Finite Group Databasebeta

← Group #13140080

Character table — Group #13140080

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order1222222236666666441212121233666666666666663666666612121212121212121212121212121212444444444444444444121212121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
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
χ911-1-11-11-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-11-1i−iii−i−i11-1-1ii−i−i11-1-111-1-1ii−i−i
χ1011-1-11-11-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i−i−iii-1-111-111-1−iiii−i−i11-1-1−i−iii-1-111-1-111−i−iii
χ1111-1-11-11-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iiiii−i−i-1-1111-1-11−ii−i−iii-1-111ii−i−i11-1-1-1-111−i−iii
χ1211-1-11-11-1111-1-1-11-1i−iii−i−i111111-1-1-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii11-1-1-11-11i−i−i−iii-1-111−i−iii-1-11111-1-1ii−i−i
χ1311-1-11-11-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i11-1-1-11-11−iiii−i−i-1-111ii−i−i-1-11111-1-1−i−iii
χ1411-1-11-11-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−iii-1-1111-1-11i−iii−i−i-1-111−i−iii11-1-1-1-111ii−i−i
χ1511-1-11-11-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iiiii−i−i-1-111-111-1i−i−i−iii11-1-1ii−i−i-1-111-1-111ii−i−i
χ1611-1-11-11-1111-1-1-11-1−ii−i−iii111111-1-1-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-11-11-1−ii−i−iii11-1-1−i−iii11-1-111-1-1−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
χ192222222222222222222222-12-1-122-1-122-12-12-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100002222000022000000000000-1-1-1-1-1-1-1-100000000
χ202222222222222222222222-12-1-122-1-122-12-12-12-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000-2-2-2-20000-2-20000000000001111111100000000
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
χ232222222222222222-2-2-2-2-2-2-12-1-122-1-122-12-12-12-1-1-1-1-1-1-1-111-2-211-2-211111111000022220000-2-2000000000000-1-1-1-1111100000000
χ242222222222222222-2-2-2-2-2-2-12-1-122-1-122-12-12-12-1-1-1-1-1-1-1-111-2-211-2-2111111110000-2-2-2-20000220000000000001111-1-1-1-100000000
χ25222-2-22-2-222-22-2-2-22000000222-22-22222-2-2-2-2-2-222-2-222-2-200000000000000002-22-2000000000000002-22-200000000000000000000
χ26222-2-22-2-222-22-2-2-22000000222-22-22222-2-2-2-2-2-222-2-222-2-20000000000000000-22-2200000000000000-22-2200000000000000000000
χ2722-22-2-2-2222-2-222-2-2000000222-22-2-2-2-2-222-2-22222-2-2-2-22200000000000000002i−2i−2i2i000000000000002i−2i−2i2i00000000000000000000
χ2822-22-2-2-2222-2-222-2-2000000222-22-2-2-2-2-222-2-22222-2-2-2-2220000000000000000−2i2i2i−2i00000000000000−2i2i2i−2i00000000000000000000
χ2922-2-22-22-2222-2-2-22-22i−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
χ3022-2-22-22-2222-2-2-22-22i−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
χ3122-2-22-22-2222-2-2-22-22i−2i2i2i−2i−2i-12-1-12211-2-21-2-121-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii00002i2i−2i−2i00002-2000000000000−i−iii-1-11100000000
χ3222-2-22-22-2222-2-2-22-22i−2i2i2i−2i−2i-12-1-12211-2-21-2-121-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii0000−2i−2i2i2i0000-22000000000000ii−i−i11-1-100000000
