Finite Group Databasebeta

← Group #10701890

Character table — Group #10701890

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1222222222344444444666121212126666661212121212124444888888881212121212121212242424242424242424242424242424242222224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111-1-1-1-111111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111-1-1-1-111111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111-1-1-1-111111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111111-1-1-1-111111-1-1-1-1111111111-1-1-1-111-1-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111111-1-1-1-111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111111-1-1-1-111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-111ii−i−i−i−iii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111111-1-1-1-111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111111-1-1-1-111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-111−i−iiiii−i−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-22-22-20000000022-2-222-2-200000000000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2-22-2200000000-2-222-2-22200000000000000000000000000000000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ232222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-22-200000000-1-111-1-11133−3−333−3−333−3−333−3−30000000000000000
χ242222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-22-200000000-1-111-1-111−3−333−3−333−3−333−3−3330000000000000000
χ252222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-22-220000000011-1-111-1-133−3−333−3−3−3−333−3−3330000000000000000
χ262222222222-1-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-22-220000000011-1-111-1-1−3−333−3−33333−3−333−3−30000000000000000
χ27222222-2-2-2-22-2-2-2-22222222-2-2-2-222-2-2-2-2-2-222222-2-220000000022-2-2-2-22200000000000000000000000000000000
χ28222222-2-2-2-22-2-2-2-22222222-2-2-2-222-2-2-2-2-2-22222-222-200000000-2-22222-2-200000000000000000000000000000000
χ29222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-1111122-2-22i2i−2i−2i2i2i−2i−2i-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ30222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-1111122-2-2−2i−2i2i2i−2i−2i2i2i-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ31222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-11111-2-2222i2i−2i−2i−2i−2i2i2i1111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ32222222-2-2-2-2-12222-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-11111-2-222−2i−2i2i2i2i2i−2i−2i1111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ33222222-2-2-2-2-1-2-2-2-22222-1-1-11111-1-1111111-1-1-1-12-2-2200000000-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ34222222-2-2-2-2-1-2-2-2-22222-1-1-11111-1-1111111-1-1-1-12-2-2200000000-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ35222222-2-2-2-2-1-2-2-2-22222-1-1-11111-1-1111111-1-1-1-1-222-20000000011-1-1-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ36222222-2-2-2-2-1-2-2-2-22222-1-1-11111-1-1111111-1-1-1-1-222-20000000011-1-1-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ372222-2-22-22-2222-2-22-22-22222222-2-222-2-2-2-22-22-20000000000000000000000000000000000002-22-2000000000000
χ382222-2-22-22-2222-2-22-22-22222222-2-222-2-2-2-22-22-2000000000000000000000000000000000000-22-22000000000000
χ392222-2-22-22-22-2-222-22-22222-2-2-2-2-2-222-2-222-22-2200000000000000000000000000000000000000002-22-200000000
χ402222-2-22-22-22-2-222-22-22222-2-2-2-2-2-222-2-222-22-220000000000000000000000000000000000000000-22-2200000000
χ412222-2-2-22-22222-2-2-22-222222222-2-2-2-222-2-2-22-220000000000000000000000000000000000002-2-22000000000000
χ422222-2-2-22-22222-2-2-22-222222222-2-2-2-222-2-2-22-22000000000000000000000000000000000000-222-2000000000000
χ432222-2-2-22-222-2-2222-22-2222-2-2-2-2-2-2-2-222222-22-200000000000000000000000000000000000000002-2-2200000000
χ442222-2-2-22-222-2-2222-22-2222-2-2-2-2-2-2-2-222222-22-20000000000000000000000000000000000000000-222-200000000
χ452-2-222-222-2-222-22-22-2-222-2-222-2-22-22-22-22-22-2-2200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ462-2-222-222-2-222-22-22-2-222-2-222-2-22-22-22-22-22-2-220000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ472-2-222-222-2-22-22-22-222-22-2-2-2-2222-22-22-2-22-222-2000000002i−2i2i−2i00000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ482-2-222-222-2-22-22-22-222-22-2-2-2-2222-22-22-2-22-222-200000000−2i2i−2i2i0000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ492-2-222-222-2-2-12-22-22-2-22-111-1-111-11-11-11-11-111-100002i−2i2i−2i00003−33−33−33−3−ii−ii−ii−ii−i3i3i3−i3−i3i3i3−i30000000000000000
χ502-2-222-222-2-2-12-22-22-2-22-111-1-111-11-11-11-11-111-100002i−2i2i−2i0000−33−33−33−33−ii−ii−ii−iii3−i3−i3i3i3−i3−i3i30000000000000000
