Finite Group Databasebeta

← Group #10702990

Character table — Group #10702990

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1222222222344444444666121212126666661212121212124444444488881212121212121212121212121212121224242424242424244444888888888888
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
χ91-1-1111-1-1-111111-1-11-1-11-1-111-1-111-1-1-11111-1-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ101-1-1111-1-1-111111-1-11-1-11-1-111-1-111-1-1-11111-1-1-1ii−i−i11-1-1ii−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii-1-111−i−iii
χ111-1-1111-1-1-111111-1-11-1-11-1-111-1-111-1-1-11111-1-1-1ii−i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-1-111−i−iii
χ121-1-1111-1-1-111111-1-11-1-11-1-111-1-111-1-1-11111-1-1-1ii−i−i-1-111−i−iiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii11-1-1ii−i−i
χ131-1-1111-1-1-111111-1-11-1-11-1-111-1-111-1-1-11111-1-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii
χ141-1-1111-1-1-111111-1-11-1-11-1-111-1-111-1-1-11111-1-1-1−i−iii11-1-1−i−iii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i-1-111ii−i−i
χ151-1-1111-1-1-111111-1-11-1-11-1-111-1-111-1-1-11111-1-1-1−i−iii-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-1-111ii−i−i
χ161-1-1111-1-1-111111-1-11-1-11-1-111-1-111-1-1-11111-1-1-1−i−iii-1-111ii−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i11-1-1−i−iii
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
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
χ2322222-22-2-2-2222-222-2-2-222222222-22-2-2-22-2-22-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ2422222-22-2-2-2222-222-2-2-222222222-22-2-2-22-2-22-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ2522222-22-2-2-22-2-22-2-2222222-2-2-2-22-22-2-2-2-222-2222-22-20000000022-2-222-2-200000000000000000000000000000000
χ2622222-22-2-2-22-2-22-2-2222222-2-2-2-22-22-2-2-2-222-222-22-2200000000-2-222-2-22200000000000000000000000000000000
χ2722222-22-2-2-2-1-2-22-2-2222-1-1-11111-11-11111-1-11-1-12-22-200000000-1-111-1-11133−3−333−3−333−3−333−3−30000000000000000
χ2822222-22-2-2-2-1-2-22-2-2222-1-1-11111-11-11111-1-11-1-12-22-200000000-1-111-1-111−3−333−3−333−3−333−3−3330000000000000000
χ2922222-22-2-2-2-1-2-22-2-2222-1-1-11111-11-11111-1-11-1-1-22-220000000011-1-111-1-133−3−333−3−3−3−333−3−3330000000000000000
χ3022222-22-2-2-2-1-2-22-2-2222-1-1-11111-11-11111-1-11-1-1-22-220000000011-1-111-1-1−3−333−3−33333−3−333−3−30000000000000000
χ312222-22-22-2-222-222-2-22-2222-2-2-2-2-22-22-2-222-222-200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ322222-22-22-2-222-222-2-22-2222-2-2-2-2-22-22-2-222-222-20000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ332222-22-22-2-22-22-2-222-222222222-22-22-2-2-2-22-2-2200000000000000000000000000000000000000002-22-200000000
χ342222-22-22-2-22-22-2-222-222222222-22-22-2-2-2-22-2-220000000000000000000000000000000000000000-22-2200000000
χ352222-22-22-2-2-12-222-2-22-2-1-1-111111-11-111-1-11-1-1100002i−2i2i−2i0000−i3i3−i3i3−i3i3−i3i3−ii−ii−ii−ii3−33−33−33−30000000000000000
χ362222-22-22-2-2-12-222-2-22-2-1-1-111111-11-111-1-11-1-1100002i−2i2i−2i0000i3−i3i3−i3i3−i3i3−i3−ii−ii−ii−ii−33−33−33−330000000000000000
