Finite Group Databasebeta

← Group #10823684

Character table — Group #10823684

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222234444444444446661212121266121212121212121212124444888888881212121212121212242424242424242424242424242424242244444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11-1111-111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-11-1-1-11-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11-1-1-11-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1111-1111-1-1-1-1
χ91111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1
χ101111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111
χ111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ121111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-111-1-1
χ131111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11-11111-1-1-1-1-111
χ141111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-11-1-1-1-111111-1-1
χ151111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11-11-1-11-11111-1-1
χ161111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-111-11-111-11-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-222-2-22222-2-2-2-22-22-20000000022-2-222-2-200000000000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-222-2-22222-2-2-2-2-22-2200000000-2-222-2-22200000000000000000000000000000000
χ192222222-2-2-2-22222-2-2-2-222222222222-2-2-2-2-2-2-2-22-2-220000000022-2-2-2-22200000000000000000000000000000000
χ202222222-2-2-2-22222-2-2-2-222222222222-2-2-2-2-2-2-2-2-222-200000000-2-22222-2-200000000000000000000000000000000
χ21222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ23222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000000000
χ24222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000000000
χ25222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-111112-22-200000000-1-111-1-11133−3−333−3−333−3−333−3−30000000000000000
χ26222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-111112-22-200000000-1-111-1-111−3−333−3−333−3−333−3−3330000000000000000
χ27222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-11111-22-220000000011-1-111-1-133−3−333−3−3−3−333−3−3330000000000000000
χ28222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-11111-22-220000000011-1-111-1-1−3−333−3−33333−3−333−3−30000000000000000
χ29222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-2-2200000000-1-11111-1-133−3−3−3−33333−3−3−3−3330000000000000000
χ30222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111112-2-2200000000-1-11111-1-1−3−33333−3−3−3−33333−3−30000000000000000
χ31222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-222-20000000011-1-1-1-11133−3−3−3−333−3−33333−3−30000000000000000
χ32222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111-222-20000000011-1-1-1-111−3−33333−3−333−3−3−3−3330000000000000000
χ33222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000000000000
χ34222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000000000000
χ35222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-1-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ36222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-1-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ372222-2-2222-2-222-2-222-2-22222222-2-2-2-222-2-222-2-20000000000000000000000000000000000002020-2000-20000000
χ382222-2-2222-2-222-2-222-2-22222222-2-2-2-222-2-222-2-2000000000000000000000000000000000000-20-20200020000000
