Finite Group Databasebeta

← Group #10823673

Character table — Group #10823673

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order1222223444444444444666121212126612121212121212121212224466668888888812121212242424242424242424242424242424242244444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ511111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-11-1111-111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-11-1-1-11-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11-1-1-11-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1111-1111-1-1-1-1
χ91111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-111-111-11-1-111-1-1
χ101111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-11-1-11-111-1-111
χ111111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-111-1-1-1-1111-1-111
χ121111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-11111-1-1-111-1-1
χ131111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ141111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ151111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1
χ161111111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-22-22-222-2-20000000022-2-200000000000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-2222222-2-2-2-2-2-2-22-22-2-22200000000-2-22200000000000000000000000000000000
χ192222222-2-2-2-22222-2-2-2-2222222222-2-2-2-222-2-2-2-22-2-2222-2-200000000-2-22200000000000000000000000000000000
χ202222222-2-2-2-22222-2-2-2-2222222222-2-2-2-222-2-2-2-2-222-2-2-2220000000022-2-200000000000000000000000000000000
χ21222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111110000000000000000
χ23222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211112222-2-2-2-21111-1-1-1-1-1-1-1-1111111110000000000000000
χ24222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-2-2-2-22222111111111111-1-1-1-1-1-1-1-10000000000000000
χ25222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-22-2-1-11100000000-1-11133−3−333−3−333−3−333−3−30000000000000000
χ26222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-22-2-1-11100000000-1-111−3−333−3−333−3−333−3−3330000000000000000
χ27222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-22-2211-1-10000000011-1-133−3−333−3−3−3−333−3−3330000000000000000
χ28222222-12222-2-2-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-22-2211-1-10000000011-1-1−3−333−3−33333−3−333−3−30000000000000000
χ29222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-111112-2-22-1-1110000000011-1-133−3−3−3−33333−3−3−3−3330000000000000000
χ30222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-111112-2-22-1-1110000000011-1-1−3−33333−3−3−3−33333−3−30000000000000000
χ31222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-11111-222-211-1-100000000-1-11133−3−3−3−333−3−33333−3−30000000000000000
χ32222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-11111-222-211-1-100000000-1-111−3−33333−3−333−3−3−3−3330000000000000000
χ33222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-122-2-2-1-1-1-122-2-222-2-21111-1-1-1-11111-1-1-1-111110000000000000000
χ34222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-122-2-2-1-1-1-1-2-222-2-22211111111-1-1-1-11111-1-1-1-10000000000000000
