Finite Group Databasebeta

← Group #10694034

Character table — Group #10694034

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222222222223444444446666666666666664444444412121212121212121212121212121212121212121212121244444444121212121212121212121212121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ121111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ131111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ18222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-1-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ21222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ22222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-11111111122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ2522222222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-2222222-2-222-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ2622222222-2-2-2-2222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-222-2-222-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2722222222-2-2-2-22-2-22222-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ2822222222-2-2-2-22-2-22222-2-2222-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2922222222-2-2-2-2-122-2-2-2-222-1-1-111111111-1-1-1-122-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3022222222-2-2-2-2-122-2-2-2-222-1-1-111111111-1-1-1-122-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3122222222-2-2-2-2-122-2-2-2-222-1-1-111111111-1-1-1-1-2-222-2-2221111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3222222222-2-2-2-2-122-2-2-2-222-1-1-111111111-1-1-1-1-2-222-2-2221111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3322222222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3422222222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ3522222222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ3622222222-2-2-2-2-1-2-22222-2-2-1-1-111111111-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111111111-1-1-1-100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ3722-2-22-22-222-2-222i−2i2i2i−2i−2i2i−2i2-2-22222-2-2-2-22-22-20000000000000000000000002i2i−2i−2i2i2i−2i−2i002-2002i−2i00002-22-200002i−2i2i−2i0000000000000000
χ3822-2-22-22-222-2-222i−2i2i2i−2i−2i2i−2i2-2-22222-2-2-2-22-22-20000000000000000000000002i2i−2i−2i2i2i−2i−2i00-2200−2i2i0000-22-220000−2i2i−2i2i0000000000000000
χ3922-2-22-22-222-2-22−2i2i−2i−2i2i2i−2i2i2-2-22222-2-2-2-22-22-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i002-200−2i2i00002-22-20000−2i2i−2i2i0000000000000000
χ4022-2-22-22-222-2-22−2i2i−2i−2i2i2i−2i2i2-2-22222-2-2-2-22-22-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i00-22002i−2i0000-22-2200002i−2i2i−2i0000000000000000
χ4122-2-22-22-222-2-2-12i−2i2i2i−2i−2i2i−2i-111-1-1-1-11111-11-1100000000−i3−i3i3i3−i3−i3i3i333−3−333−3−3−i−iii−i−iii002-2002i−2i−i3i3−i3i3-11-113−33−3−ii−ii0000000000000000
χ4222-2-22-22-222-2-2-12i−2i2i2i−2i−2i2i−2i-111-1-1-1-11111-11-1100000000−i3−i3i3i3−i3−i3i3i333−3−333−3−3−i−iii−i−iii00-2200−2i2ii3−i3i3−i31-11-1−33−33i−ii−i0000000000000000
χ4322-2-22-22-222-2-2-12i−2i2i2i−2i−2i2i−2i-111-1-1-1-11111-11-1100000000i3i3−i3−i3i3i3−i3−i3−3−333−3−333−i−iii−i−iii002-2002i−2ii3−i3i3−i3-11-11−33−33−ii−ii0000000000000000
