Finite Group Databasebeta

← Group #10690191

Character table — Group #10690191

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222244444444444444444444888888888888888888888888888888888824242424242424242424242424242424
order1222222222223666666644444444666612121212121212122244444444666612121212121212121212121212121212121212124444444488888888
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
χ511111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111-1-1-1-111-1-111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111-1-1-1-111-1-111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111-1-1-1-111-1-111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ12111-1-1-1-111-1-111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ13111-1-1-1-111-1-111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-11ii−i−i−i−iii-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ14111-1-1-1-111-1-111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-11ii−i−i−i−iii-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ15111-1-1-1-111-1-111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-11−i−iiiii−i−i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ16111-1-1-1-111-1-111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-11−i−iiiii−i−i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222222222222222222-2-2-2-2222222222222-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222000000002222-2-2-2-200000000000000000000000000000000
χ19222222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000000000
χ21222222222222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ22222222222222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-20000000011111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ23222222222222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-111111111-2-22222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-1-1111111110000000000000000
χ24222222222222-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-111111111-2-2-2-2-2-222221111-1-1-1-111111111-1-1-1-1-1-1-1-10000000000000000
χ25222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112200000000-1-1-1-11111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ26222222222222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112200000000-1-1-1-11111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ2722222222-2-2-2-22222222200002-22-2-2-2-2-2000000000000002-22-200002-22-2000000002-22-22-22-20000000000000000
χ2822222222-2-2-2-22222222200002-22-2-2-2-2-200000000000000-22-2200002-22-200000000-22-22-22-220000000000000000
χ2922222222-2-2-2-2222222220000-22-22-2-2-2-200000000002-22-200000000-22-222-22-22-22-2000000000000000000000000
χ3022222222-2-2-2-2222222220000-22-22-2-2-2-20000000000-22-2200000000-22-22-22-22-22-22000000000000000000000000
χ3122222222-2-2-2-2-1-1-1-1-1-1-1-100002-22-21111−i3−i3i3i3−i3−i3i3i30000002-22-2−i3i3−i3i3-11-11−i3i3i3−i3−i3i3i3−i3-11-11-11-110000000000000000
χ3222222222-2-2-2-2-1-1-1-1-1-1-1-100002-22-21111−i3−i3i3i3−i3−i3i3i3000000-22-22−i3i3−i3i3-11-11i3−i3−i3i3i3−i3−i3i31-11-11-11-10000000000000000
χ3322222222-2-2-2-2-1-1-1-1-1-1-1-100002-22-21111i3i3−i3−i3i3i3−i3−i30000002-22-2i3−i3i3−i3-11-11i3−i3−i3i3i3−i3−i3i3-11-11-11-110000000000000000
χ3422222222-2-2-2-2-1-1-1-1-1-1-1-100002-22-21111i3i3−i3−i3i3i3−i3−i3000000-22-22i3−i3i3−i3-11-11−i3i3i3−i3−i3i3i3−i31-11-11-11-10000000000000000
χ3522222222-2-2-2-2-1-1-1-1-1-1-1-10000-22-221111−i3−i3i3i3−i3−i3i3i3002-22-20000i3−i3i3−i31-11-1-11-11-11-11−i3i3i3−i3−i3i3i3−i30000000000000000
