Finite Group Databasebeta

← Group #13140254

Character table — Group #13140254

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636363636363636363636363636363636363636
order122222223666666644121212123366666666666666366666661212121212121212121212121212121222224444444444444466661212121212121212121212121212121212121212
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
χ911-1-111-1-111-1-1-1-1111-111-1-1111111-1-1-1-1-111-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−i1-1i−ii−i11-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-111-1-111-1-1-1-1111-111-1-1111111-1-1-1-1-111-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii1-1−ii−ii11-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-111-1-111-1-1-1-1111-111-1-1111111-1-1-1-1-111-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111ii−i−i−i−iii-11i−i−ii-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211-1-111-1-111-1-1-1-1111-111-1-1111111-1-1-1-1-111-1-1-1111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111−i−iiiii−i−i-11−iii−i-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311-1-111-1-111-1-1-1-111-11-1-111111111-1-1-1-1-111-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-1ii−i−iii−i−i-11−ii−ii11-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411-1-111-1-111-1-1-1-111-11-1-111111111-1-1-1-1-111-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-1−i−iii−i−iii-11i−ii−i11-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511-1-111-1-111-1-1-1-111-11-1-111111111-1-1-1-1-111-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111ii−i−i−i−iii1-1−iii−i-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611-1-111-1-111-1-1-1-111-11-1-111111111-1-1-1-1-111-1-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-111−i−iiiii−i−i1-1i−i−ii-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222222222-122-1-1222-1-12-1-1-12-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100002222000000220000000000-1-1-1-1-1-1-1-100000000
χ1822222222222222222222222-122-1-1222-1-12-1-1-12-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-2000000-2-200000000001111111100000000
χ192222222222222222222222-12-1-122-1-1-122-1222-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000000022220000220000000000000000-1-1-1-1-1-1-1-1
χ202222222222222222222222-12-1-122-1-1-122-1222-1-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-100000000-2-2-2-20000-2-2000000000000000011111111
χ212222222222222222-2-2-2-2-2-22-122-1-1222-1-12-1-1-12-1-1-1-1-1-1-1-1-2-211-2-2111111111100002222000000-2-20000000000-1-1-1-1111100000000
χ222222222222222222-2-2-2-2-2-22-122-1-1222-1-12-1-1-12-1-1-1-1-1-1-1-1-2-211-2-211111111110000-2-2-2-20000002200000000001111-1-1-1-100000000
χ232222222222222222-2-2-2-2-2-2-12-1-122-1-1-122-1222-1-1-1-1-1-1-1-1-111-2-211-2-2111111110000000022220000-2-20000000000000000-1-1-1-11111
χ242222222222222222-2-2-2-2-2-2-12-1-122-1-1-122-1222-1-1-1-1-1-1-1-1-111-2-211-2-21111111100000000-2-2-2-200002200000000000000001111-1-1-1-1
χ252222-2-2-2-22222-2-2-2-2000000222-22-222-222-2-2-2-2-222-222-2-2-200000000000000002-22-2000000000000002-22-200000000000000000000
χ262222-2-2-2-22222-2-2-2-2000000222-22-222-222-2-2-2-2-222-222-2-2-20000000000000000-22-2200000000000000-22-2200000000000000000000
