2-2-2222-2-2-22-2−2i2i−2i−2i2i2i2-122-1-1-2-211-212-1-21-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i00000000-2-22200002i−2i000000000000000011-1-1−i−iii
χ452-2222-2-2-2222-2-2-22-2−2i2i−2i−2i2i2i-12-1-12211-2-21-2-121-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i000022-2-2000000−2i2i0000000000-1-111ii−i−i00000000
χ462-2222-2-2-2222-2-2-22-2−2i2i−2i−2i2i2i-12-1-12211-2-21-2-121-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i0000-2-2220000002i−2i000000000011-1-1−i−iii00000000
χ472-22-2-2-22222-2-22-2-22000000222-2-2-222-22-2-2-22-2222-2-2-222-200000000000000002i−2i−2i2i000000000000002i−2i−2i2i00000000000000000000
χ482-22-2-2-22222-2-22-2-22000000222-2-2-222-22-2-2-22-2222-2-2-222-20000000000000000−2i2i2i−2i00000000000000−2i2i2i−2i00000000000000000000
χ492-2-22-22-222-2222-2-2-200000022-2-22-2-222-2-2-22-2222-22-22-22-20000000000000000000000002i−2i−2i2i00000000000000000000002i−2i−2i2i0000
χ502-2-22-22-222-2222-2-2-200000022-2-22-2-222-2-2-22-2222-22-22-22-2000000000000000000000000−2i2i2i−2i0000000000000000000000−2i2i2i−2i0000
χ512-2-22-22-222-2222-2-2-20000002-1-2-2-11-22-11-21212-1-11-11-11-11003−300−3333−3−3−3−333000000002i−2i−2i2i0000000000000000000000−iii−ii3−i3−i3i3
χ522-2-22-22-222-2222-2-2-20000002-1-2-2-11-22-11-21212-1-11-11-11-11003−300−3333−3−3−3−33300000000−2i2i2i−2i0000000000000000000000i−i−ii−i3i3i3−i3
χ532-2-22-22-222-2222-2-2-20000002-1-2-2-11-22-11-21212-1-11-11-11-1100−33003−3−3−33333−3−3000000002i−2i−2i2i0000000000000000000000−iii−i−i3i3i3−i3
χ542-2-22-22-222-2222-2-2-20000002-1-2-2-11-22-11-21212-1-11-11-11-1100−33003−3−3−33333−3−300000000−2i2i2i−2i0000000000000000000000i−i−iii3−i3−i3i3
χ552-2-2-2222-22-2-22-2-22200000022-22-222-222-2-2-2-22-22-2-2222-2-2000000000000000000002i−2i−2i2i0000000000000000002i−2i−2i2i000000000000
χ562-2-2-2222-22-2-22-2-22200000022-22-222-222-2-2-2-22-22-2-2222-2-200000000000000000000−2i2i2i−2i000000000000000000−2i2i2i−2i000000000000
χ572-2-2-2222-22-2-22-2-222000000-121-1-22-11221-21-2-1-2-111-1-1-1113−300−33003−33−3−33−3300002i−2i−2i2i000000000000000000−iii−ii3−i3−i3i300000000
χ582-2-2-2222-22-2-22-2-222000000-121-1-22-11221-21-2-1-2-111-1-1-1113−300−33003−33−3−33−330000−2i2i2i−2i000000000000000000i−i−ii−i3i3i3−i300000000
χ592-2-2-2222-22-2-22-2-222000000-121-1-22-11221-21-2-1-2-111-1-1-111−33003−300−33−333−33−300002i−2i−2i2i000000000000000000−iii−i−i3i3i3−i300000000
χ602-2-2-2222-22-2-22-2-222000000-121-1-22-11221-21-2-1-2-111-1-1-111−33003−300−33−333−33−30000−2i2i2i−2i000000000000000000i−i−iii3−i3−i3i300000000
χ614444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000000000
χ624444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000
χ63444-4-44-4-444-44-44-4-40000004-24-422-4-4-224-2-4-242-2-222-222-20000000000000000000000000000000000000000000000000000000000
χ64444-4-44-4-444-44-44-4-4000000-24-22-4-4224-4-2424-2-4-2-222-222-20000000000000000000000000000000000000000000000000000000000
χ65444-4-44-4-444-44-44-4-4000000-2-2-222222-22-2-22-2-2211-1-11-1-11000000003-3-333-3-33000000000000000000000000000000000000000000
χ66444-4-44-4-444-44-44-4-4000000-2-2-222222-22-2-22-2-2211-1-11-1-1100000000-333-3-333-3000000000000000000000000000000000000000000
χ6744-44-4-44-44-44-4-44-44000000-24224-4-22-44-24-2-42-4-22-222-22-20000000000000000000000000000000000000000000000000000000000
χ6844-44-4-44-44-44-4-44-44000000-2-222-22-222-2-2-2-22221-11-1-11-1100−2i32i300−2i32i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000000000
χ6944-44-4-44-44-44-4-44-44000000-2-222-22-222-2-2-2-22221-11-1-11-11002i3−2i3002i3−2i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000000000
χ7044-4-44-4-444-4-4-4444-40000004-2-442-2-44224-2-42-4-2-222-222-2-20000000000000000000000000000000000000000000000000000000000
χ7144-4-44-4-444-4-4-4444-4000000-2-22-22-22-222-2-2222-21-1-11-1-111−2i32i300−2i32i300i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000000000
χ7244-4-44-4-444-4-4-4444-4000000-2-22-22-22-222-2-2222-21-1-11-1-1112i3−2i3002i3−2i300−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000000000