χ392222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-22222-2-2-2-222000000000000000000000000000000000000020-202000-2000000
χ402222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-22222-2-2-2-2220000000000000000000000000000000000000-2020-20002000000
χ412222-2-22-2-22222-2-2-2-2222222222-2-2-2-2-2-222-2-22200000000000000000000000000000000000002020-2000-2000000
χ422222-2-22-2-22222-2-2-2-2222222222-2-2-2-2-2-222-2-2220000000000000000000000000000000000000-20-2020002000000
χ432222-2-22-2-222-2-22222-2-2222-2-2-2-2-2-222-2-22222-2-200000000000000000000000000000000000020-202000-20000000
χ442222-2-22-2-222-2-22222-2-2222-2-2-2-2-2-222-2-22222-2-2000000000000000000000000000000000000-2020-200020000000
χ452-2-222-222i−2i2i−2i2i−2i2i−2i2-22-2-22-22i2i−2i−2i2-22i−2i2i−2i2i−2i2-22-20000000000000000000000000000000000000000000000002-22i−2i
χ462-2-222-222i−2i2i−2i2i−2i2i−2i2-22-2-22-22i2i−2i−2i2-22i−2i2i−2i2i−2i2-22-2000000000000000000000000000000000000000000000000-22−2i2i
χ472-2-222-222i−2i2i−2i−2i2i−2i2i-22-22-22-2−2i−2i2i2i2-2−2i2i2i−2i2i−2i-22-220000000000000000000000000000000000000000002i−2i002-20000
χ482-2-222-222i−2i2i−2i−2i2i−2i2i-22-22-22-2−2i−2i2i2i2-2−2i2i2i−2i2i−2i-22-22000000000000000000000000000000000000000000−2i2i00-220000
χ492-2-222-22−2i2i−2i2i2i−2i2i−2i-22-22-22-22i2i−2i−2i2-22i−2i−2i2i−2i2i-22-220000000000000000000000000000000000000000002i−2i00-220000
χ502-2-222-22−2i2i−2i2i2i−2i2i−2i-22-22-22-22i2i−2i−2i2-22i−2i−2i2i−2i2i-22-22000000000000000000000000000000000000000000−2i2i002-20000
χ512-2-222-22−2i2i−2i2i−2i2i−2i2i2-22-2-22-2−2i−2i2i2i2-2−2i2i−2i2i−2i2i2-22-20000000000000000000000000000000000000000000000002-2−2i2i
χ522-2-222-22−2i2i−2i2i−2i2i−2i2i2-22-2-22-2−2i−2i2i2i2-2−2i2i−2i2i−2i2i2-22-2000000000000000000000000000000000000000000000000-222i−2i
χ532-2-22-2222i−2i−2i2i2i−2i−2i2i2-2-22-22-22i2i−2i−2i-22−2i2i2i−2i−2i2i2-2-22000000002i−2i2-200000000000000002i−2i2i−2i2-22-20000000000000000
χ542-2-22-2222i−2i−2i2i2i−2i−2i2i2-2-22-22-22i2i−2i−2i-22−2i2i2i−2i−2i2i2-2-2200000000−2i2i-220000000000000000−2i2i−2i2i-22-220000000000000000
χ552-2-22-2222i−2i−2i2i−2i2i2i−2i-222-2-22-2−2i−2i2i2i-222i−2i2i−2i−2i2i-222-200002i−2i2-20000000000002i−2i2i−2i2-22-2000000000000000000000000
χ562-2-22-2222i−2i−2i2i−2i2i2i−2i-222-2-22-2−2i−2i2i2i-222i−2i2i−2i−2i2i-222-20000−2i2i-22000000000000−2i2i−2i2i-22-22000000000000000000000000
χ572-2-22-222−2i2i2i−2i2i−2i−2i2i-222-2-22-22i2i−2i−2i-22−2i2i−2i2i2i−2i-222-200002i−2i-220000000000002i−2i2i−2i-22-22000000000000000000000000
χ582-2-22-222−2i2i2i−2i2i−2i−2i2i-222-2-22-22i2i−2i−2i-22−2i2i−2i2i2i−2i-222-20000−2i2i2-2000000000000−2i2i−2i2i2-22-2000000000000000000000000
χ592-2-22-222−2i2i2i−2i−2i2i2i−2i2-2-22-22-2−2i−2i2i2i-222i−2i−2i2i2i−2i2-2-22000000002i−2i-2200000000000000002i−2i2i−2i-22-220000000000000000
χ602-2-22-222−2i2i2i−2i−2i2i2i−2i2-2-22-22-2−2i−2i2i2i-222i−2i−2i2i2i−2i2-2-2200000000−2i2i2-20000000000000000−2i2i−2i2i2-22-20000000000000000
χ612-2-22-22-12i−2i−2i2i2i−2i−2i2i2-2-221-11−i−iii1-1i−i−iii−i-111-1000000002i−2i2-23−33−3−i3i3−i3i3−i3i3i3−i3−333−3−ii−ii-11-110000000000000000
χ622-2-22-22-12i−2i−2i2i2i−2i−2i2i2-2-221-11−i−iii1-1i−i−iii−i-111-1000000002i−2i2-2−33−33i3−i3i3−i3i3−i3−i3i33−3−33−ii−ii-11-110000000000000000
χ632-2-22-22-12i−2i−2i2i2i−2i−2i2i2-2-221-11−i−iii1-1i−i−iii−i-111-100000000−2i2i-223−33−3−i3i3−i3i3i3−i3−i3i33−3−33i−ii−i1-11-10000000000000000