χ2722-2-222-2-222-2-2-2-2222-222-2-22-122-1-1-2-2-2112-111-2-1-1-11111-122-1-1-2-211-1-1-1-1111100002i2i−2i−2i0000002i−2i0000000000−i−iii−i−iii00000000
χ2822-2-222-2-222-2-2-2-2222-222-2-22-122-1-1-2-2-2112-111-2-1-1-11111-122-1-1-2-211-1-1-1-111110000−2i−2i2i2i000000−2i2i0000000000ii−i−iii−i−i00000000
χ2922-2-222-2-222-2-2-2-2222-222-2-2-12-1-122111-2-2-12-2-21-1-1-11111-1-1-12211-2-2-1-1-1-11111000000002i2i−2i−2i00002i−2i0000000000000000−i−iii−i−iii
χ3022-2-222-2-222-2-2-2-2222-222-2-2-12-1-122111-2-2-12-2-21-1-1-11111-1-1-12211-2-2-1-1-1-1111100000000−2i−2i2i2i0000−2i2i0000000000000000ii−i−iii−i−i
χ3122-2-222-2-222-2-2-2-222-22-2-2222-122-1-1-2-2-2112-111-2-1-1-11111-1-2-21122-1-11111-1-1-1-100002i2i−2i−2i000000−2i2i0000000000−i−iiiii−i−i00000000
χ3222-2-222-2-222-2-2-2-222-22-2-2222-122-1-1-2-2-2112-111-2-1-1-11111-1-2-21122-1-11111-1-1-1-10000−2i−2i2i2i0000002i−2i0000000000ii−i−i−i−iii00000000
χ3322-2-222-2-222-2-2-2-222-22-2-222-12-1-122111-2-2-12-2-21-1-1-11111-111-2-2-1-1221111-1-1-1-1000000002i2i−2i−2i0000−2i2i0000000000000000−i−iiiii−i−i
χ3422-2-222-2-222-2-2-2-222-22-2-222-12-1-122111-2-2-12-2-21-1-1-11111-111-2-2-1-1221111-1-1-1-100000000−2i−2i2i2i00002i−2i0000000000000000ii−i−i−i−iii
χ3522-2-2-2-22222-2-222-2-2000000222-22-2-2-22-2-2-2-222222-2-2-222-200000000000000002-2-22000000000000002-2-2200000000000000000000
χ3622-2-2-2-22222-2-222-2-2000000222-22-2-2-22-2-2-2-222222-2-2-222-20000000000000000-222-200000000000000-222-200000000000000000000
χ372-22-22-22-22-22-22-22-200000022-2-2-2-22-222-2222-2-22-2-22-22-220000000000000000000000002i−2i2i−2i00000000000000000000002i−2i2i−2i0000
χ382-22-22-22-22-22-22-22-200000022-2-2-2-22-222-2222-2-22-2-22-22-22000000000000000000000000−2i2i−2i2i0000000000000000000000−2i2i−2i2i0000
χ392-22-22-22-22-22-22-22-2000000-1211-2-2-11-12-2-122-21-111-11-11-1−i3i300−i3i300−i3−i3i3i3−i3−i3i3i3000000002i−2i2i−2i0000000000000000000000−ii−ii3−33−3
χ402-22-22-22-22-22-22-22-2000000-1211-2-2-11-12-2-122-21-111-11-11-1−i3i300−i3i300−i3−i3i3i3−i3−i3i3i300000000−2i2i−2i2i0000000000000000000000i−ii−i−33−33
χ412-22-22-22-22-22-22-22-2000000-1211-2-2-11-12-2-122-21-111-11-11-1i3−i300i3−i300i3i3−i3−i3i3i3−i3−i3000000002i−2i2i−2i0000000000000000000000−ii−ii−33−33
χ422-22-22-22-22-22-22-22-2000000-1211-2-2-11-12-2-122-21-111-11-11-1i3−i300i3−i300i3i3−i3−i3i3i3−i3−i300000000−2i2i−2i2i0000000000000000000000i−ii−i3−33−3
χ432-22-2-22-222-22-2-22-2200000022-22-222-2-22-2-2-2-2222-222-2-22-2000000000000000000002-22-20000000000000000002-22-2000000000000
χ442-22-2-22-222-22-2-22-2200000022-22-222-2-22-2-2-2-2222-222-2-22-200000000000000000000-22-22000000000000000000-22-22000000000000
χ452-22-2-22-222-22-2-22-220000002-1-221-12-2-2-11-211-12-11-1-111-11003−3003−33−33−33−33−300002-22-2000000000000000000-11-113−33−300000000
χ462-22-2-22-222-22-2-22-220000002-1-221-12-2-2-11-211-12-11-1-111-11003−3003−33−33−33−33−30000-22-220000000000000000001-11-1−33−3300000000
χ472-22-2-22-222-22-2-22-220000002-1-221-12-2-2-11-211-12-11-1-111-1100−3300−33−33−33−33−3300002-22-2000000000000000000-11-11−33−3300000000
χ482-22-2-22-222-22-2-22-220000002-1-221-12-2-2-11-211-12-11-1-111-1100−3300−33−33−33−33−330000-22-220000000000000000001-11-13−33−300000000
χ492-2-222-2-222-2-22-222-200000022-2-2-2-2-22-2-2222-2222-2-2-22-2220000000000000000000000002-2-2200000000000000000000002-2-220000
