Finite Group Databasebeta

← Group #10691205

Character table — Group #10691205

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order122222344446661212121244444444661212121212121212121224668888888812121212121224242424242424242424242424242424888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11-1-1ii−i−iii−i−i11-1-111iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11-1-1ii−i−iii−i−i11-1-111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11-1-1−i−iii−i−iii11-1-111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-11-1-1−i−iii−i−iii11-1-111−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-111111-111ii−i−i−i−iii11-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-111111-111ii−i−i−i−iii11-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-111111-111−i−iiiii−i−i11-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111-1-1-1-1111-1-1-1-111-1-111-1-111-1-1-1-1-1-111111-111−i−iiiii−i−i11-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ17222222222222222222-2-22222-2-2222222222222-2-2-2-200000000-2-2-2-2-2-20000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000-2-2-2-2220000000000000000000000000000
χ192222222-2-2-2-2222-2-2-2-2-2-222-2-22222-2-22222-2-2-2-22-22200000000-2-222-2-20000000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-22222-22-2-200000000-2-222220000000000000000000000000000
χ21222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-11111111111111111000000000000
χ23222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-2-2112222-2-2-2-2-1-1-1-111-1-1-1-1-1-1-1-111111111000000000000
χ24222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-2-211-2-2-2-22222-1-1-1-11111111111-1-1-1-1-1-1-1-1000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-21100000000111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111122-1-1000000001111-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111122-1-1000000001111-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3000000000000
χ29222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-111-1-1-1-11111-22112i2i−2i−2i2i2i−2i−2i-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii000000000000
χ30222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-111-1-1-1-11111-2211−2i−2i2i2i−2i−2i2i2i-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i000000000000
χ31222222-1-2-2-2-2-1-1-1111122-2-222-2-2-1-1111111-1-1-1-12-2-1-12i2i−2i−2i−2i−2i2i2i-1-11111−i−i−i−iiiiiiiii−i−i−i−i000000000000
χ32222222-1-2-2-2-2-1-1-1111122-2-222-2-2-1-1111111-1-1-1-12-2-1-1−2i−2i2i2i2i2i−2i−2i-1-11111iiii−i−i−i−i−i−i−i−iiiii000000000000
χ33222222-1-2-2-2-2-1-1-11111-2-222-2-222-1-111-1-1-1-111112-2-1-10000000011-1-11133−3−3−3−33333−3−3−3−333000000000000
χ34222222-1-2-2-2-2-1-1-11111-2-222-2-222-1-111-1-1-1-111112-2-1-10000000011-1-111−3−33333−3−3−3−33333−3−3000000000000
χ35222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-22110000000011-1-1-1-133−3−3−3−333−3−33333−3−3000000000000
χ36222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-22110000000011-1-1-1-1−3−33333−3−333−3−3−3−333000000000000
χ372222-2-2222-2-2222-2-2-2-22-200002-2-2-22200000000000000002i−2i2i−2i2-22-200000000002i−2i2i−2i2i−2i2i−2i000000000000
χ382222-2-2222-2-2222-2-2-2-22-200002-2-2-2220000000000000000−2i2i−2i2i2-22-20000000000−2i2i−2i2i−2i2i−2i2i000000000000
χ392222-2-2222-2-2222-2-2-2-2-220000-22-2-2220000000000002i−2i2i−2i0000-22-22002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ402222-2-2222-2-2222-2-2-2-2-220000-22-2-222000000000000−2i2i−2i2i0000-22-2200−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ412222-2-22-2-22222222222-20000-22-2-2-2-200000000000000002-2-222-2-2200000000002-22-2-22-22000000000000
χ422222-2-22-2-22222222222-20000-22-2-2-2-20000000000000000-222-22-2-220000000000-22-222-22-2000000000000
χ432222-2-22-2-2222222222-2200002-2-2-2-2-20000000000002-2-220000-222-2002-22-2-22-2200000000000000000000
χ442222-2-22-2-2222222222-2200002-2-2-2-2-2000000000000-222-20000-222-200-22-222-22-200000000000000000000
χ452222-2-2-122-2-2-1-1-111112-200002-211-1-1−i3−i3i3i3−i3−i3i3i300−i3i300002i−2i2i−2i-11-11−i3i33−3−333−3−33−ii−ii−ii−ii000000000000
χ462222-2-2-122-2-2-1-1-111112-200002-211-1-1−i3−i3i3i3−i3−i3i3i300−i3i30000−2i2i−2i2i-11-11−i3i3−333−3−333−3i−ii−ii−ii−i000000000000
χ472222-2-2-122-2-2-1-1-111112-200002-211-1-1i3i3−i3−i3i3i3−i3−i300i3−i300002i−2i2i−2i-11-11i3−i3−333−3−333−3−ii−ii−ii−ii000000000000