χ3322-2-22-22-2222-2-2-22-2−2i2i−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
χ3422-2-22-22-2222-2-2-22-2−2i2i−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
χ3522-2-22-22-2222-2-2-22-2−2i2i−2i−2i2i2i-12-1-12211-2-21-2-121-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i00002i2i−2i−2i0000-22000000000000−i−iii11-1-100000000
χ3622-2-22-22-2222-2-2-22-2−2i2i−2i−2i2i2i-12-1-12211-2-21-2-121-2-1-1-1-11111ii−2i−2i−i−i2i2iiiii−i−i−i−i0000−2i−2i2i2i00002-2000000000000ii−i−i-1-11100000000
χ372-222-2-22-22-2-22-222-200000022-22-2-22-22-222-22-2-22-22-22-2-22000000000000000000002i−2i2i−2i0000000000000000002i−2i2i−2i000000000000
χ382-222-2-22-22-2-22-222-200000022-22-2-22-22-222-22-2-22-22-22-2-2200000000000000000000−2i2i−2i2i000000000000000000−2i2i−2i2i000000000000
χ392-222-2-22-22-2-22-222-2000000-121-1-2-2-112-2-12121-2-11-11-111-1−i3i300−i3i300−i3−i3i3i3−i3−i3i3i300002i−2i2i−2i000000000000000000−ii−ii3−33−300000000
χ402-222-2-22-22-2-22-222-2000000-121-1-2-2-112-2-12121-2-11-11-111-1−i3i300−i3i300−i3−i3i3i3−i3−i3i3i30000−2i2i−2i2i000000000000000000i−ii−i−33−3300000000
χ412-222-2-22-22-2-22-222-2000000-121-1-2-2-112-2-12121-2-11-11-111-1i3−i300i3−i300i3i3−i3−i3i3i3−i3−i300002i−2i2i−2i000000000000000000−ii−ii−33−3300000000
χ422-222-2-22-22-2-22-222-2000000-121-1-2-2-112-2-12121-2-11-11-111-1i3−i300i3−i300i3i3−i3−i3i3i3−i3−i30000−2i2i−2i2i000000000000000000i−ii−i3−33−300000000
χ432-22-22-2-222-2222-2-2-200000022-2-2-222-22-2-2-22-2222-2-222-22-20000000000000000000000002i−2i2i−2i00000000000000000000002i−2i2i−2i0000
χ442-22-22-2-222-2222-2-2-200000022-2-2-222-22-2-2-22-2222-2-222-22-2000000000000000000000000−2i2i−2i2i0000000000000000000000−2i2i−2i2i0000
χ452-22-22-2-222-2222-2-2-20000002-1-2-21-12-2-11-21212-1-111-1-11-11003−3003−33−33−33−33−3000000002i−2i2i−2i0000000000000000000000−ii−ii−i3i3−i3i3
χ462-22-22-2-222-2222-2-2-20000002-1-2-21-12-2-11-21212-1-111-1-11-11003−3003−33−33−33−33−300000000−2i2i−2i2i0000000000000000000000i−ii−ii3−i3i3−i3
χ472-22-22-2-222-2222-2-2-20000002-1-2-21-12-2-11-21212-1-111-1-11-1100−3300−33−33−33−33−33000000002i−2i2i−2i0000000000000000000000−ii−iii3−i3i3−i3
χ482-22-22-2-222-2222-2-2-20000002-1-2-21-12-2-11-21212-1-111-1-11-1100−3300−33−33−33−33−3300000000−2i2i−2i2i0000000000000000000000i−ii−i−i3i3−i3i3
χ492-2-2222-2-22-22-2-22-2200000022-2-2-22-22-22222-2-2-22-2-22-22-220000000000000000000000002i−2i−2i2i00000000000000000000002i−2i−2i2i0000
χ502-2-2222-2-22-22-2-22-2200000022-2-2-22-22-22222-2-2-22-2-22-22-22000000000000000000000000−2i2i2i−2i0000000000000000000000−2i2i2i−2i0000
χ512-2-2222-2-22-22-2-22-220000002-1-2-21-1-221-12-121-21-111-11-11-100−i3i300i3−i3−i3i3−i3i3i3−i3i3−i3000000002i−2i−2i2i0000000000000000000000−iii−i−333−3
χ522-2-2222-2-22-22-2-22-220000002-1-2-21-1-221-12-121-21-111-11-11-100−i3i300i3−i3−i3i3−i3i3i3−i3i3−i300000000−2i2i2i−2i0000000000000000000000i−i−ii3−3−33
χ532-2-2222-2-22-22-2-22-220000002-1-2-21-1-221-12-121-21-111-11-11-100i3−i300−i3i3i3−i3i3−i3−i3i3−i3i3000000002i−2i−2i2i0000000000000000000000−iii−i3−3−33
χ542-2-2222-2-22-22-2-22-220000002-1-2-21-1-221-12-121-21-111-11-11-100i3−i300−i3i3i3−i3i3−i3−i3i3−i3i300000000−2i2i2i−2i0000000000000000000000i−i−ii−333−3