χ512-2-222-222-2-2-12-22-22-2-22-111-1-111-11-11-11-11-111-10000−2i2i−2i2i00003−33−33−33−3i−ii−ii−ii−ii3−i3−i3i3i3−i3−i3i30000000000000000
χ522-2-222-222-2-2-12-22-22-2-22-111-1-111-11-11-11-11-111-10000−2i2i−2i2i0000−33−33−33−33i−ii−ii−ii−i−i3i3i3−i3−i3i3i3−i30000000000000000
χ532-2-222-222-2-2-1-22-22-222-2-11111-1-1-11-11-111-11-1-11000000002i−2i2i−2i3−3−333−3−33i3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii0000000000000000
χ542-2-222-222-2-2-1-22-22-222-2-11111-1-1-11-11-111-11-1-11000000002i−2i2i−2i−333−3−333−3−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii0000000000000000
χ552-2-222-222-2-2-1-22-22-222-2-11111-1-1-11-11-111-11-1-1100000000−2i2i−2i2i3−3−333−3−33−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i0000000000000000
χ562-2-222-222-2-2-1-22-22-222-2-11111-1-1-11-11-111-11-1-1100000000−2i2i−2i2i−333−3−333−3i3−i3−i3i3i3−i3−i3i3i−ii−ii−ii−i0000000000000000
χ572-2-222-2-2-22222-22-2-222-22-2-222-2-22-2-22-222-2-222-200002-2-220000000000002-22-2-22-22000000000000000000000000
χ582-2-222-2-2-22222-22-2-222-22-2-222-2-22-2-22-222-2-222-20000-222-2000000000000-22-222-22-2000000000000000000000000
χ592-2-222-2-2-2222-22-222-2-222-2-2-2-2222-2-22-22-222-2-22000000002-2-2200000000000000002-22-2-22-220000000000000000
χ602-2-222-2-2-2222-22-222-2-222-2-2-2-2222-2-22-22-222-2-2200000000-222-20000000000000000-22-222-22-20000000000000000
χ612-2-222-2-2-222-12-22-2-222-2-111-1-111-111-11-1-111-1-1100002-2-2200003−33−3−33−33-11-111-11-1−333−33−3−330000000000000000
χ622-2-222-2-2-222-12-22-2-222-2-111-1-111-111-11-1-111-1-1100002-2-220000−33−333−33−3-11-111-11-13−3−33−333−30000000000000000
χ632-2-222-2-2-222-12-22-2-222-2-111-1-111-111-11-1-111-1-110000-222-200003−33−3−33−331-11-1-11-113−3−33−333−30000000000000000
χ642-2-222-2-2-222-12-22-2-222-2-111-1-111-111-11-1-111-1-110000-222-20000−33−333−33−31-11-1-11-11−333−33−3−330000000000000000
χ652-2-222-2-2-222-1-22-222-2-22-11111-1-1-111-11-11-1-111-1000000002-2-223−3−33−333−33−3−33−333−3-11-111-11-10000000000000000
χ662-2-222-2-2-222-1-22-222-2-22-11111-1-1-111-11-11-1-111-1000000002-2-22−333−33−3−33−333−33−3−33-11-111-11-10000000000000000
χ672-2-222-2-2-222-1-22-222-2-22-11111-1-1-111-11-11-1-111-100000000-222-23−3−33−333−3−333−33−3−331-11-1-11-110000000000000000
χ682-2-222-2-2-222-1-22-222-2-22-11111-1-1-111-11-11-1-111-100000000-222-2−333−33−3−333−3−33−333−31-11-1-11-110000000000000000
χ692-2-22-222-2-2222-2-2222-2-22-2-222-2-2-222-2-22-2222-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ702-2-22-222-2-2222-2-2222-2-22-2-222-2-2-222-2-22-2222-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ712-2-22-222-2-222-222-2-2-2222-2-2-2-222-222-2-222-2-2-2220000000000000000000000000000000000000000000000002-22-2
χ722-2-22-222-2-222-222-2-2-2222-2-2-2-222-222-2-222-2-2-222000000000000000000000000000000000000000000000000-22-22
χ732-2-22-22-222-222-2-22-2-2222-2-222-2-2-22-222-2-22-2-222000000000000000000000000000000000000000000002-2-220000
χ742-2-22-22-222-222-2-22-2-2222-2-222-2-2-22-222-2-22-2-22200000000000000000000000000000000000000000000-222-20000
χ752-2-22-22-222-22-222-222-2-22-2-2-2-222-22-222-22-222-2-20000000000000000000000000000000000000000000000002i−2i−2i2i
χ762-2-22-22-222-22-222-222-2-22-2-2-2-222-22-222-22-222-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i
χ774444-4-44-44-4-244-4-44-44-4-2-2-2-2-2-2-222-2-22222-22-220000000000000000000000000000000000000000000000000000
χ784444-4-44-44-4-2-4-444-44-44-2-2-2222222-2-222-2-22-22-20000000000000000000000000000000000000000000000000000
χ794444-4-4-44-44-244-4-4-44-44-2-2-2-2-2-2-22222-2-2222-22-20000000000000000000000000000000000000000000000000000
χ804444-4-4-44-44-2-4-4444-44-4-2-2-222222222-2-2-2-2-22-220000000000000000000000000000000000000000000000000000
χ814-4-44-444-4-44-24-4-4444-4-4-222-2-2222-2-222-22-2-2-2220000000000000000000000000000000000000000000000000000
χ824-4-44-444-4-44-2-444-4-4-444-22222-2-22-2-222-2-2222-2-20000000000000000000000000000000000000000000000000000
χ834-4-44-44-444-4-24-4-44-4-444-222-2-2222-22-2-222-222-2-20000000000000000000000000000000000000000000000000000
χ844-4-44-44-444-4-2-444-444-4-4-22222-2-22-22-2-22-22-2-2220000000000000000000000000000000000000000000000000000
χ8588-8-8000000800000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-8000000-4000000004-4443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ8788-8-8000000-4000000004-44−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-88-8000000800000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ898-88-8000000-40000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-88-8000000-40000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000

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