χ4422-2-22-22-222-2-2-12i−2i2i2i−2i−2i2i−2i-111-1-1-1-11111-11-1100000000i3i3−i3−i3i3i3−i3−i3−3−333−3−333−i−iii−i−iii00-2200−2i2i−i3i3−i3i31-11-13−33−3i−ii−i0000000000000000
χ4522-2-22-22-222-2-2-1−2i2i−2i−2i2i2i−2i2i-111-1-1-1-11111-11-1100000000−i3−i3i3i3−i3−i3i3i3−3−333−3−333ii−i−iii−i−i002-200−2i2i−i3i3−i3i3-11-11−33−33i−ii−i0000000000000000
χ4622-2-22-22-222-2-2-1−2i2i−2i−2i2i2i−2i2i-111-1-1-1-11111-11-1100000000−i3−i3i3i3−i3−i3i3i3−3−333−3−333ii−i−iii−i−i00-22002i−2ii3−i3i3−i31-11-13−33−3−ii−ii0000000000000000
χ4722-2-22-22-222-2-2-1−2i2i−2i−2i2i2i−2i2i-111-1-1-1-11111-11-1100000000i3i3−i3−i3i3i3−i3−i333−3−333−3−3ii−i−iii−i−i002-200−2i2ii3−i3i3−i3-11-113−33−3i−ii−i0000000000000000
χ4822-2-22-22-222-2-2-1−2i2i−2i−2i2i2i−2i2i-111-1-1-1-11111-11-1100000000i3i3−i3−i3i3i3−i3−i333−3−333−3−3ii−i−iii−i−i00-22002i−2i−i3i3−i3i31-11-1−33−33−ii−ii0000000000000000
χ4922-2-22-22-2-2-22222i−2i−2i−2i2i2i2i−2i2-2-2-2-2-2-222222-22-20000000000000000000000002i2i−2i−2i−2i−2i2i2i2-2002i−2i002-2-2200002i−2i−2i2i00000000000000000000
χ5022-2-22-22-2-2-22222i−2i−2i−2i2i2i2i−2i2-2-2-2-2-2-222222-22-20000000000000000000000002i2i−2i−2i−2i−2i2i2i-2200−2i2i00-222-20000−2i2i2i−2i00000000000000000000
χ5122-2-22-22-2-2-2222−2i2i2i2i−2i−2i−2i2i2-2-2-2-2-2-222222-22-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i2-200−2i2i002-2-220000−2i2i2i−2i00000000000000000000
χ5222-2-22-22-2-2-2222−2i2i2i2i−2i−2i−2i2i2-2-2-2-2-2-222222-22-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i-22002i−2i00-222-200002i−2i−2i2i00000000000000000000
χ5322-2-22-22-2-2-222-12i−2i−2i−2i2i2i2i−2i-1111111-1-1-1-1-11-1100000000−i3−i3i3i3i3i3−i3−i333−3−3−3−333−i−iiiii−i−i2-2002i−2i00-111-1−i3i3i3−i3−iii−i3−3−330000000000000000
χ5422-2-22-22-2-2-222-12i−2i−2i−2i2i2i2i−2i-1111111-1-1-1-1-11-1100000000−i3−i3i3i3i3i3−i3−i333−3−3−3−333−i−iiiii−i−i-2200−2i2i001-1-11i3−i3−i3i3i−i−ii−333−30000000000000000
χ5522-2-22-22-2-2-222-12i−2i−2i−2i2i2i2i−2i-1111111-1-1-1-1-11-1100000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−3−i−iiiii−i−i2-2002i−2i00-111-1i3−i3−i3i3−iii−i−333−30000000000000000
χ5622-2-22-22-2-2-222-12i−2i−2i−2i2i2i2i−2i-1111111-1-1-1-1-11-1100000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−3−i−iiiii−i−i-2200−2i2i001-1-11−i3i3i3−i3i−i−ii3−3−330000000000000000
χ5722-2-22-22-2-2-222-1−2i2i2i2i−2i−2i−2i2i-1111111-1-1-1-1-11-1100000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−3ii−i−i−i−iii2-200−2i2i00-111-1−i3i3i3−i3i−i−ii−333−30000000000000000
χ5822-2-22-22-2-2-222-1−2i2i2i2i−2i−2i−2i2i-1111111-1-1-1-1-11-1100000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−3ii−i−i−i−iii-22002i−2i001-1-11i3−i3−i3i3−iii−i3−3−330000000000000000
χ5922-2-22-22-2-2-222-1−2i2i2i2i−2i−2i−2i2i-1111111-1-1-1-1-11-1100000000i3i3−i3−i3−i3−i3i3i333−3−3−3−333ii−i−i−i−iii2-200−2i2i00-111-1i3−i3−i3i3i−i−ii3−3−330000000000000000
χ6022-2-22-22-2-2-222-1−2i2i2i2i−2i−2i−2i2i-1111111-1-1-1-1-11-1100000000i3i3−i3−i3−i3−i3i3i333−3−3−3−333ii−i−i−i−iii-22002i−2i001-1-11−i3i3i3−i3−iii−i−333−30000000000000000
