Finite Group Databasebeta

← Group #13161227

Character table — Group #13161227

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size111122222222222222222222224444444444444444444444444488888888888888888888888888888888888121212121212121212121212121212121212242424242424242424363636363636727272108108216
order12223333344666666666666666333366666666666612121212121212121212412121212121212121212121212121212121212121212121212121212121212121212882424242424242424242424242424242441212121212121212441212121241212884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ51111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-111-1
χ61111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-11
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111111-1
χ9222222222-2-22222222222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000000002-222-2-2000000
χ10222222222-2-22222222222222222222222222222222-2-2-2-2-2-2-2-2-2-200000000000-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000-22-2-222000000
χ1122222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000022-1-1-1-12-1-1000
χ1222222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000-2-21111-211000
χ1322222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-2-2-2-2-2-2-2-2-211-1-1-1-1-1-1-1-1111111111111111100000000000000000000000000022-1-1-1-1-211000
χ1422222222-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-12222-2-2-2-2-2-2-2-2-211-1-1-1-1-1-1-1-11111111111111111000000000000000000000000000-2-211112-1-1000
χ1522222222-1-2-2222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-2000000000−i3i311111111−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i30000000000000000000000000002-2-1-1110−i3i3000
χ1622222222-1-2-2222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-2000000000−i3i311111111−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3000000000000000000000000000-2211-1-10i3−i3000
χ1722222222-1-2-2222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-2000000000i3−i311111111i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i30000000000000000000000000002-2-1-1110i3−i3000
χ1822222222-1-2-2222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211-2-2-2-2000000000i3−i311111111i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3000000000000000000000000000-2211-1-10−i3i3000
χ1922222-1-1-12222-1-1-12-1-1-12-1-1-12222-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1000000000000
χ2022222-1-1-12222-1-1-12-1-1-12-1-1-12222-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2111111111111-2-2-2111111000000000000
χ2122222-1-1-12222-1-1-12-1-1-12-1-1-12222-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1222-1-1-1-2-2-2111111-2-222-1-1-1-1-1-1-2-2111111-2-2111111222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111111000000000000
χ2222222-1-1-12222-1-1-12-1-1-12-1-1-12222-1-1-122-1-1-1-1-1-12-1-1-12-1-1-1222-1-1-1-2-2-2111111-2-222-1-1-1-1-1-1-2-2111111-2-2111111-2-2-2-2-2-2111111111111222-1-1-1-1-1-1000000000000
χ232222-12-1-1222-12-1-1-12-1-1-12-1-1222-12-1-1-1-122-1-1-1-1-12-1-1-12-1-122-12-1-12-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-1-1-1-1000000000000