χ502-2-222-2-222-2-22-222-200000022-2-2-2-2-22-2-2222-2222-2-2-22-222000000000000000000000000-222-20000000000000000000000-222-20000
χ512-2-222-2-222-2-22-222-2000000-1211-2-21-11-22-12-22-1-1111-11-1-1−i3i300i3−i300−i3−i3i3i3i3i3−i3−i3000000002-2-220000000000000000000000-111-1−i3i3i3−i3
χ522-2-222-2-222-2-22-222-2000000-1211-2-21-11-22-12-22-1-1111-11-1-1−i3i300i3−i300−i3−i3i3i3i3i3−i3−i300000000-222-200000000000000000000001-1-11i3−i3−i3i3
χ532-2-222-2-222-2-22-222-2000000-1211-2-21-11-22-12-22-1-1111-11-1-1i3−i300−i3i300i3i3−i3−i3−i3−i3i3i3000000002-2-220000000000000000000000-111-1i3−i3−i3i3
χ542-2-222-2-222-2-22-222-2000000-1211-2-21-11-22-12-22-1-1111-11-1-1i3−i300−i3i300i3i3−i3−i3−i3−i3i3i300000000-222-200000000000000000000001-1-11−i3i3i3−i3
χ552-2-22-222-22-2-222-2-2200000022-22-22-222-22-2-22-2-22-22-222-2-2000000000000000000002i−2i−2i2i0000000000000000002i−2i−2i2i000000000000
χ562-2-22-222-22-2-222-2-2200000022-22-22-222-22-2-22-2-22-22-222-2-200000000000000000000−2i2i2i−2i000000000000000000−2i2i2i−2i000000000000
χ572-2-22-222-22-2-222-2-220000002-1-221-1-2221-1-21-11-2-11-11-1-111003−300−333−33−3−33−3300002i−2i−2i2i000000000000000000−iii−ii3−i3−i3i300000000
χ582-2-22-222-22-2-222-2-220000002-1-221-1-2221-1-21-11-2-11-11-1-111003−300−333−33−3−33−330000−2i2i2i−2i000000000000000000i−i−ii−i3i3i3−i300000000
χ592-2-22-222-22-2-222-2-220000002-1-221-1-2221-1-21-11-2-11-11-1-11100−33003−3−33−333−33−300002i−2i−2i2i000000000000000000−iii−i−i3i3i3−i300000000
χ602-2-22-222-22-2-222-2-220000002-1-221-1-2221-1-21-11-2-11-11-1-11100−33003−3−33−333−33−30000−2i2i2i−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
χ634444-4-4-4-44444-4-4-4-40000004-24-4-2244-4-2-2-4222-4-2-22-2-22220000000000000000000000000000000000000000000000000000000000
χ644444-4-4-4-44444-4-4-4-4000000-24-224-4-2-22442-4-4-42-2-22-2-22220000000000000000000000000000000000000000000000000000000000
χ654444-4-4-4-44444-4-4-4-4000000-2-2-22-22-2-22-2-22222211-111-1-1-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000000000000000000
χ664444-4-4-4-44444-4-4-4-4000000-2-2-22-22-2-22-2-22222211-111-1-1-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000000000000000
χ6744-4-444-4-444-4-4-4-4444-444-4-4-2-2-2-2-2-222222-2-2222111-1-1-1-11-2-2-2-222221111-1-1-1-1000000000000000000000000000000000000000000
χ6844-4-444-4-444-4-4-4-444-44-4-444-2-2-2-2-2-222222-2-2222111-1-1-1-112222-2-2-2-2-1-1-1-11111000000000000000000000000000000000000000000
χ6944-4-4-4-44444-4-444-4-40000004-24-4-22-4-4422-42-2-24-2-2222-2-220000000000000000000000000000000000000000000000000000000000
χ7044-4-4-4-44444-4-444-4-4000000-24-224-422-2-4-42-444-2-2-2222-2-220000000000000000000000000000000000000000000000000000000000
χ7144-4-4-4-44444-4-444-4-4000000-2-2-22-2222-22222-2-2-211-1-1-111-1000000003i−3i−3i3i−3i3i3i−3i000000000000000000000000000000000000000000
χ7244-4-4-4-44444-4-444-4-4000000-2-2-22-2222-22222-2-2-211-1-1-111-100000000−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000000000000000
χ734-44-44-44-44-44-44-44-40000004-2-4-4224-44-224-2-22-4-222-22-22-20000000000000000000000000000000000000000000000000000000000
χ744-44-44-44-44-44-44-44-4000000-2-22222-22-2-22-2-2-2221-1-11-11-11−2i32i300−2i32i300i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000000000