χ552-2-2-2-22222-2-2-22-22200000022-22-2-2-22-22-2-2-22222-22-2-222-2000000000000000000002-2-220000000000000000002-2-22000000000000
χ562-2-2-2-22222-2-2-22-22200000022-22-2-2-22-22-2-2-22222-22-2-222-200000000000000000000-222-2000000000000000000-222-2000000000000
χ572-2-2-2-22222-2-2-22-222000000-121-1-2-21-1-221-212-12-11-111-1-113−300−330033−3−3−3−33300002-2-22000000000000000000-111-1−333−300000000
χ582-2-2-2-22222-2-2-22-222000000-121-1-2-21-1-221-212-12-11-111-1-113−300−330033−3−3−3−3330000-222-20000000000000000001-1-113−3−3300000000
χ592-2-2-2-22222-2-2-22-222000000-121-1-2-21-1-221-212-12-11-111-1-11−33003−300−3−33333−3−300002-2-22000000000000000000-111-13−3−3300000000
χ602-2-2-2-22222-2-2-22-222000000-121-1-2-21-1-221-212-12-11-111-1-11−33003−300−3−33333−3−30000-222-20000000000000000001-1-11−333−300000000
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
χ63444-4-44-4-444-44-4-4-440000004-24-4-2244-2-2-42-42-42-2-222-2-2220000000000000000000000000000000000000000000000000000000000
χ64444-4-44-4-444-44-4-4-44000000-24-224-4-2-2442-42-42-4-2-222-2-2220000000000000000000000000000000000000000000000000000000000
χ65444-4-44-4-444-44-4-4-44000000-2-2-22-22-2-2-2-222222211-1-111-1-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000000000000000000
χ66444-4-44-4-444-44-4-4-44000000-2-2-22-22-2-2-2-222222211-1-111-1-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000000000000000
χ6744-44-4-4-4444-4-444-4-40000004-24-4-22-4-4224-2-424-2-2-22222-2-20000000000000000000000000000000000000000000000000000000000
χ6844-44-4-4-4444-4-444-4-4000000-24-224-422-4-4-242-4-24-2-22222-2-20000000000000000000000000000000000000000000000000000000000
χ6944-44-4-4-4444-4-444-4-4000000-2-2-22-222222-2-222-2-211-1-1-1-111000000003-3-33-333-3000000000000000000000000000000000000000000
χ7044-44-4-4-4444-4-444-4-4000000-2-2-22-222222-2-222-2-211-1-1-1-11100000000-333-33-3-33000000000000000000000000000000000000000000
χ7144-4-44-44-4444-4-4-44-44i−4i4i4i−4i−4i-2-2-2-2-2-2222222-2-2221111-1-1-1-1−2i−2i−2i−2i2i2i2i2iiiii−i−i−i−i000000000000000000000000000000000000000000
χ7244-4-44-44-4444-4-4-44-4−4i4i−4i−4i4i4i-2-2-2-2-2-2222222-2-2221111-1-1-1-12i2i2i2i−2i−2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000000000
χ734-444-4-44-44-4-44-444-40000004-2-44224-4-224-2-4-2-42-22-22-222-20000000000000000000000000000000000000000000000000000000000
χ744-444-4-44-44-4-44-444-4000000-2-22-222-22-22-2-22-2221-11-11-1-11−2i32i300−2i32i300i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000000000
χ754-444-4-44-44-4-44-444-4000000-2-22-222-22-22-2-22-2221-11-11-1-112i3−2i3002i3−2i300−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000000000
χ764-44-44-4-444-4444-4-4-4000000-2422-44-224-42-4-2-4-24-222-2-22-220000000000000000000000000000000000000000000000000000000000
χ774-44-44-4-444-4444-4-4-4000000-2-2222-2-22-2222-22-2-21-1-111-11-10023−230023−23−33−33−33−33000000000000000000000000000000000000000000
χ784-44-44-4-444-4444-4-4-4000000-2-2222-2-22-2222-22-2-21-1-111-11-100−232300−23233−33−33−33−3000000000000000000000000000000000000000000
χ794-4-4444-4-44-44-4-44-44000000-2422-442-2-44-24-2-42-4-222-22-22-20000000000000000000000000000000000000000000000000000000000