χ372222-22-22-2-2-12-222-2-22-2-1-1-111111-11-111-1-11-1-110000−2i2i−2i2i0000−i3i3−i3i3−i3i3−i3i3i−ii−ii−ii−i−33−33−33−330000000000000000
χ382222-22-22-2-2-12-222-2-22-2-1-1-111111-11-111-1-11-1-110000−2i2i−2i2i0000i3−i3i3−i3i3−i3i3−i3i−ii−ii−ii−i3−33−33−33−30000000000000000
χ392222-2-2-2-22222-2-22-22-22222-2-2-2-2-2-2-2-2222-222-220000000000000000000000000000000000002-22-2000000000000
χ402222-2-2-2-22222-2-22-22-22222-2-2-2-2-2-2-2-2222-222-22000000000000000000000000000000000000-22-22000000000000
χ412222-2-2-2-2222-222-22-22-22222222-2-2-2-222-22-2-22-2000000002-22-200000000000000002-2-222-2-220000000000000000
χ422222-2-2-2-2222-222-22-22-22222222-2-2-2-222-22-2-22-200000000-22-220000000000000000-222-2-222-20000000000000000
χ432222-2-2-2-222-1-222-22-22-2-1-1-1-1-1-1-11111-1-11-111-11000000002-22-2−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3-111-1-111-10000000000000000
χ442222-2-2-2-222-1-222-22-22-2-1-1-1-1-1-1-11111-1-11-111-11000000002-22-2i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3-111-1-111-10000000000000000
χ452222-2-2-2-222-1-222-22-22-2-1-1-1-1-1-1-11111-1-11-111-1100000000-22-22−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i31-1-111-1-110000000000000000
χ462222-2-2-2-222-1-222-22-22-2-1-1-1-1-1-1-11111-1-11-111-1100000000-22-22i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i31-1-111-1-110000000000000000
χ472-2-2222-2-2-222-2-2-222-2222-2-2-2-22222-2-2-22-2-2-22220000000000000000000000000000000000000000000000002-2-22
χ482-2-2222-2-2-222-2-2-222-2222-2-2-2-22222-2-2-22-2-2-2222000000000000000000000000000000000000000000000000-222-2
χ492-2-2222-2-2-22-1222-2-22-2-2-111-1-111-1-1111-1-1-1-11112i2i−2i−2i22-2-22i2i−2i−2i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii0000000000000000
χ502-2-2222-2-2-22-1222-2-22-2-2-111-1-111-1-1111-1-1-1-11112i2i−2i−2i-2-222−2i−2i2i2i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i0000000000000000
χ512-2-2222-2-2-22-1222-2-22-2-2-111-1-111-1-1111-1-1-1-1111−2i−2i2i2i22-2-2−2i−2i2i2iiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i0000000000000000
χ522-2-2222-2-2-22-1222-2-22-2-2-111-1-111-1-1111-1-1-1-1111−2i−2i2i2i-2-2222i2i−2i−2iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii0000000000000000
χ532-2-222-2-222-2222-2-2-2-2222-2-222-2-22-2-222-22-2-2-222000000000000000000000000000000000000000000002i−2i−2i2i0000
χ542-2-222-2-222-2222-2-2-2-2222-2-222-2-22-2-222-22-2-2-22200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ552-2-222-2-222-22-2-22222-2-22-2-2-2-2222-2-222-2-2222-2-22i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ562-2-222-2-222-22-2-22222-2-22-2-2-2-2222-2-222-2-2222-2-2−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ572-2-222-2-222-2-1-2-22222-2-2-11111-1-1-111-1-111-1-1-1112i−2i−2i2i00000000−i−iiiii−i−i33−3−3−3−333i3i3−i3−i3−i3−i3i3i30000000000000000
χ582-2-222-2-222-2-1-2-22222-2-2-11111-1-1-111-1-111-1-1-1112i−2i−2i2i00000000−i−iiiii−i−i−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000000000000000
χ592-2-222-2-222-2-1-2-22222-2-2-11111-1-1-111-1-111-1-1-111−2i2i2i−2i00000000ii−i−i−i−iii33−3−3−3−333−i3−i3i3i3i3i3−i3−i30000000000000000