χ612-22-2-222-22-22-222i−2i2i−2i2i−2i−2i2i-22-222-2-222-2-2-222-20000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ622-22-2-222-22-22-222i−2i2i−2i2i−2i−2i2i-22-222-2-222-2-2-222-20000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ632-22-2-222-22-22-22−2i2i−2i2i−2i2i2i−2i-22-222-2-222-2-2-222-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ642-22-2-222-22-22-22−2i2i−2i2i−2i2i2i−2i-22-222-2-222-2-2-222-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ652-22-2-222-2-22-2222i−2i−2i2i−2i2i−2i2i-22-2-2-222-2-222-222-20000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ662-22-2-222-2-22-2222i−2i−2i2i−2i2i−2i2i-22-2-2-222-2-222-222-20000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ672-22-2-222-2-22-222−2i2i2i−2i2i−2i2i−2i-22-2-2-222-2-222-222-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ682-22-2-222-2-22-222−2i2i2i−2i2i−2i2i−2i-22-2-2-222-2-222-222-2000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ692-2-22-2-2222-2-222222-2-22-2-2-2-2222-2-2-2-222-2-2220000000000000000000000002-2-222-2-2200000000000000000000000000002i−2i2i−2i00000000
χ702-2-22-2-2222-2-222222-2-22-2-2-2-2222-2-2-2-222-2-2220000000000000000000000002-2-222-2-220000000000000000000000000000−2i2i−2i2i00000000
χ712-2-22-2-2222-2-222-2-2-222-222-2-2222-2-2-2-222-2-222000000000000000000000000-222-2-222-200000000000000000000000000002-2-2200000000
χ722-2-22-2-2222-2-222-2-2-222-222-2-2222-2-2-2-222-2-222000000000000000000000000-222-2-222-20000000000000000000000000000-222-200000000
χ732-2-22-2-222-222-2222-222-2-2-2-2-22-2-22222-2-2-2-2220000000000000000000000002-2-22-222-20000000000000000000000002i−2i2i−2i000000000000
χ742-2-22-2-222-222-2222-222-2-2-2-2-22-2-22222-2-2-2-2220000000000000000000000002-2-22-222-2000000000000000000000000−2i2i−2i2i000000000000
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χ762-2-22-2-222-222-22-2-22-2-2222-2-22-2-22222-2-2-2-222000000000000000000000000-222-22-2-22000000000000000000000000-222-2000000000000
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χ994-4-44-4-4444-4-44-2444-4-44-4-422-2-2-22222-2-222-2-2000000000000000000000000-222-2-222-20000000000000000000000000000000000000000
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χ1014-4-44-4-444-444-4-244-444-4-4-422-222-2-2-2-22222-2-2000000000000000000000000-222-22-2-220000000000000000000000000000000000000000
χ1024-4-44-4-444-444-4-2-4-44-4-444422-222-2-2-2-22222-2-20000000000000000000000002-2-22-222-20000000000000000000000000000000000000000
χ1034-4-4-444-440000400000000-4-4-40000000044-444-40000004-4-44000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-444-440000400000000-4-4-40000000044-44-44000000-444-4000000000000000000000000000000000000000000000000000000000000
χ1054-4-4-444-440000-200000000222−2i32i32i3−2i32i3−2i3−2i32i3-2-22-24-4000000-222-2−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000
χ1064-4-4-444-440000-200000000222−2i32i32i3−2i32i3−2i3−2i32i3-2-22-2-440000002-2-222i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ1074-4-4-444-440000-2000000002222i3−2i3−2i32i3−2i32i32i3−2i3-2-22-24-4000000-222-22i3−2i3−2i32i300000000000000000000000000000000000000000000000000000000
χ1084-4-4-444-440000-2000000002222i3−2i3−2i32i3−2i32i32i3−2i3-2-22-2-440000002-2-22−2i32i32i3−2i300000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.