χ804-4-4444-4-44-44-4-44-44000000-2-2222-22-22-2-2-2-22221-1-11-11-1100−2i32i3002i3−2i3i3−i3i3−i3−i3i3−i3i3000000000000000000000000000000000000000000
χ814-4-4444-4-44-44-4-44-44000000-2-2222-22-22-2-2-2-22221-1-11-11-11002i3−2i300−2i32i3−i3i3−i3i3i3−i3i3−i3000000000000000000000000000000000000000000
χ824-4-4-4-44444-4-4-44-4440000004-2-4422-442-2-42-4-24-2-22-222-2-220000000000000000000000000000000000000000000000000000000000
χ834-4-4-4-44444-4-4-44-444000000-2-22-2222-22-2222-2-2-21-11-1-111-123−2300−232300−3−33333−3−3000000000000000000000000000000000000000000
χ844-4-4-4-44444-4-4-44-444000000-2-22-2222-22-2222-2-2-21-11-1-111-1−23230023−230033−3−3−3−333000000000000000000000000000000000000000000
χ8566666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000222200000000002200-1-1-1-1-1-1-1-10000000000000000
χ8666666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000-2-2-2-20000000000-2-200111111110000000000000000
χ8766666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000022220000000000-2-200-1-1-1-111110000000000000000
χ8866666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000-2-2-2-2000000000022001111-1-1-1-10000000000000000
χ89666-6-66-6-6-3-33-3333-30033−3333−3300000000000000000000000000000000000000002-22-200000000000000-11-113−33−30000000000000000
χ90666-6-66-6-6-3-33-3333-30033−3333−330000000000000000000000000000000000000000-22-22000000000000001-11-1−33−330000000000000000
χ91666-6-66-6-6-3-33-3333-300−3333−333300000000000000000000000000000000000000002-22-200000000000000-11-11−33−330000000000000000
χ92666-6-66-6-6-3-33-3333-300−3333−33330000000000000000000000000000000000000000-22-22000000000000001-11-13−33−30000000000000000
χ9366-66-6-6-66-3-333-3-33300−3i33i33i3−3i300000000000000000000000000000000000000002i−2i−2i2i00000000000000−iii−i−333−30000000000000000
χ9466-66-6-6-66-3-333-3-33300−3i33i33i3−3i30000000000000000000000000000000000000000−2i2i2i−2i00000000000000i−i−ii3−3−330000000000000000
χ9566-66-6-6-66-3-333-3-333003i3−3i3−3i33i300000000000000000000000000000000000000002i−2i−2i2i00000000000000−iii−i3−3−330000000000000000
χ9666-66-6-6-66-3-333-3-333003i3−3i3−3i33i30000000000000000000000000000000000000000−2i2i2i−2i00000000000000i−i−ii−333−30000000000000000
χ9766-6-66-66-6-3-3-3333-336i−6i−3i−3i3i3i00000000000000000000000000000000000000002i2i−2i−2i00000000002-200−i−iii-1-1110000000000000000
χ9866-6-66-66-6-3-3-3333-336i−6i−3i−3i3i3i0000000000000000000000000000000000000000−2i−2i2i2i0000000000-2200ii−i−i11-1-10000000000000000
χ9966-6-66-66-6-3-3-3333-33−6i6i3i3i−3i−3i00000000000000000000000000000000000000002i2i−2i−2i0000000000-2200−i−iii11-1-10000000000000000
χ10066-6-66-66-6-3-3-3333-33−6i6i3i3i−3i−3i0000000000000000000000000000000000000000−2i−2i2i2i00000000002-200ii−i−i-1-1110000000000000000
χ10112-121212-12-1212-12-666-66-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-1212-12-1212-66-6-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-12121212-12-12-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-12-12-12121212-6666-66-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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