Finite Group Databasebeta

← Group #11721722

Character table — Group #11721722

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106
size1111111111112222222222222222226666666666666666666666666666666666666666666666666666666666666666363636363636363636363636
order1222336666664444441212121212121212121212123333666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212244466121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ411111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ6111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ7111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1111-1-1-1-111
χ8111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-111-1-1-11111-1-1
χ92222222222222222222222222222222-1-1-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ10222222222222222222222222222222-12-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ11222222222222222222222222222222-1-12-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1000000000000
χ12222222222222222222222222222222-1-1-12-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222000000000000
χ1322222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-1-1-1222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-2111111111111000000000000
χ1422222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-11111-2-2-2-2111111111111-2-2-2-211111111000000000000
χ1522222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-12-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-111111111-2-2-2-2111111111111-2-2-2-21111000000000000
χ1622222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-1-1-12-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222111111111111-2-2-2-2111111111111-2-2-2-2000000000000
χ17222222222222-2-222-2-2-2-2-2-22222-2-2-2-22-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000000000
χ18222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-12-1-1-1-1-1222-1-1-1-1-1-11111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-11111-2-2-2-211111111000000000000
χ19222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-1-12-1-1-1-1-1-1-1222-1-1-111111111-2-2-2-21111-1-1-1-1-1-1-1-12222-1-1-1-111111111-2-2-2-21111000000000000
χ20222222222222-2-222-2-2-2-2-2-22222-2-2-2-2-1-1-12-1-1-1-1-1-1-1-1-1222111111111111-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222111111111111-2-2-2-2000000000000
χ21222222222222-2-2-2-222-2-2-2-2-2-2-2-222222-1-1-1222-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-21111111111112222-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-12-1-1-1-1-1222-1-1-1-1-1-11111-2-2-2-2111111111111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ23222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-1-12-1-1-1-1-1-1-1222-1-1-111111111-2-2-2-2111111111111-2-2-2-21111-1-1-1-1-1-1-1-12222-1-1-1-1000000000000
χ24222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-1-1-12-1-1-1-1-1-1-1-1-1222111111111111-2-2-2-2111111111111-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222000000000000
χ2522-2-22222-2-2-2-200002i−2i000000002i2i−2i−2i22222-2-22-2-22-2-22-2-2000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000
χ2622-2-22222-2-2-2-200002i−2i000000002i2i−2i−2i2-1-1-12-2-2-111-111-1110000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000033−3−333−3−333−3−32i2i−2i−2i−i−iii−i−iii−i−iii000000000000
χ2722-2-22222-2-2-2-200002i−2i000000002i2i−2i−2i2-1-1-12-2-2-111-111-1110000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000−3−333−3−333−3−3332i2i−2i−2i−i−iii−i−iii−i−iii000000000000