χ602-2-222-2-222-2-1-2-22222-2-2-11111-1-1-111-1-111-1-1-111−2i2i2i−2i00000000ii−i−i−i−iii−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000000000000000
χ612-2-22-222-22-222-22-22-2-222-2-2-2-222-222-22-222-2-2-2200002i−2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ622-2-22-222-22-222-22-22-2-222-2-2-2-222-222-22-222-2-2-220000−2i2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ632-2-22-222-22-22-22-22-222-22-2-222-2-2-222-22-2-2-2222-200000000000000000000000000000000000000002i−2i−2i2i00000000
χ642-2-22-222-22-22-22-22-222-22-2-222-2-2-222-22-2-2-2222-20000000000000000000000000000000000000000−2i2i2i−2i00000000
χ652-2-22-222-22-2-12-22-22-2-22-11111-1-11-1-11-11-1-1111-100002i−2i−2i2i00003−33−3−33−33−ii−iii−ii−ii3−i3i3−i3−i3i3−i3i30000000000000000
χ662-2-22-222-22-2-12-22-22-2-22-11111-1-11-1-11-11-1-1111-100002i−2i−2i2i0000−33−333−33−3−ii−iii−ii−i−i3i3−i3i3i3−i3i3−i30000000000000000
χ672-2-22-222-22-2-12-22-22-2-22-11111-1-11-1-11-11-1-1111-10000−2i2i2i−2i00003−33−3−33−33i−ii−i−ii−ii−i3i3−i3i3i3−i3i3−i30000000000000000
χ682-2-22-222-22-2-12-22-22-2-22-11111-1-11-1-11-11-1-1111-10000−2i2i2i−2i0000−33−333−33−3i−ii−i−ii−iii3−i3i3−i3−i3i3−i3i30000000000000000
χ692-2-22-2-222-2222-2-2-2222-22-2-2-2-222-2-222-222-22-22-20000000000000000000000000000000000002-2-22000000000000
χ702-2-22-2-222-2222-2-2-2222-22-2-2-2-222-2-222-222-22-22-2000000000000000000000000000000000000-222-2000000000000
χ712-2-22-2-222-222-2222-2-2-222-2-222-2-2-2-222-22-22-22-22000000002i−2i−2i2i00000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ722-2-22-2-222-222-2222-2-2-222-2-222-2-2-2-222-22-22-22-2200000000−2i2i2i−2i0000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ732-2-22-2-222-22-1-2222-2-2-22-111-1-11111-1-11-11-11-11-1000000002i−2i−2i2i3−3−33−333−3−i3i3i3−i3i3−i3−i3i3−iii−ii−i−ii0000000000000000
χ742-2-22-2-222-22-1-2222-2-2-22-111-1-11111-1-11-11-11-11-1000000002i−2i−2i2i−333−33−3−33i3−i3−i3i3−i3i3i3−i3−iii−ii−i−ii0000000000000000
χ752-2-22-2-222-22-1-2222-2-2-22-111-1-11111-1-11-11-11-11-100000000−2i2i2i−2i3−3−33−333−3i3−i3−i3i3−i3i3i3−i3i−i−ii−iii−i0000000000000000
χ762-2-22-2-222-22-1-2222-2-2-22-111-1-11111-1-11-11-11-11-100000000−2i2i2i−2i−333−33−3−33−i3i3i3−i3i3−i3−i3i3i−i−ii−iii−i0000000000000000
χ774444444444-2-4-4-4-4-4-4-4-4-2-2-22222-2-2-2-2-2-22222220000000000000000000000000000000000000000000000000000
χ7844444-44-4-4-4-244-444-4-4-4-2-2-2-2-2-2-2-22-2222-222-2220000000000000000000000000000000000000000000000000000
χ794444-44-44-4-4-2-44-4-444-44-2-2-2-2-2-2-22-22-22222-222-20000000000000000000000000000000000000000000000000000
χ804444-4-4-4-444-24-4-44-44-44-2-2-222222222-2-2-22-2-22-20000000000000000000000000000000000000000000000000000
χ814-4-4444-4-4-44-2-4-4-444-444-22222-2-2-2-2222-2222-2-2-20000000000000000000000000000000000000000000000000000
χ824-4-444-4-444-4-244-4-4-4-444-222-2-222-222-2-22-2222-2-20000000000000000000000000000000000000000000000000000
χ834-4-44-444-44-4-2-44-44-444-4-222-2-2222-2-22-2222-2-2-220000000000000000000000000000000000000000000000000000
χ844-4-44-4-444-44-24-4-4-4444-4-22222-2-222-2-22-2-22-22-220000000000000000000000000000000000000000000000000000
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).