χ734-4444-4-4-4444-4-4-44-44i−4i4i4i−4i−4i-2-2-2-2-2-2222222-2-2221111-1-1-1-1−2i−2i−2i−2i2i2i2i2iiiii−i−i−i−i000000000000000000000000000000000000000000
χ744-4444-4-4-4444-4-4-44-4−4i4i−4i−4i4i4i-2-2-2-2-2-2222222-2-2221111-1-1-1-12i2i2i2i−2i−2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000000000
χ754-44-4-4-44444-4-44-4-440000004-24-422442-2-42-4-2-4-2-2-2222-2-220000000000000000000000000000000000000000000000000000000000
χ764-44-4-4-44444-4-44-4-44000000-24-22-4-4-2-2-442-42424-2-2222-2-220000000000000000000000000000000000000000000000000000000000
χ774-44-4-4-44444-4-44-4-44000000-2-2-2222-2-22-2222-22-211-1-1-111-1000000003i−3i−3i3i−3i3i3i−3i000000000000000000000000000000000000000000
χ784-44-4-4-44444-4-44-4-44000000-2-2-2222-2-22-2222-22-211-1-1-111-100000000−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000000000000000
χ794-4-44-44-444-4444-4-4-4000000-24224-42-24-42-4-2-4-24-22-22-22-220000000000000000000000000000000000000000000000000000000000
χ804-4-44-44-444-4444-4-4-4000000-2-222-222-2-2222-22-2-21-11-11-11-10023−2300−2323−3−33333−3−3000000000000000000000000000000000000000000
χ814-4-44-44-444-4444-4-4-4000000-2-222-222-2-2222-22-2-21-11-11-11-100−23230023−2333−3−3−3−333000000000000000000000000000000000000000000
χ824-4-4-4444-44-4-44-4-4440000004-2-442-24-4-2-2-42-4242-222-2-2-2220000000000000000000000000000000000000000000000000000000000
χ834-4-4-4444-44-4-44-4-444000000-2-22-22-2-22-2-22222-221-1-1111-1-123−2300−232300−33−333−33−3000000000000000000000000000000000000000000
χ844-4-4-4444-44-4-44-4-444000000-2-22-22-2-22-2-22222-221-1-1111-1-1−23230023−23003−33−3−33−33000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000222200000000220000-1-1-1-1-1-1-1-10000000000000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000-2-2-2-200000000-2-20000111111110000000000000000
χ8766666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000222200000000-2-20000-1-1-1-111110000000000000000
χ8866666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000-2-2-2-2000000002200001111-1-1-1-10000000000000000
χ89666-6-66-6-6-3-33-33-33300−3i33i3−3i33i300000000000000000000000000000000000000002i−2i2i−2i00000000000000−ii−ii3−33−30000000000000000
χ90666-6-66-6-6-3-33-33-33300−3i33i3−3i33i30000000000000000000000000000000000000000−2i2i−2i2i00000000000000i−ii−i−33−330000000000000000
χ91666-6-66-6-6-3-33-33-333003i3−3i33i3−3i300000000000000000000000000000000000000002i−2i2i−2i00000000000000−ii−ii−33−330000000000000000
χ92666-6-66-6-6-3-33-33-333003i3−3i33i3−3i30000000000000000000000000000000000000000−2i2i−2i2i00000000000000i−ii−i3−33−30000000000000000
χ936-6666-6-6-6-3-3-3333-336i−6i−3i−3i3i3i000000000000000000000000000000000000000022-2-2000000002i−2i0000-1-111−i−iii0000000000000000
χ946-6666-6-6-6-3-3-3333-336i−6i−3i−3i3i3i0000000000000000000000000000000000000000-2-22200000000−2i2i000011-1-1ii−i−i0000000000000000
χ956-6666-6-6-6-3-3-3333-33−6i6i3i3i−3i−3i000000000000000000000000000000000000000022-2-200000000−2i2i0000-1-111ii−i−i0000000000000000
χ966-6666-6-6-6-3-3-3333-33−6i6i3i3i−3i−3i0000000000000000000000000000000000000000-2-222000000002i−2i000011-1-1−i−iii0000000000000000
χ976-66-6-6-666-3-333-333-30033−33−333300000000000000000000000000000000000000002i−2i−2i2i00000000000000−iii−ii3−i3−i3i30000000000000000
χ986-66-6-6-666-3-333-333-30033−33−33330000000000000000000000000000000000000000−2i2i2i−2i00000000000000i−i−ii−i3i3i3−i30000000000000000
χ996-66-6-6-666-3-333-333-300−333333−3300000000000000000000000000000000000000002i−2i−2i2i00000000000000−iii−i−i3i3i3−i30000000000000000
χ1006-66-6-6-666-3-333-333-300−333333−330000000000000000000000000000000000000000−2i2i2i−2i00000000000000i−i−iii3−i3−i3i30000000000000000
χ1011212-1212-12-1212-12-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1021212-12-1212-12-1212-6666-6-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-1212-1212-1212-66-6-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-12-12121212-12-666-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).