χ2822-2-22222-2-2-2-200002i−2i000000002i2i−2i−2i-12-1-1-1112-2-2-111-111−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i333−3−3000033−3−3−3−333−i−iii2i2i−2i−2i−i−iii−i−iii000000000000
χ2922-2-22222-2-2-2-200002i−2i000000002i2i−2i−2i-12-1-1-1112-2-2-111-111i3i3−i3−i30000i3i3−i3−i3−i3−i3i3i3−3−3330000−3−33333−3−3−i−iii2i2i−2i−2i−i−iii−i−iii000000000000
χ3022-2-22222-2-2-2-200002i−2i000000002i2i−2i−2i-1-12-1-111-1112-2-2-111−i3−i3i3i3i3i3−i3−i30000−i3−i3i3i333−3−3−3−333000033−3−3−i−iii−i−iii2i2i−2i−2i−i−iii000000000000
χ3122-2-22222-2-2-2-200002i−2i000000002i2i−2i−2i-1-12-1-111-1112-2-2-111i3i3−i3−i3−i3−i3i3i30000i3i3−i3−i3−3−33333−3−30000−3−333−i−iii−i−iii2i2i−2i−2i−i−iii000000000000
χ3222-2-22222-2-2-2-200002i−2i000000002i2i−2i−2i-1-1-12-111-111-1112-2-2−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3000033−3−333−3−3−3−3330000−i−iii−i−iii−i−iii2i2i−2i−2i000000000000
χ3322-2-22222-2-2-2-200002i−2i000000002i2i−2i−2i-1-1-12-111-111-1112-2-2i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000−3−333−3−33333−3−30000−i−iii−i−iii−i−iii2i2i−2i−2i000000000000
χ3422-2-22222-2-2-2-20000−2i2i00000000−2i−2i2i2i22222-2-22-2-22-2-22-2-200000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000
χ3522-2-22222-2-2-2-20000−2i2i00000000−2i−2i2i2i2-1-1-12-2-2-111-111-1110000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000−3−333−3−333−3−333−2i−2i2i2iii−i−iii−i−iii−i−i000000000000
χ3622-2-22222-2-2-2-20000−2i2i00000000−2i−2i2i2i2-1-1-12-2-2-111-111-1110000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000033−3−333−3−333−3−3−2i−2i2i2iii−i−iii−i−iii−i−i000000000000
χ3722-2-22222-2-2-2-20000−2i2i00000000−2i−2i2i2i-12-1-1-1112-2-2-111-111−i3−i3i3i30000−i3−i3i3i3i3i3−i3−i3−3−3330000−3−33333−3−3ii−i−i−2i−2i2i2iii−i−iii−i−i000000000000
χ3822-2-22222-2-2-2-20000−2i2i00000000−2i−2i2i2i-12-1-1-1112-2-2-111-111i3i3−i3−i30000i3i3−i3−i3−i3−i3i3i333−3−3000033−3−3−3−333ii−i−i−2i−2i2i2iii−i−iii−i−i000000000000
χ3922-2-22222-2-2-2-20000−2i2i00000000−2i−2i2i2i-1-12-1-111-1112-2-2-111−i3−i3i3i3i3i3−i3−i30000−i3−i3i3i3−3−33333−3−30000−3−333ii−i−iii−i−i−2i−2i2i2iii−i−i000000000000
χ4022-2-22222-2-2-2-20000−2i2i00000000−2i−2i2i2i-1-12-1-111-1112-2-2-111i3i3−i3−i3−i3−i3i3i30000i3i3−i3−i333−3−3−3−333000033−3−3ii−i−iii−i−i−2i−2i2i2iii−i−i000000000000
χ4122-2-22222-2-2-2-20000−2i2i00000000−2i−2i2i2i-1-1-12-111-111-1112-2-2−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000−3−333−3−33333−3−30000ii−i−iii−i−iii−i−i−2i−2i2i2i000000000000
χ4222-2-22222-2-2-2-20000−2i2i00000000−2i−2i2i2i-1-1-12-111-111-1112-2-2i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3000033−3−333−3−3−3−3330000ii−i−iii−i−iii−i−i−2i−2i2i2i000000000000
χ432-22-222-2-222-2-2002i−2i0000002i2i−2i−2i00002222-22-2-22-2-22-2-22-200000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ442-22-222-2-222-2-2002i−2i0000002i2i−2i−2i00002-1-1-1-22-21-111-111-1100003−33−33−33−33−33−32i−2i2i−2i−ii−ii−ii−ii−ii−ii0000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000
χ452-22-222-2-222-2-2002i−2i0000002i2i−2i−2i00002-1-1-1-22-21-111-111-110000−33−33−33−33−33−332i−2i2i−2i−ii−ii−ii−ii−ii−ii0000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000
χ462-22-222-2-222-2-2002i−2i0000002i2i−2i−2i0000-12-1-11-11-22-21-111-113−33−300003−33−3−33−33−ii−ii2i−2i2i−2i−ii−ii−ii−ii−i3i3−i3i30000−i3i3−i3i3i3−i3i3−i3000000000000
χ472-22-222-2-222-2-2002i−2i0000002i2i−2i−2i0000-12-1-11-11-22-21-111-11−33−330000−33−333−33−3−ii−ii2i−2i2i−2i−ii−ii−ii−iii3−i3i3−i30000i3−i3i3−i3−i3i3−i3i3000000000000