χ35222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-1-2-222111122-2-2-2-222-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ36222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-1-2-2221111-2-22222-2-2-1-1-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ372222-2-2222-2-222-2-222-2-22222222-2-222-2-2-2-222-2-20000000000000000000000000000000000002020-2000-20000000
χ382222-2-2222-2-222-2-222-2-22222222-2-222-2-2-2-222-2-2000000000000000000000000000000000000-20-20200020000000
χ392222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-222-2-222-2-222000000000000000000000000000000000000020-20-20002000000
χ402222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-222-2-222-2-2220000000000000000000000000000000000000-20202000-2000000
χ412222-2-22-2-22222-2-2-2-2222222222-2-2-2-222-2-2-2-22200000000000000000000000000000000000002020-2000-2000000
χ422222-2-22-2-22222-2-2-2-2222222222-2-2-2-222-2-2-2-2220000000000000000000000000000000000000-20-2020002000000
χ432222-2-22-2-222-2-22222-2-2222-2-2-2-2-2-2-2-2222222-2-200000000000000000000000000000000000020-20-200020000000
χ442222-2-22-2-222-2-22222-2-2222-2-2-2-2-2-2-2-2222222-2-2000000000000000000000000000000000000-20202000-20000000
χ452-22-22-222i−2i2i−2i2i−2i2i−2i2-22-22-2-22i2i−2i−2i2-22i−2i2i−2i2i−2i2-22-20000000000000000000000000000000000000000002-2002i−2i0000
χ462-22-22-222i−2i2i−2i2i−2i2i−2i2-22-22-2-22i2i−2i−2i2-22i−2i2i−2i2i−2i2-22-2000000000000000000000000000000000000000000-2200−2i2i0000
χ472-22-22-222i−2i2i−2i−2i2i−2i2i-22-222-2-2−2i−2i2i2i2-22i−2i2i−2i−2i2i-22-220000000000000000000000000000000000000000000000002-22i−2i
χ482-22-22-222i−2i2i−2i−2i2i−2i2i-22-222-2-2−2i−2i2i2i2-22i−2i2i−2i−2i2i-22-22000000000000000000000000000000000000000000000000-22−2i2i
χ492-22-22-22−2i2i−2i2i2i−2i2i−2i-22-222-2-22i2i−2i−2i2-2−2i2i−2i2i2i−2i-22-220000000000000000000000000000000000000000000000002-2−2i2i
χ502-22-22-22−2i2i−2i2i2i−2i2i−2i-22-222-2-22i2i−2i−2i2-2−2i2i−2i2i2i−2i-22-22000000000000000000000000000000000000000000000000-222i−2i
χ512-22-22-22−2i2i−2i2i−2i2i−2i2i2-22-22-2-2−2i−2i2i2i2-2−2i2i−2i2i−2i2i2-22-20000000000000000000000000000000000000000002-200−2i2i0000
χ522-22-22-22−2i2i−2i2i−2i2i−2i2i2-22-22-2-2−2i−2i2i2i2-2−2i2i−2i2i−2i2i2-22-2000000000000000000000000000000000000000000-22002i−2i0000
χ532-22-2-2222i−2i−2i2i2i−2i−2i2i2-2-222-2-22i2i−2i−2i-222i−2i−2i2i−2i2i2-2-22000000002-22i−2i000000002-22-22i−2i2i−2i000000000000000000000000
χ542-22-2-2222i−2i−2i2i2i−2i−2i2i2-2-222-2-22i2i−2i−2i-222i−2i−2i2i−2i2i2-2-2200000000-22−2i2i00000000-22-22−2i2i−2i2i000000000000000000000000
χ552-22-2-2222i−2i−2i2i−2i2i2i−2i-222-22-2-2−2i−2i2i2i-222i−2i−2i2i2i−2i-222-20000000000002i−2i2-20000000000002i−2i2i−2i2-22-20000000000000000
χ562-22-2-2222i−2i−2i2i−2i2i2i−2i-222-22-2-2−2i−2i2i2i-222i−2i−2i2i2i−2i-222-2000000000000−2i2i-22000000000000−2i2i−2i2i-22-220000000000000000
χ572-22-2-222−2i2i2i−2i2i−2i−2i2i-222-22-2-22i2i−2i−2i-22−2i2i2i−2i−2i2i-222-20000000000002i−2i-220000000000002i−2i2i−2i-22-220000000000000000
χ582-22-2-222−2i2i2i−2i2i−2i−2i2i-222-22-2-22i2i−2i−2i-22−2i2i2i−2i−2i2i-222-2000000000000−2i2i2-2000000000000−2i2i−2i2i2-22-20000000000000000
χ592-22-2-222−2i2i2i−2i−2i2i2i−2i2-2-222-2-2−2i−2i2i2i-22−2i2i2i−2i2i−2i2-2-22000000002-2−2i2i000000002-22-2−2i2i−2i2i000000000000000000000000
χ602-22-2-222−2i2i2i−2i−2i2i2i−2i2-2-222-2-2−2i−2i2i2i-22−2i2i2i−2i2i−2i2-2-2200000000-222i−2i00000000-22-222i−2i2i−2i000000000000000000000000