χ242222-12-1-1222-12-1-1-12-1-1-12-1-1222-12-1-1-1-122-1-1-1-1-12-1-1-12-1-122-12-1-12-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-21111-2-2-2-211111111-211-2-21111000000000000
χ252222-12-1-1222-12-1-1-12-1-1-12-1-1222-12-1-1-1-122-1-1-1-1-12-1-1-12-1-122-12-1-1-211-2-21111-2-2-1-122-1-1-1-111-2-2111111-2-2111122-1-1-1-12222-1-1-1-1-1-1-1-1-211-2-21111000000000000
χ262222-12-1-1222-12-1-1-12-1-1-12-1-1222-12-1-1-1-122-1-1-1-1-12-1-1-12-1-122-12-1-1-211-2-21111-2-2-1-122-1-1-1-111-2-2111111-2-21111-2-21111-2-2-2-2111111112-1-122-1-1-1-1000000000000
χ272222-1-12-1222-1-12-1-1-12-1-1-12-1222-1-12-1-1-1-1-122-1-1-1-12-1-1-12-122-1-12-12-1-1-1-122-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-12-1-1-1-122-1-1000000000000
χ282222-1-12-1222-1-12-1-1-12-1-1-12-1222-1-12-1-1-1-1-122-1-1-1-12-1-1-12-122-1-12-12-1-1-1-122-1-122-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-2-211111111-2-2-2-21111-21111-2-211000000000000
χ292222-1-12-1222-1-12-1-1-12-1-1-12-1222-1-12-1-1-1-1-122-1-1-1-12-1-1-12-122-1-12-1-21111-2-211-2-2-1-1-1-122-1-11111-2-2111111-2-21122-1-1-1-1-1-1-1-12222-1-1-1-1-21111-2-211000000000000
χ302222-1-12-1222-1-12-1-1-12-1-1-12-1222-1-12-1-1-1-1-122-1-1-1-12-1-1-12-122-1-12-1-21111-2-211-2-2-1-1-1-122-1-11111-2-2111111-2-211-2-211111111-2-2-2-211112-1-1-1-122-1-1000000000000
χ312222-1-1-12222-1-1-12-1-1-12-1-1-12222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1222-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-1-1-1-122000000000000
χ322222-1-1-12222-1-1-12-1-1-12-1-1-12222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1222-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-2-2111111111111-2-2-2-2-2111111-2-2000000000000
χ332222-1-1-12222-1-1-12-1-1-12-1-1-12222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1222-1-1-12-2111111-2-2-2-2-1-1-1-1-1-122111111-2-2111111-2-222-1-1-1-1-1-1-1-1-1-1-1-12222-2111111-2-2000000000000
χ342222-1-1-12222-1-1-12-1-1-12-1-1-12222-1-1-12-1-1-1-1-1-122-1-1-12-1-1-1222-1-1-12-2111111-2-2-2-2-1-1-1-1-1-122111111-2-2111111-2-2-2-2111111111111-2-2-2-22-1-1-1-1-1-122000000000000
χ352-22-2222222-2-2-2-2-22222-2-2-2-2-2-222222-2-2-2-2-2-2-2-22222-2-2-2-22-22222000000000002-22-22-22-200000000000000000000000000000000000000000000000000002i−2i0
χ362-22-2222222-2-2-2-2-22222-2-2-2-2-2-222222-2-2-2-2-2-2-2-22222-2-2-2-22-22222000000000002-22-22-22-20000000000000000000000000000000000000000000000000000−2i2i0
χ372-22-222222-22-2-2-2-22222-2-2-2-2-2-222222-2-2-2-2-2-2-2-222222222-22-2-2-2-200000000000-22-22-22-2200000000000000002i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000
χ382-22-222222-22-2-2-2-22222-2-2-2-2-2-222222-2-2-2-2-2-2-2-222222222-22-2-2-2-200000000000-22-22-22-220000000000000000−2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000
χ392-22-22-1-1-12-22-21112-1-1-1-2111-2-222-1-1-1-2-21111112-1-1-12-1-1-1-22-2111000−i3i3−i3i3−i3i300-221-11-11-100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i32i−2i2i2i−2i−2i−i−iii−i−iii−i−iii0003−33−33−3000000000000
χ402-22-22-1-1-12-22-21112-1-1-1-2111-2-222-1-1-1-2-21111112-1-1-12-1-1-1-22-2111000−i3i3−i3i3−i3i300-221-11-11-100−i3i3−i3i3−i3i300−i3i3−i3i3−i3i3−2i2i−2i−2i2i2iii−i−iii−i−iii−i−i000−33−33−33000000000000