χ482-22-222-2-222-2-2002i−2i0000002i2i−2i−2i0000-1-12-11-111-11-22-21-113−33−3−33−3300003−33−3−ii−ii−ii−ii2i−2i2i−2i−ii−ii−i3i3−i3i3i3−i3i3−i30000−i3i3−i3i3000000000000
χ492-22-222-2-222-2-2002i−2i0000002i2i−2i−2i0000-1-12-11-111-11-22-21-11−33−333−33−30000−33−33−ii−ii−ii−ii2i−2i2i−2i−ii−iii3−i3i3−i3−i3i3−i3i30000i3−i3i3−i3000000000000
χ502-22-222-2-222-2-2002i−2i0000002i2i−2i−2i0000-1-1-121-111-111-11-22-23−33−33−33−3−33−330000−ii−ii−ii−ii−ii−ii2i−2i2i−2i−i3i3−i3i3−i3i3−i3i3i3−i3i3−i30000000000000000
χ512-22-222-2-222-2-2002i−2i0000002i2i−2i−2i0000-1-1-121-111-111-11-22-2−33−33−33−333−33−30000−ii−ii−ii−ii−ii−ii2i−2i2i−2ii3−i3i3−i3i3−i3i3−i3−i3i3−i3i30000000000000000
χ522-22-222-2-222-2-200−2i2i000000−2i−2i2i2i00002222-22-2-22-2-22-2-22-20000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ532-22-222-2-222-2-200−2i2i000000−2i−2i2i2i00002-1-1-1-22-21-111-111-1100003−33−33−33−33−33−3−2i2i−2i2ii−ii−ii−ii−ii−ii−i0000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000
χ542-22-222-2-222-2-200−2i2i000000−2i−2i2i2i00002-1-1-1-22-21-111-111-110000−33−33−33−33−33−33−2i2i−2i2ii−ii−ii−ii−ii−ii−i0000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000
χ552-22-222-2-222-2-200−2i2i000000−2i−2i2i2i0000-12-1-11-11-22-21-111-113−33−300003−33−3−33−33i−ii−i−2i2i−2i2ii−ii−ii−ii−ii3−i3i3−i30000i3−i3i3−i3−i3i3−i3i3000000000000
χ562-22-222-2-222-2-200−2i2i000000−2i−2i2i2i0000-12-1-11-11-22-21-111-11−33−330000−33−333−33−3i−ii−i−2i2i−2i2ii−ii−ii−ii−i−i3i3−i3i30000−i3i3−i3i3i3−i3i3−i3000000000000
χ572-22-222-2-222-2-200−2i2i000000−2i−2i2i2i0000-1-12-11-111-11-22-21-113−33−3−33−3300003−33−3i−ii−ii−ii−i−2i2i−2i2ii−ii−ii3−i3i3−i3−i3i3−i3i30000i3−i3i3−i3000000000000
χ582-22-222-2-222-2-200−2i2i000000−2i−2i2i2i0000-1-12-11-111-11-22-21-11−33−333−33−30000−33−33i−ii−ii−ii−i−2i2i−2i2ii−ii−i−i3i3−i3i3i3−i3i3−i30000−i3i3−i3i3000000000000
χ592-22-222-2-222-2-200−2i2i000000−2i−2i2i2i0000-1-1-121-111-111-11-22-23−33−33−33−3−33−330000i−ii−ii−ii−ii−ii−i−2i2i−2i2ii3−i3i3−i3i3−i3i3−i3−i3i3−i3i30000000000000000
χ602-22-222-2-222-2-200−2i2i000000−2i−2i2i2i0000-1-1-121-111-111-11-22-2−33−33−33−333−33−30000i−ii−ii−ii−ii−ii−i−2i2i−2i2i−i3i3−i3i3−i3i3−i3i3i3−i3i3−i30000000000000000
χ612-2-2222-2-2-2-2222i−2i00002i2i−2i−2i000000002222-2-22-2-22-2-22-2-222i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000000000000000
χ622-2-2222-2-2-2-2222i−2i00002i2i−2i−2i000000002-1-1-1-2-2211-111-111-12i−2i−2i2i−iii−i−iii−i−iii−i0000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i30000−333−3−333−3−333−3000000000000
χ632-2-2222-2-2-2-2222i−2i00002i2i−2i−2i000000002-1-1-1-2-2211-111-111-12i−2i−2i2i−iii−i−iii−i−iii−i0000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300003−3−333−3−333−3−33000000000000
χ642-2-2222-2-2-2-2222i−2i00002i2i−2i−2i00000000-12-1-111-1-2-2211-111-1−iii−i2i−2i−2i2i−iii−i−iii−i−i3i3i3−i30000−i3i3i3−i3i3−i3−i3i3−333−30000−333−33−3−33000000000000
χ652-2-2222-2-2-2-2222i−2i00002i2i−2i−2i00000000-12-1-111-1-2-2211-111-1−iii−i2i−2i−2i2i−iii−i−iii−ii3−i3−i3i30000i3−i3−i3i3−i3i3i3−i33−3−3300003−3−33−333−3000000000000
χ662-2-2222-2-2-2-2222i−2i00002i2i−2i−2i00000000-1-12-111-111-1-2-2211-1−iii−i−iii−i2i−2i−2i2i−iii−i−i3i3i3−i3i3−i3−i3i30000−i3i3i3−i3−333−33−3−330000−333−3000000000000
χ672-2-2222-2-2-2-2222i−2i00002i2i−2i−2i00000000-1-12-111-111-1-2-2211-1−iii−i−iii−i2i−2i−2i2i−iii−ii3−i3−i3i3−i3i3i3−i30000i3−i3−i3i33−3−33−333−300003−3−33000000000000
χ682-2-2222-2-2-2-2222i−2i00002i2i−2i−2i00000000-1-1-1211-111-111-1-2-22−iii−i−iii−i−iii−i2i−2i−2i2i−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000−333−3−333−33−3−330000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.