χ482222-2-2-122-2-2-1-1-111112-200002-211-1-1i3i3−i3−i3i3i3−i3−i300i3−i30000−2i2i−2i2i-11-11i3−i33−3−333−3−33i−ii−ii−ii−i000000000000
χ492222-2-2-122-2-2-1-1-11111-220000-2211-1-1−i3−i3i3i3−i3−i3i3i300i3−i32i−2i2i−2i00001-11-1i3−i3−ii−ii−ii−ii3−3−333−3−33000000000000
χ502222-2-2-122-2-2-1-1-11111-220000-2211-1-1−i3−i3i3i3−i3−i3i3i300i3−i3−2i2i−2i2i00001-11-1i3−i3i−ii−ii−ii−i−333−3−333−3000000000000
χ512222-2-2-122-2-2-1-1-11111-220000-2211-1-1i3i3−i3−i3i3i3−i3−i300−i3i32i−2i2i−2i00001-11-1−i3i3−ii−ii−ii−ii−333−3−333−3000000000000
χ522222-2-2-122-2-2-1-1-11111-220000-2211-1-1i3i3−i3−i3i3i3−i3−i300−i3i3−2i2i−2i2i00001-11-1−i3i3i−ii−ii−ii−i3−3−333−3−33000000000000
χ532222-2-2-1-2-222-1-1-1-1-1-1-12-20000-221111−i3−i3i3i3i3i3−i3−i300i3−i300002-2-22-111-1−i3i3−i3i3i3−i3i3−i3−i3i3-11-111-11-1000000000000
χ542222-2-2-1-2-222-1-1-1-1-1-1-12-20000-221111−i3−i3i3i3i3i3−i3−i300i3−i30000-222-2-111-1−i3i3i3−i3−i3i3−i3i3i3−i31-11-1-11-11000000000000
χ552222-2-2-1-2-222-1-1-1-1-1-1-12-20000-221111i3i3−i3−i3−i3−i3i3i300−i3i300002-2-22-111-1i3−i3i3−i3−i3i3−i3i3i3−i3-11-111-11-1000000000000
χ562222-2-2-1-2-222-1-1-1-1-1-1-12-20000-221111i3i3−i3−i3−i3−i3i3i300−i3i30000-222-2-111-1i3−i3−i3i3i3−i3i3−i3−i3i31-11-1-11-11000000000000
χ572222-2-2-1-2-222-1-1-1-1-1-1-1-2200002-21111−i3−i3i3i3i3i3−i3−i300−i3i32-2-2200001-1-11i3−i3-11-111-11-1−i3i3i3−i3i3−i3−i3i3000000000000
χ582222-2-2-1-2-222-1-1-1-1-1-1-1-2200002-21111−i3−i3i3i3i3i3−i3−i300−i3i3-222-200001-1-11i3−i31-11-1-11-11i3−i3−i3i3−i3i3i3−i3000000000000
χ592222-2-2-1-2-222-1-1-1-1-1-1-1-2200002-21111i3i3−i3−i3−i3−i3i3i300i3−i32-2-2200001-1-11−i3i3-11-111-11-1i3−i3−i3i3−i3i3i3−i3000000000000
χ602222-2-2-1-2-222-1-1-1-1-1-1-1-2200002-21111i3i3−i3−i3−i3−i3i3i300i3−i3-222-200001-1-11−i3i31-11-1-11-11−i3i3i3−i3i3−i3−i3i3000000000000
χ6122-2-2-2222-22-22-2-222-2-2002i−2i2i−2i002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000−i2i2−i2i22−22−20000
χ6222-2-2-2222-22-22-2-222-2-2002i−2i2i−2i002-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000i2−i2i2−i2−22−220000
χ6322-2-2-2222-22-22-2-222-2-200−2i2i−2i2i002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000−i2i2−i2i2−22−220000
χ6422-2-2-2222-22-22-2-222-2-200−2i2i−2i2i002-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000i2−i2i2−i22−22−20000
χ6522-2-2-222-22-222-2-2-2-222002i−2i−2i2i002-2-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000002−2−22i2−i2−i2i20000
χ6622-2-2-222-22-222-2-2-2-222002i−2i−2i2i002-2-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000−222−2−i2i2i2−i20000
χ6722-2-2-222-22-222-2-2-2-22200−2i2i2i−2i002-2-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000002−2−22−i2i2i2−i20000
χ6822-2-2-222-22-222-2-2-2-22200−2i2i2i−2i002-2-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000−222−2i2−i2−i2i20000
χ6944-4-44-444-4-444-4-4-4-44400000000-444-4000000000000000000000000000000000000000000000000000000
χ7044-4-44-44-444-44-4-444-4-400000000-44-44000000000000000000000000000000000000000000000000000000
χ7144-4-44-4-24-4-44-22222-2-2000000002-2-2223−23−232323−23−23230000000000000000000000000000000000000000000000
χ7244-4-44-4-24-4-44-22222-2-2000000002-2-22−232323−23−232323−230000000000000000000000000000000000000000000000
χ7344-4-44-4-2-444-4-222-2-222000000002-22-223−23−2323−232323−230000000000000000000000000000000000000000000000
χ7444-4-44-4-2-444-4-222-2-222000000002-22-2−232323−2323−23−23230000000000000000000000000000000000000000000000
χ7544-4-4-44-24-44-4-222-2-222004i−4i4i−4i00-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7644-4-4-44-24-44-4-222-2-22200−4i4i−4i4i00-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7744-4-4-44-2-44-44-22222-2-2004i−4i−4i4i00-222-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7844-4-4-44-2-44-44-22222-2-200−4i4i4i−4i00-222-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ798-88-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ808-88-800-400004-4443−4343−43000000000000000000000000000000000000000000000000000000000000000000
χ818-88-800-400004-44−4343−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-4000044-443−43−4343000000000000000000000000000000000000000000000000000000000000000000
χ848-8-8800-4000044-4−434343−43000000000000000000000000000000000000000000000000000000000000000000

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