χ412-22-22-1-1-12-22-21112-1-1-1-2111-2-222-1-1-1-2-21111112-1-1-12-1-1-1-22-2111000i3−i3i3−i3i3−i300-221-11-11-100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i32i−2i2i2i−2i−2i−i−iii−i−iii−i−iii000−33−33−33000000000000
χ422-22-22-1-1-12-22-21112-1-1-1-2111-2-222-1-1-1-2-21111112-1-1-12-1-1-1-22-2111000i3−i3i3−i3i3−i300-221-11-11-100i3−i3i3−i3i3−i300i3−i3i3−i3i3−i3−2i2i−2i−2i2i2iii−i−iii−i−iii−i−i0003−33−33−3000000000000
χ432-22-2-12-1-12-221-211-12-1-11-211-2-22-12-1-111-2-21111-12-1-1-12-1-1-221-2110−i3i300−i3i3i3−i3001-1-221-11-1−i3i300−i3i3i3−i3−i3i300−i3i3i3−i32i−2i−i−iii2i2i−2i−2i−i−iii−i−iii03−3003−3−33000000000000
χ442-22-2-12-1-12-221-211-12-1-11-211-2-22-12-1-111-2-21111-12-1-1-12-1-1-221-2110−i3i300−i3i3i3−i3001-1-221-11-1−i3i300−i3i3i3−i3−i3i300−i3i3i3−i3−2i2iii−i−i−2i−2i2i2iii−i−iii−i−i0−3300−333−3000000000000
χ452-22-2-12-1-12-221-211-12-1-11-211-2-22-12-1-111-2-21111-12-1-1-12-1-1-221-2110i3−i300i3−i3−i3i3001-1-221-11-1i3−i300i3−i3−i3i3i3−i300i3−i3−i3i32i−2i−i−iii2i2i−2i−2i−i−iii−i−iii0−3300−333−3000000000000
χ462-22-2-12-1-12-221-211-12-1-11-211-2-22-12-1-111-2-21111-12-1-1-12-1-1-221-2110i3−i300i3−i3−i3i3001-1-221-11-1i3−i300i3−i3−i3i3i3−i300i3−i3−i3i3−2i2iii−i−i−2i−2i2i2iii−i−iii−i−i03−3003−3−33000000000000
χ472-22-2-1-12-12-2211-21-1-12-111-21-2-22-1-12-11111-2-211-1-12-1-1-12-1-2211-210−i3i3i3−i300−i3i3001-11-1-221-1−i3i3i3−i300−i3i3−i3i3i3−i300−i3i32i−2i−i−iii−i−iii2i2i−2i−2i−i−iii03−3−33003−3000000000000
χ482-22-2-1-12-12-2211-21-1-12-111-21-2-22-1-12-11111-2-211-1-12-1-1-12-1-2211-210−i3i3i3−i300−i3i3001-11-1-221-1−i3i3i3−i300−i3i3−i3i3i3−i300−i3i3−2i2iii−i−iii−i−i−2i−2i2i2iii−i−i0−333−300−33000000000000
χ492-22-2-1-12-12-2211-21-1-12-111-21-2-22-1-12-11111-2-211-1-12-1-1-12-1-2211-210i3−i3−i3i300i3−i3001-11-1-221-1i3−i3−i3i300i3−i3i3−i3−i3i300i3−i32i−2i−i−iii−i−iii2i2i−2i−2i−i−iii0−333−300−33000000000000
χ502-22-2-1-12-12-2211-21-1-12-111-21-2-22-1-12-11111-2-211-1-12-1-1-12-1-2211-210i3−i3−i3i300i3−i3001-11-1-221-1i3−i3−i3i300i3−i3i3−i3−i3i300i3−i3−2i2iii−i−iii−i−i−2i−2i2i2iii−i−i03−3−33003−3000000000000
χ512-22-2-1-1-122-22111-2-1-1-12111-2-2-22-1-1-12111111-2-2-1-1-12-1-1-12-22111-20−i3i3−i3i3i3−i300001-11-11-1-22−i3i3−i3i3i3−i300−i3i3−i3i3i3−i3002i−2i−i−iii−i−iii−i−iii2i2i−2i−2i03−33−3−3300000000000000
χ522-22-2-1-1-122-22111-2-1-1-12111-2-2-22-1-1-12111111-2-2-1-1-12-1-1-12-22111-20−i3i3−i3i3i3−i300001-11-11-1-22−i3i3−i3i3i3−i300−i3i3−i3i3i3−i300−2i2iii−i−iii−i−iii−i−i−2i−2i2i2i0−33−333−300000000000000
χ532-22-2-1-1-122-22111-2-1-1-12111-2-2-22-1-1-12111111-2-2-1-1-12-1-1-12-22111-20i3−i3i3−i3−i3i300001-11-11-1-22i3−i3i3−i3−i3i300i3−i3i3−i3−i3i3002i−2i−i−iii−i−iii−i−iii2i2i−2i−2i0−33−333−300000000000000
χ542-22-2-1-1-122-22111-2-1-1-12111-2-2-22-1-1-12111111-2-2-1-1-12-1-1-12-22111-20i3−i3i3−i3−i3i300001-11-11-1-22i3−i3i3−i3−i3i300i3−i3i3−i3−i3i300−2i2iii−i−iii−i−iii−i−i−2i−2i2i2i03−33−3−3300000000000000
χ5544444-2-2-24-4-44-2-2-24-2-2-24-2-2-24444-2-2-244-2-2-2-2-2-24-2-2-2-4222-4-4-422200000000000-4-42222220000000000000000000000000000000000000000000000000000000
χ5644444-2-2-2-2444-2-2-24-2-2-24-2-2-2-2-2-2-2111-2-2111111-21114-2-2-2-2-24-2-2-2444-2-2-2-2-2-2-2-2-2-2111111-2-2111111-2-2111111000000000000000000000000000000000000000