χ612-22-2-22-12i−2i−2i2i2i−2i−2i2i2-2-22-111−i−iii1-1−iii−ii−i-111-10000−i3i3−i3i32-22i−2i00003−33−3-11-11−ii−ii−i3i3i3−i3−333−30000000000000000
χ622-22-2-22-12i−2i−2i2i2i−2i−2i2i2-2-22-111−i−iii1-1−iii−ii−i-111-10000−i3i3−i3i3-22−2i2i00003−33−31-11-1i−ii−ii3−i3−i3i33−3−330000000000000000
χ632-22-2-22-12i−2i−2i2i2i−2i−2i2i2-2-22-111−i−iii1-1−iii−ii−i-111-10000i3−i3i3−i32-22i−2i0000−33−33-11-11−ii−iii3−i3−i3i33−3−330000000000000000
χ642-22-2-22-12i−2i−2i2i2i−2i−2i2i2-2-22-111−i−iii1-1−iii−ii−i-111-10000i3−i3i3−i3-22−2i2i0000−33−331-11-1i−ii−i−i3i3i3−i3−333−30000000000000000
χ652-22-2-22-12i−2i−2i2i−2i2i2i−2i-222-2-111ii−i−i1-1−iii−i−ii1-1-110000−i3i3i3−i300002i−2i2-23−3−333−3−33i3−i3−i3i3−ii−ii-11-110000000000000000
χ662-22-2-22-12i−2i−2i2i−2i2i2i−2i-222-2-111ii−i−i1-1−iii−i−ii1-1-110000−i3i3i3−i30000−2i2i-223−3−33−333−3−i3i3i3−i3i−ii−i1-11-10000000000000000
χ672-22-2-22-12i−2i−2i2i−2i2i2i−2i-222-2-111ii−i−i1-1−iii−i−ii1-1-110000i3−i3−i3i300002i−2i2-2−333−3−333−3−i3i3i3−i3−ii−ii-11-110000000000000000
χ682-22-2-22-12i−2i−2i2i−2i2i2i−2i-222-2-111ii−i−i1-1−iii−i−ii1-1-110000i3−i3−i3i30000−2i2i-22−333−33−3−33i3−i3−i3i3i−ii−i1-11-10000000000000000
χ692-22-2-22-1−2i2i2i−2i2i−2i−2i2i-222-2-111−i−iii1-1i−i−iii−i1-1-110000−i3i3i3−i300002i−2i-22−333−33−3−33−i3i3i3−i3−ii−ii1-11-10000000000000000
χ702-22-2-22-1−2i2i2i−2i2i−2i−2i2i-222-2-111−i−iii1-1i−i−iii−i1-1-110000−i3i3i3−i30000−2i2i2-2−333−3−333−3i3−i3−i3i3i−ii−i-11-110000000000000000
χ712-22-2-22-1−2i2i2i−2i2i−2i−2i2i-222-2-111−i−iii1-1i−i−iii−i1-1-110000i3−i3−i3i300002i−2i-223−3−33−333−3i3−i3−i3i3−ii−ii1-11-10000000000000000
χ722-22-2-22-1−2i2i2i−2i2i−2i−2i2i-222-2-111−i−iii1-1i−i−iii−i1-1-110000i3−i3−i3i30000−2i2i2-23−3−333−3−33−i3i3i3−i3i−ii−i-11-110000000000000000
χ732-22-2-22-1−2i2i2i−2i−2i2i2i−2i2-2-22-111ii−i−i1-1i−i−ii−ii-111-10000−i3i3−i3i32-2−2i2i0000−33−33-11-11i−ii−i−i3i3i3−i33−3−330000000000000000
χ742-22-2-22-1−2i2i2i−2i−2i2i2i−2i2-2-22-111ii−i−i1-1i−i−ii−ii-111-10000−i3i3−i3i3-222i−2i0000−33−331-11-1−ii−iii3−i3−i3i3−333−30000000000000000
χ752-22-2-22-1−2i2i2i−2i−2i2i2i−2i2-2-22-111ii−i−i1-1i−i−ii−ii-111-10000i3−i3i3−i32-2−2i2i00003−33−3-11-11i−ii−ii3−i3−i3i3−333−30000000000000000
χ762-22-2-22-1−2i2i2i−2i−2i2i2i−2i2-2-22-111ii−i−i1-1i−i−ii−ii-111-10000i3−i3i3−i3-222i−2i00003−33−31-11-1−ii−ii−i3i3i3−i33−3−330000000000000000
χ774444-4-4-244-4-444-4-444-4-4-2-2-2-2-2-2-222-2-22222-2-2220000000000000000000000000000000000000000000000000000
χ784444-4-4-244-4-4-4-444-4-444-2-2-2222222-2-222-2-222-2-20000000000000000000000000000000000000000000000000000
χ794444-4-4-2-4-44444-4-4-4-444-2-2-2-2-2-2-22222-2-22222-2-20000000000000000000000000000000000000000000000000000
χ804444-4-4-2-4-444-4-44444-4-4-2-2-222222222-2-2-2-2-2-2220000000000000000000000000000000000000000000000000000
χ814-44-44-4-24i−4i4i−4i4i−4i4i−4i4-44-4-222−2i−2i2i2i-22−2i2i−2i2i−2i2i-22-220000000000000000000000000000000000000000000000000000
χ824-44-44-4-24i−4i4i−4i−4i4i−4i4i-44-44-2222i2i−2i−2i-22−2i2i−2i2i2i−2i2-22-20000000000000000000000000000000000000000000000000000
χ834-44-44-4-2−4i4i−4i4i4i−4i4i−4i-44-44-222−2i−2i2i2i-222i−2i2i−2i−2i2i2-22-20000000000000000000000000000000000000000000000000000
χ844-44-44-4-2−4i4i−4i4i−4i4i−4i4i4-44-4-2222i2i−2i−2i-222i−2i2i−2i2i−2i-22-220000000000000000000000000000000000000000000000000000
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).