Finite Group Databasebeta

← Group #10824924

Character table — Group #10824924

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222234444444444446661212121266121212121212121212122224444466666688881212121212121212121224242424242424244444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111111111-1-1111-1-11-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111-1-1111-1-11-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111111-11-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111111-11-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ111111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-11111-11-1-1-111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ121111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-11111-11-1-1-111111-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ131111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-11-1111-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ141111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-11-1111-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ151111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-1-11-1111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111111-1-1-1-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-111-1-1-11-1111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-222-2-22222-2-2-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-222-2-22222-2-2-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ192222222-2-2-2-22222-2-2-2-2222222222-2-2-2-2-2-222-2-20000000000000000000000000000000000000000000000002i−2i−2i2i
χ202222222-2-2-2-22222-2-2-2-2222222222-2-2-2-2-2-222-2-2000000000000000000000000000000000000000000000000−2i2i2i−2i
χ21222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-222-2-1-1-1-111-2-2-2-21111-1-1-1-111111111110000000000000000
χ23222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2222-2-221111-1-1-2-2-2-2-1-1-1-11111-1-1111111110000000000000000
χ24222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111122221111111111-1-1-1-1-1-1-1-10000000000000000
χ25222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1-1-1111111-1-1222-22-2-2-2-1-1-1-1-1-122-2-2-1-111111111-1-1-1-111110000000000000000
χ26222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1-1-1111111-1-122-22-2-2-22-1-1-1-111-2-22211-1-11111-1-11111-1-1-1-10000000000000000
χ27222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1-1-1111111-1-1-2-22-2222-21111-1-1-2-222-1-111-1-1-1-1111111-1-1-1-10000000000000000
χ28222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1-1-1111111-1-1-2-2-22-222211111122-2-211-1-1-1-1-1-1-1-1-1-1-1-111110000000000000000
χ292222-2-2222-2-222-2-222-2-22222222-2-2-2-222-2-2-2-222002-2-20020000220000-2-2-2-2000022000000000000000000000000
χ302222-2-2222-2-222-2-222-2-22222222-2-2-2-222-2-2-2-22200-22200-20000-2-2000022220000-2-2000000000000000000000000
χ312222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-22222-2-222-2-2000000000000000000000000000000000000000000002-22-20000
χ322222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-22222-2-222-2-200000000000000000000000000000000000000000000-22-220000
χ332222-2-22-2-22222-2-2-2-2222222222-2-222-2-222-2-2-2-2000000000000000000000000000000000000000000002-2-220000
χ342222-2-22-2-22222-2-2-2-2222222222-2-222-2-222-2-2-2-200000000000000000000000000000000000000000000-222-20000
χ352222-2-22-2-222-2-22222-2-2222-2-2-2-2-2-2-2-2-2-22222220022-200-20000220000-2-2220000-2-2000000000000000000000000
χ362222-2-22-2-222-2-22222-2-2222-2-2-2-2-2-2-2-2-2-222222200-2-220020000-2-2000022-2-2000022000000000000000000000000