χ5744444-2-2-2-2444-2-2-24-2-2-24-2-2-2-2-2-2-2111-2-2111111-21114-2-2-2-2-24-2-2-2-4-4-422222222-2-211111122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000000000000000000000
χ5844444-2-2-2-2-4-44-2-2-24-2-2-24-2-2-2-2-2-2-2111-2-2111111-2111-422222-4222000000000−2i32i322-1-1-1-1-1-1−2i3−2i3i3i3i3i3i3i32i32i3−i3−i3−i3−i3−i3−i3000000000000000000000000000000000000000
χ5944444-2-2-2-2-4-44-2-2-24-2-2-24-2-2-2-2-2-2-2111-2-2111111-2111-422222-42220000000002i3−2i322-1-1-1-1-1-12i32i3−i3−i3−i3−i3−i3−i3−2i3−2i3i3i3i3i3i3i3000000000000000000000000000000000000000
χ604444-24-2-24-4-4-24-2-2-24-2-2-24-2-2444-24-2-2-2-244-2-2-2-2-24-2-22-422-4-42-4220000000000022-4-422220000000000000000000000000000000000000000000000000000000
χ614444-24-2-2-244-24-2-2-24-2-2-24-2-2-2-2-21-21111-2-211111-211-24-2-2-2-2-24-2-24-2-244-2-2-2-2-2-211-2-2111111-2-2111111-2-21111000000000000000000000000000000000000000
χ624444-24-2-2-244-24-2-2-24-2-2-24-2-2-2-2-21-21111-2-211111-211-24-2-2-2-2-24-2-2-422-4-422222211-2-21111-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000000000000000000000
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χ704444-2-2-244-4-4-2-2-24-2-2-24-2-2-24444-2-2-24-2-2-2-2-2-244-2-2-24222-4-4-4222-400000000000222222-4-40000000000000000000000000000000000000000000000000000000
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χ864-44-44444-24-4-4-4-4-44444-4-4-4-422-2-2-2-2-222222222-2-2-2-2-4-4-4-4-22444400000000000-22-22-22-220000000000000000000000000000000000000000000000000000000
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χ884-44-44-2-2-244-4-42224-2-2-2-4222-4-444-2-2-2-4-42222224-2-2-2-42224-44-2-2-2000000000004-4-22-22-220000000000000000000000000000000000000000000000000000000
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χ1034-44-4-2-2-2444-4222-4-2-2-24222-4-4-44-2-2-24222222-4-4-2-2-24222-44-4-2-2-2400000000000-22-22-224-40000000000000000000000000000000000000000000000000000000
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χ1124-4-444-2-2-24004-2-2-2-4222-4222-44-44-2-2-2-442-22-22-2-4222000000000000000000000000000000000000000000000000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6000000000000000000000
χ1134-4-44-24-2-2400-24-2-22-4222-422-44-4-24-2-22-2-442-22-22-42200000000000000000000000000000000000000000000000i6−i6−i6i60000i6−i6−i6i6−i6i6i6−i6000000000000000000000
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χ11988-8-88-4-4-4-400-8444-84448-4-4-4-444-4222-442-22-22-24-2-2-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12088-8-8-48-4-4-4004-8444-844-48-4-4-4442-4222-2-442-22-2-24-2-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12188-8-8-4-48-4-40044-8444-84-4-48-4-44422-422-22-2-442-2-2-24-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12288-8-8-4-4-48-400444-8444-8-4-4-48-444222-42-22-22-2-44-2-2-24000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1238-8-888-4-4-4-4008-4-4-4-8444-84444-44-42224-4-22-22-224-2-2-2000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1268-8-88-4-4-48-400-4-4-48444-8444-84-44222-4-22-22-224-4-2-2-24000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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