χ642-2-22-22-12i−2i−2i2i2i−2i−2i2i2-2-221-11−i−iii1-1i−i−iii−i-111-100000000−2i2i-22−33−33i3−i3i3−i3−i3i3i3−i3−333−3i−ii−i1-11-10000000000000000
χ652-2-22-22-12i−2i−2i2i−2i2i2i−2i-222-21-11ii−i−i1-1−ii−iii−i1-1-1100002i−2i2-200003−3−33−i3i3i3−i3−ii−ii-11-11i3−i3−i3i33−3−330000000000000000
χ662-2-22-22-12i−2i−2i2i−2i2i2i−2i-222-21-11ii−i−i1-1−ii−iii−i1-1-1100002i−2i2-20000−333−3i3−i3−i3i3−ii−ii-11-11−i3i3i3−i3−333−30000000000000000
χ672-2-22-22-12i−2i−2i2i−2i2i2i−2i-222-21-11ii−i−i1-1−ii−iii−i1-1-110000−2i2i-2200003−3−33−i3i3i3−i3i−ii−i1-11-1−i3i3i3−i3−333−30000000000000000
χ682-2-22-22-12i−2i−2i2i−2i2i2i−2i-222-21-11ii−i−i1-1−ii−iii−i1-1-110000−2i2i-220000−333−3i3−i3−i3i3i−ii−i1-11-1i3−i3−i3i33−3−330000000000000000
χ692-2-22-22-1−2i2i2i−2i2i−2i−2i2i-222-21-11−i−iii1-1i−ii−i−ii1-1-1100002i−2i-2200003−3−33i3−i3−i3i3−ii−ii1-11-1i3−i3−i3i3−333−30000000000000000
χ702-2-22-22-1−2i2i2i−2i2i−2i−2i2i-222-21-11−i−iii1-1i−ii−i−ii1-1-1100002i−2i-220000−333−3−i3i3i3−i3−ii−ii1-11-1−i3i3i3−i33−3−330000000000000000
χ712-2-22-22-1−2i2i2i−2i2i−2i−2i2i-222-21-11−i−iii1-1i−ii−i−ii1-1-110000−2i2i2-200003−3−33i3−i3−i3i3i−ii−i-11-11−i3i3i3−i33−3−330000000000000000
χ722-2-22-22-1−2i2i2i−2i2i−2i−2i2i-222-21-11−i−iii1-1i−ii−i−ii1-1-110000−2i2i2-20000−333−3−i3i3i3−i3i−ii−i-11-11i3−i3−i3i3−333−30000000000000000
χ732-2-22-22-1−2i2i2i−2i−2i2i2i−2i2-2-221-11ii−i−i1-1−iii−i−ii-111-1000000002i−2i-223−33−3i3−i3i3−i3−i3i3i3−i33−3−33−ii−ii1-11-10000000000000000
χ742-2-22-22-1−2i2i2i−2i−2i2i2i−2i2-2-221-11ii−i−i1-1−iii−i−ii-111-1000000002i−2i-22−33−33−i3i3−i3i3i3−i3−i3i3−333−3−ii−ii1-11-10000000000000000
χ752-2-22-22-1−2i2i2i−2i−2i2i2i−2i2-2-221-11ii−i−i1-1−iii−i−ii-111-100000000−2i2i2-23−33−3i3−i3i3−i3i3−i3−i3i3−333−3i−ii−i-11-110000000000000000
χ762-2-22-22-1−2i2i2i−2i−2i2i2i−2i2-2-221-11ii−i−i1-1−iii−i−ii-111-100000000−2i2i2-2−33−33−i3i3−i3i3−i3i3i3−i33−3−33i−ii−i-11-110000000000000000
χ774444-4-4-244-4-444-4-444-4-4-2-2-2-2-2-2-22222-2-222-2-2220000000000000000000000000000000000000000000000000000
χ784444-4-4-244-4-4-4-444-4-444-2-2-2222222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ794444-4-4-2-4-44444-4-4-4-444-2-2-2-2-2-2-2222222-2-222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-4-2-4-444-4-44444-4-4-2-2-2222222-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ814-4-444-4-24i−4i4i−4i4i−4i4i−4i4-44-42-22−2i−2i2i2i-22−2i2i−2i2i−2i2i-22-220000000000000000000000000000000000000000000000000000
χ824-4-444-4-24i−4i4i−4i−4i4i−4i4i-44-442-222i2i−2i−2i-222i−2i−2i2i−2i2i2-22-20000000000000000000000000000000000000000000000000000
χ834-4-444-4-2−4i4i−4i4i4i−4i4i−4i-44-442-22−2i−2i2i2i-22−2i2i2i−2i2i−2i2-22-20000000000000000000000000000000000000000000000000000
χ844-4-444-4-2−4i4i−4i4i−4i4i−4i4i4-44-42-222i2i−2i−2i-222i−2i2i−2i2i−2i-22-220000000000000000000000000000000000000000000000000000
χ8588-8-8008000000000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-400000000000044-443−4343−430000000000000000000000000000000000000000000000000000000000000000
χ8788-8-800-400000000000044-4−4343−43430000000000000000000000000000000000000000000000000000000000000000
χ888-88-80080000000000008-8-800000000000000000000000000000000000000000000000000000000000000000000
χ898-88-800-4000000000000-444−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ908-88-800-4000000000000-4444i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000000

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