χ372222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-11111-1-1002-2-2002−i3−i3i3i3-1-100001111−i3−i3i3i3-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ382222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-11111-1-1002-2-2002i3i3−i3−i3-1-100001111i3i3−i3−i3-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ392222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-11111-1-100-22200-2−i3−i3i3i3110000-1-1-1-1−i3−i3i3i311i3i3−i3−i3i3i3−i3−i30000000000000000
χ402222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-11111-1-100-22200-2i3i3−i3−i3110000-1-1-1-1i3i3−i3−i311−i3−i3i3i3−i3−i3i3i30000000000000000
χ412222-2-2-1-2-222-2-22222-2-2-1-1-11111111111-1-1-1-1-1-10022-200-2−i3−i3i3i3-1-1000011-1-1i3i3−i3−i311−i3−i3i3i3i3i3−i3−i30000000000000000
χ422222-2-2-1-2-222-2-22222-2-2-1-1-11111111111-1-1-1-1-1-10022-200-2i3i3−i3−i3-1-1000011-1-1−i3−i3i3i311i3i3−i3−i3−i3−i3i3i30000000000000000
χ432222-2-2-1-2-222-2-22222-2-2-1-1-11111111111-1-1-1-1-1-100-2-22002−i3−i3i3i3110000-1-111i3i3−i3−i3-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ442222-2-2-1-2-222-2-22222-2-2-1-1-11111111111-1-1-1-1-1-100-2-22002i3i3−i3−i3110000-1-111−i3−i3i3i3-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ452-22-22-222i−2i2i−2i2i−2i2i−2i2-22-22-2-22i2i−2i−2i2-22-22i−2i2i−2i2i−2i2-200000000000000000000000000000000000000002-22i−2i00000000
χ462-22-22-222i−2i2i−2i2i−2i2i−2i2-22-22-2-22i2i−2i−2i2-22-22i−2i2i−2i2i−2i2-20000000000000000000000000000000000000000-22−2i2i00000000
χ472-22-22-222i−2i2i−2i−2i2i−2i2i-22-222-2-2−2i−2i2i2i2-2-222i−2i2i−2i−2i2i-222-20002i−2i02-22-200000000002i−2i2i−2i00000000000000000000000000
χ482-22-22-222i−2i2i−2i−2i2i−2i2i-22-222-2-2−2i−2i2i2i2-2-222i−2i2i−2i−2i2i-22-22000−2i2i0-22-220000000000−2i2i−2i2i00000000000000000000000000
χ492-22-22-22−2i2i−2i2i2i−2i2i−2i-22-222-2-22i2i−2i−2i2-2-22−2i2i−2i2i2i−2i-222-2000−2i2i02-22-20000000000−2i2i−2i2i00000000000000000000000000
χ502-22-22-22−2i2i−2i2i2i−2i2i−2i-22-222-2-22i2i−2i−2i2-2-22−2i2i−2i2i2i−2i-22-220002i−2i0-22-2200000000002i−2i2i−2i00000000000000000000000000
χ512-22-22-22−2i2i−2i2i−2i2i−2i2i2-22-22-2-2−2i−2i2i2i2-22-2−2i2i−2i2i−2i2i2-200000000000000000000000000000000000000002-2−2i2i00000000
χ522-22-22-22−2i2i−2i2i−2i2i−2i2i2-22-22-2-2−2i−2i2i2i2-22-2−2i2i−2i2i−2i2i2-20000000000000000000000000000000000000000-222i−2i00000000
χ532-22-22-2-12i−2i2i−2i−2i2i−2i2i-22-22-111ii−i−i-111-1−ii−iii−i1-12-20002i−2i0-11-11−i3i30000−i3i33−3−ii−ii3−3−i3i3−i3i33−33−30000000000000000
χ542-22-22-2-12i−2i2i−2i−2i2i−2i2i-22-22-111ii−i−i-111-1−ii−iii−i1-12-20002i−2i0-11-11i3−i30000i3−i3−33−ii−ii−33i3−i3i3−i3−33−330000000000000000
χ552-22-22-2-12i−2i2i−2i−2i2i−2i2i-22-22-111ii−i−i-111-1−ii−iii−i1-1-22000−2i2i01-11-1−i3i30000−i3i33−3i−ii−i3−3i3−i3i3−i3−33−330000000000000000
χ562-22-22-2-12i−2i2i−2i−2i2i−2i2i-22-22-111ii−i−i-111-1−ii−iii−i1-1-22000−2i2i01-11-1i3−i30000i3−i3−33i−ii−i−33−i3i3−i3i33−33−30000000000000000
χ572-22-22-2-1−2i2i−2i2i2i−2i2i−2i-22-22-111−i−iii-111-1i−ii−i−ii1-12-2000−2i2i0-11-11−i3i30000−i3i3−33i−ii−i−33−i3i3−i3i3−33−330000000000000000
χ582-22-22-2-1−2i2i−2i2i2i−2i2i−2i-22-22-111−i−iii-111-1i−ii−i−ii1-12-2000−2i2i0-11-11i3−i30000i3−i33−3i−ii−i3−3i3−i3i3−i33−33−30000000000000000
χ592-22-22-2-1−2i2i−2i2i2i−2i2i−2i-22-22-111−i−iii-111-1i−ii−i−ii1-1-220002i−2i01-11-1−i3i30000−i3i3−33−ii−ii−33i3−i3i3−i33−33−30000000000000000
χ602-22-22-2-1−2i2i−2i2i2i−2i2i−2i-22-22-111−i−iii-111-1i−ii−i−ii1-1-220002i−2i01-11-1i3−i30000i3−i33−3−ii−ii3−3−i3i3−i3i3−33−330000000000000000
χ612-22-2-2222i−2i−2i2i2i−2i−2i2i2-2-222-2-22i2i−2i−2i-22-222i−2i−2i2i−2i2i2-20000000000000000000000000000000000002-22i−2i000000000000