χ3622222222-2-2-2-2-1-1-1-1-1-1-1-10000-22-221111−i3−i3i3i3−i3−i3i3i300-22-220000i3−i3i3−i31-11-11-11-11-11-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ3722222222-2-2-2-2-1-1-1-1-1-1-1-10000-22-221111i3i3−i3−i3i3i3−i3−i3002-22-20000−i3i3−i3i31-11-1-11-11-11-11i3−i3−i3i3i3−i3−i3i30000000000000000
χ3822222222-2-2-2-2-1-1-1-1-1-1-1-10000-22-221111i3i3−i3−i3i3i3−i3−i300-22-220000−i3i3−i3i31-11-11-11-11-11-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ39222-2-2-2-222-2-222222-2-2-2-222-2-2-2-22222-2-22222-2-2-2-2-2200000000-2-222-2-22200000000000000000000000000000000
χ40222-2-2-2-222-2-222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-222222-20000000022-2-2-2-22200000000000000000000000000000000
χ41222-2-2-2-222-2-22-1-1-1-1111122-2-222-2-2-1-111-1-1-1-111112-22i2i−2i−2i2i2i−2i−2i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ42222-2-2-2-222-2-22-1-1-1-1111122-2-222-2-2-1-111-1-1-1-111112-2−2i−2i2i2i−2i−2i2i2i-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ43222-2-2-2-222-2-22-1-1-1-1111122-2-2-2-222-1-111-1-1-1-11111-220000000011-1-111-1-133−3−3−3−33333−3−3−3−3330000000000000000
χ44222-2-2-2-222-2-22-1-1-1-1111122-2-2-2-222-1-111-1-1-1-11111-220000000011-1-111-1-1−3−33333−3−3−3−33333−3−30000000000000000
χ45222-2-2-2-222-2-22-1-1-1-11111-2-22222-2-2-1-1111111-1-1-1-1-222i2i−2i−2i−2i−2i2i2i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ46222-2-2-2-222-2-22-1-1-1-11111-2-22222-2-2-1-1111111-1-1-1-1-22−2i−2i2i2i2i2i−2i−2i11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ47222-2-2-2-222-2-22-1-1-1-11111-2-222-2-222-1-1111111-1-1-1-12-200000000-1-11111-1-133−3−3−3−333−3−33333−3−30000000000000000
χ48222-2-2-2-222-2-22-1-1-1-11111-2-222-2-222-1-1111111-1-1-1-12-200000000-1-11111-1-1−3−33333−3−333−3−3−3−3330000000000000000
χ49222-2-2-2-22-222-22222-2-2-2-200002-2-22-2-222000000000000002i−2i−2i2i00002-2-22000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ50222-2-2-2-22-222-22222-2-2-2-200002-2-22-2-22200000000000000−2i2i2i−2i00002-2-2200000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ51222-2-2-2-22-222-22222-2-2-2-20000-222-2-2-22200000000002i−2i−2i2i00000000-222-22i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ52222-2-2-2-22-222-22222-2-2-2-20000-222-2-2-2220000000000−2i2i2i−2i00000000-222-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ53222-2-2-2-22-222-2-1-1-1-1111100002-2-2211-1-1−i3−i3i3i3i3i3−i3−i30000002i−2i−2i2i−i3i3i3−i3-111-13−3−33−333−3−ii−iii−ii−i0000000000000000
χ54222-2-2-2-22-222-2-1-1-1-1111100002-2-2211-1-1−i3−i3i3i3i3i3−i3−i3000000−2i2i2i−2i−i3i3i3−i3-111-1−333−33−3−33i−ii−i−ii−ii0000000000000000
χ55222-2-2-2-22-222-2-1-1-1-1111100002-2-2211-1-1i3i3−i3−i3−i3−i3i3i30000002i−2i−2i2ii3−i3−i3i3-111-1−333−33−3−33−ii−iii−ii−i0000000000000000
χ56222-2-2-2-22-222-2-1-1-1-1111100002-2-2211-1-1i3i3−i3−i3−i3−i3i3i3000000−2i2i2i−2ii3−i3−i3i3-111-13−3−33−333−3i−ii−i−ii−ii0000000000000000
χ57222-2-2-2-22-222-2-1-1-1-111110000-222-211-1-1−i3−i3i3i3i3i3−i3−i3002i−2i−2i2i0000i3−i3−i3i31-1-11−ii−iii−ii−i3−3−33−333−30000000000000000
χ58222-2-2-2-22-222-2-1-1-1-111110000-222-211-1-1−i3−i3i3i3i3i3−i3−i300−2i2i2i−2i0000i3−i3−i3i31-1-11i−ii−i−ii−ii−333−33−3−330000000000000000
χ59222-2-2-2-22-222-2-1-1-1-111110000-222-211-1-1i3i3−i3−i3−i3−i3i3i3002i−2i−2i2i0000−i3i3i3−i31-1-11−ii−iii−ii−i−333−33−3−330000000000000000