χ754-44-44-44-44-44-44-44-4000000-2-22222-22-2-22-2-2-2221-1-11-11-112i3−2i3002i3−2i300−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000000000
χ764-44-4-44-444-44-4-44-44000000-242-2-44-2224-42-4-44-2-22-2-222-220000000000000000000000000000000000000000000000000000000000
χ774-44-4-44-444-44-4-44-44000000-2-22-22-2-222-22222-2-21-111-1-11-10023−230023−23−33−33−33−33000000000000000000000000000000000000000000
χ784-44-4-44-444-44-4-44-44000000-2-22-22-2-222-22222-2-21-111-1-11-100−232300−23233−33−33−33−3000000000000000000000000000000000000000000
χ794-4-444-4-444-4-44-444-40000004-2-4-422-44-42-24-22-24-2222-22-2-20000000000000000000000000000000000000000000000000000000000
χ804-4-444-4-444-4-44-444-4000000-2-222222-222-2-2-22-2-21-1-1-11-111−2i32i3002i3−2i300i3i3−i3−i3−i3−i3i3i3000000000000000000000000000000000000000000
χ814-4-444-4-444-4-44-444-4000000-2-222222-222-2-2-22-2-21-1-1-11-1112i3−2i300−2i32i300−i3−i3i3i3i3i3−i3−i3000000000000000000000000000000000000000000
χ824-4-44-444-44-4-444-4-44000000-242-2-442-2-2-442-44-42-22-22-2-2220000000000000000000000000000000000000000000000000000000000
χ834-4-44-444-44-4-444-4-44000000-2-22-22-22-2-22-222-2221-11-111-1-10023−2300−2323−33−333−33−3000000000000000000000000000000000000000000
χ844-4-44-444-44-4-444-4-44000000-2-22-22-22-2-22-222-2221-11-111-1-100−23230023−233−33−3−33−33000000000000000000000000000000000000000000
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
χ896666-6-6-6-6-3-3-3-333330033−3333−3300000000000000000000000000000000000000002-22-200000000000000-11-113−33−30000000000000000
χ906666-6-6-6-6-3-3-3-333330033−3333−330000000000000000000000000000000000000000-22-22000000000000001-11-1−33−330000000000000000
χ916666-6-6-6-6-3-3-3-3333300−3333−333300000000000000000000000000000000000000002-22-200000000000000-11-11−33−330000000000000000
χ926666-6-6-6-6-3-3-3-3333300−3333−33330000000000000000000000000000000000000000-22-22000000000000001-11-13−33−30000000000000000
χ9366-6-666-6-6-3-33333-3-36-6-3-333000000000000000000000000000000000000000022-2-2000000002-20000-1-111-1-1110000000000000000
χ9466-6-666-6-6-3-33333-3-36-6-3-3330000000000000000000000000000000000000000-2-22200000000-22000011-1-111-1-10000000000000000
χ9566-6-666-6-6-3-33333-3-3-6633-3-3000000000000000000000000000000000000000022-2-200000000-220000-1-11111-1-10000000000000000
χ9666-6-666-6-6-3-33333-3-3-6633-3-30000000000000000000000000000000000000000-2-222000000002-2000011-1-1-1-1110000000000000000
χ9766-6-6-6-666-3-333-3-3330033−33−333300000000000000000000000000000000000000002-2-2200000000000000-111-13−3−330000000000000000
χ9866-6-6-6-666-3-333-3-3330033−33−33330000000000000000000000000000000000000000-222-2000000000000001-1-11−333−30000000000000000
χ9966-6-6-6-666-3-333-3-33300−333333−3300000000000000000000000000000000000000002-2-2200000000000000-111-1−333−30000000000000000
χ10066-6-6-6-666-3-333-3-33300−333333−330000000000000000000000000000000000000000-222-2000000000000001-1-113−3−330000000000000000
χ10112-1212-1212-1212-12-66-66-66-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10212-1212-12-1212-1212-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10312-12-121212-12-1212-666-66-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10412-12-1212-121212-12-666-6-666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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