χ622-22-2-2222i−2i−2i2i2i−2i−2i2i2-2-222-2-22i2i−2i−2i-22-222i−2i−2i2i−2i2i2-2000000000000000000000000000000000000-22−2i2i000000000000
χ632-22-2-2222i−2i−2i2i−2i2i2i−2i-222-22-2-2−2i−2i2i2i-222-22i−2i−2i2i2i−2i-22000000000000002-22i−2i00000000002-2-222i−2i−2i2i0000000000000000
χ642-22-2-2222i−2i−2i2i−2i2i2i−2i-222-22-2-2−2i−2i2i2i-222-22i−2i−2i2i2i−2i-2200000000000000-22−2i2i0000000000-222-2−2i2i2i−2i0000000000000000
χ652-22-2-222−2i2i2i−2i2i−2i−2i2i-222-22-2-22i2i−2i−2i-222-2−2i2i2i−2i−2i2i-22000000000000002-2−2i2i00000000002-2-22−2i2i2i−2i0000000000000000
χ662-22-2-222−2i2i2i−2i2i−2i−2i2i-222-22-2-22i2i−2i−2i-222-2−2i2i2i−2i−2i2i-2200000000000000-222i−2i0000000000-222-22i−2i−2i2i0000000000000000
χ672-22-2-222−2i2i2i−2i−2i2i2i−2i2-2-222-2-2−2i−2i2i2i-22-22−2i2i2i−2i2i−2i2-20000000000000000000000000000000000002-2−2i2i000000000000
χ682-22-2-222−2i2i2i−2i−2i2i2i−2i2-2-222-2-2−2i−2i2i2i-22-22−2i2i2i−2i2i−2i2-2000000000000000000000000000000000000-222i−2i000000000000
χ692-22-2-22-12i−2i−2i2i−2i2i2i−2i-222-2-111ii−i−i1-1-11−iii−i−ii1-100000000−i3i3i3−i3−i3i32-22i−2ii3−i3−333−3−333−3-111-1−iii−i0000000000000000
χ702-22-2-22-12i−2i−2i2i−2i2i2i−2i-222-2-111ii−i−i1-1-11−iii−i−ii1-100000000−i3i3i3−i3i3−i3-22−2i2i−i3i33−33−3−33−331-1-11i−i−ii0000000000000000
χ712-22-2-22-12i−2i−2i2i−2i2i2i−2i-222-2-111ii−i−i1-1-11−iii−i−ii1-100000000i3−i3−i3i3−i3i3-22−2i2ii3−i3−33−333−33−31-1-11i−i−ii0000000000000000
χ722-22-2-22-12i−2i−2i2i−2i2i2i−2i-222-2-111ii−i−i1-1-11−iii−i−ii1-100000000i3−i3−i3i3i3−i32-22i−2i−i3i33−3−333−3−33-111-1−iii−i0000000000000000
χ732-22-2-22-1−2i2i2i−2i2i−2i−2i2i-222-2-111−i−iii1-1-11i−i−iii−i1-100000000−i3i3i3−i3−i3i32-2−2i2ii3−i33−3−333−3−33-111-1i−i−ii0000000000000000
χ742-22-2-22-1−2i2i2i−2i2i−2i−2i2i-222-2-111−i−iii1-1-11i−i−iii−i1-100000000−i3i3i3−i3i3−i3-222i−2i−i3i3−33−333−33−31-1-11−iii−i0000000000000000
χ752-22-2-22-1−2i2i2i−2i2i−2i−2i2i-222-2-111−i−iii1-1-11i−i−iii−i1-100000000i3−i3−i3i3−i3i3-222i−2ii3−i33−33−3−33−331-1-11−iii−i0000000000000000
χ762-22-2-22-1−2i2i2i−2i2i−2i−2i2i-222-2-111−i−iii1-1-11i−i−iii−i1-100000000i3−i3−i3i3i3−i32-2−2i2i−i3i3−333−3−333−3-111-1i−i−ii0000000000000000
χ77444444-24444-4-4-4-4-4-4-4-4-2-2-22222-2-222-2-2-2-222220000000000000000000000000000000000000000000000000000
χ78444444-2-4-4-4-44444-4-4-4-4-2-2-2-2-2-2-2-2-2222222-2-2220000000000000000000000000000000000000000000000000000
χ794444-4-4-244-4-4-4-444-4-444-2-2-2222222-2-2-2-222-2-2220000000000000000000000000000000000000000000000000000
χ804444-4-4-2-4-44444-4-4-4-444-2-2-2-2-2-2-222-2-222-2-222220000000000000000000000000000000000000000000000000000
χ814-44-44-4-24i−4i4i−4i4i−4i4i−4i4-44-4-222−2i−2i2i2i-22-22−2i2i−2i2i−2i2i-220000000000000000000000000000000000000000000000000000
χ824-44-44-4-2−4i4i−4i4i−4i4i−4i4i4-44-4-2222i2i−2i−2i-22-222i−2i2i−2i2i−2i-220000000000000000000000000000000000000000000000000000
χ834-44-4-44-24i−4i−4i4i4i−4i−4i4i4-4-44-222−2i−2i2i2i2-22-2−2i2i2i−2i2i−2i-220000000000000000000000000000000000000000000000000000
χ844-44-4-44-2−4i4i4i−4i−4i4i4i−4i4-4-44-2222i2i−2i−2i2-22-22i−2i−2i2i−2i2i-220000000000000000000000000000000000000000000000000000
χ8588-8-8008000000000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-40000000000004-4443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-40000000000004-44−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-8-88008000000000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-8800-400000000000044-4−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ908-8-8800-400000000000044-44i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000000

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