χ60222-2-2-2-22-222-2-1-1-1-111110000-222-211-1-1i3i3−i3−i3−i3−i3i3i300−2i2i2i−2i0000−i3i3i3−i31-1-11i−ii−i−ii−ii3−3−33−333−30000000000000000
χ6122-222-2-2-2-22-2222-2-222-2-22i−2i2i−2i00002-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000−i2i2−i2i22−22−2
χ6222-222-2-2-2-22-2222-2-222-2-22i−2i2i−2i00002-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000i2−i2i2−i2−22−22
χ6322-222-2-2-2-22-2222-2-222-2-2−2i2i−2i2i00002-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000−i2i2−i2i2−22−22
χ6422-222-2-2-2-22-2222-2-222-2-2−2i2i−2i2i00002-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000i2−i2i2−i22−22−2
χ6522-2-2-222-2-2-22222-2-2-2-2222i−2i−2i2i00002-2-222i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000002−2−22i2−i2−i2i2
χ6622-2-2-222-2-2-22222-2-2-2-2222i−2i−2i2i00002-2-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000−222−2−i2i2i2−i2
χ6722-2-2-222-2-2-22222-2-2-2-222−2i2i2i−2i00002-2-22−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000002−2−22−i2i2i2−i2
χ6822-2-2-222-2-2-22222-2-2-2-222−2i2i2i−2i00002-2-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000−222−2i2−i2−i2i2
χ6944-444-4-4-44-44-444-4-444-4-400000000-44-440000000000000000000000000000000000000000000000000000000000
χ7044-444-4-4-44-44-4-2-222-2-222000000002-22-223−23−232323−23−232300000000000000000000000000000000000000000000000000
χ7144-444-4-4-44-44-4-2-222-2-222000000002-22-2−232323−23−232323−2300000000000000000000000000000000000000000000000000
χ7244-444-4-4-4-44-44-2-222-2-2224i−4i4i−4i0000-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ7344-444-4-4-4-44-44-2-222-2-222−4i4i−4i4i0000-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000
χ7444-4-4-444-444-4-444-4-4-4-44400000000-444-40000000000000000000000000000000000000000000000000000000000
χ7544-4-4-444-444-4-4-2-22222-2-2000000002-2-2223−23−2323−232323−2300000000000000000000000000000000000000000000000000
χ7644-4-4-444-444-4-4-2-22222-2-2000000002-2-22−232323−2323−23−232300000000000000000000000000000000000000000000000000
χ7744-4-4-444-4-4-444-2-22222-2-24i−4i−4i4i0000-222-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000000000
χ7844-4-4-444-4-4-444-2-22222-2-2−4i4i4i−4i0000-222-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000000000
χ794-444-44-4-400004-44-44-44-400000000000000000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ804-444-44-4-400004-44-44-44-40000000000000000000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ814-44-44-44-400004-44-4-44-4400000000000000000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ824-44-44-44-400004-44-4-44-440000000000000000000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ834-4-44-4-44400004-4-444-4-440000000000000000000000000000000000000000000000000000002-22-2000000000000
χ844-4-44-4-44400004-4-444-4-44000000000000000000000000000000000000000000000000000000-22-22000000000000
χ854-4-4-444-4400004-4-44-444-40000000000000000000000000000000000000000000000000000002-2-22000000000000
χ864-4-4-444-4400004-4-44-444-4000000000000000000000000000000000000000000000000000000-222-2000000000000
χ878-888-88-8-80000-44-44-44-440000000000000000000000000000000000000000000000000000000000000000000000
χ888-88-88-88-80000-44-444-44-40000000000000000000000000000000000000000000000000000000000000000000000
χ898-8-88-8-8880000-444-4-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ908-8-8-888-880000-444-44-4-440000000000000000000000000000000000000000000000000000000000000000000000

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