Finite Group Databasebeta

← Group #10836677

Character table — Group #10836677

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888888888888888881212121224242424242448484848
order122222344444466612121212444444466121212121212121212122444446688881212121212121212121212121212242424242424242488888888884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-11-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1
χ61111111111111111111111-1-11-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1
χ91111111-1-11111111-1-1-1-1-1-111-11111-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-11-11-1
χ101111111-1-11111111-1-1-1-1-1-111-11111-1-111-1-1-1-111-1-111-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-111-11-1-111-11-11
χ111111111-1-11111111-1-1-1-1-1-111-11111-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-11-111-1-1-11-11
χ121111111-1-11111111-1-1-1-1-1-111-11111-1-111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-111-11-1-1111-11-1
χ131111111-1-11111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-1-1111-1-11
χ141111111-1-11111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1111-1-1-111-1
χ151111111-1-11111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11-1-1-111-111-1
χ161111111-1-11111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1111-1-11-1-11
χ17222222222-2-2-2-22222222-2-2002002222-2-2-2-2-2-2-2-200000000000000000000000000000000000000002i−2i2i−2i0000
χ18222222222-2-2-2-22222222-2-2002002222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000−2i2i−2i2i0000
χ192222222-2-2-2-2-2-2222-2-2-2-22200-20022-2-2-2-22222-2-200000000000000000000000000000000000000002i−2i−2i2i0000
χ202222222-2-2-2-2-2-2222-2-2-2-22200-20022-2-2-2-22222-2-20000000000000000000000000000000000000000−2i2i2i−2i0000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-2-2-2-2-1-1-1-1-1-1111111111111111100000000000000
χ23222222-1222222-1-1-1-1-1-1-122-2-22-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2222211-2-2-2-2111111-1-1-1-1-1-1-1-11111111100000000000000
χ24222222-1222222-1-1-1-1-1-1-122-2-22-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211222211111111111111-1-1-1-1-1-1-1-100000000000000
χ25222222-1-2-22222-1-1-11111-2-222-222-1-111-1-11111-1-1-2-222-2-21122-2-2-1-1-1-111-1-1-1-11111-1-1-1-1111100000000000000
χ26222222-1-2-22222-1-1-11111-2-222-222-1-111-1-11111-1-1-2-2-2-22211-2-222-1-1-1-1111111-1-1-1-11111-1-1-1-100000000000000
χ27222222-1-2-22222-1-1-11111-2-2-2-2-2-2-2-1-111-1-11111-1-12222-2-2-1-1-2-2221111-1-1-1-1-1-111111111-1-1-1-100000000000000
χ28222222-1-2-22222-1-1-11111-2-2-2-2-2-2-2-1-111-1-11111-1-122-2-222-1-122-2-21111-1-11111-1-1-1-1-1-1-1-1111100000000000000
χ292222-2-22222-2-2222222222-222-2-2-2-2-2-2-2-2-222-2-222-220000-2-20000-2-22222000000000000000000000000000000
χ302222-2-22222-2-2222222222-2-2-2-222-2-2-2-2-2-222-2-2222-2000022000022-2-2-2-2000000000000000000000000000000
χ312222-2-2222-222-22222222-2200-200-2-2-2-222-2-222-2-200000000000000000000000000000000002222-2-200000000
χ322222-2-2222-222-22222222-2200-200-2-2-2-222-2-222-2-20000000000000000000000000000000000-2-2-2-22200000000
χ332222-2-22-2-22-2-22222-2-2-2-2-22222-2-2-2-222-2-2-2-222222-20000220000-2-222-2-2000000000000000000000000000000
χ342222-2-22-2-22-2-22222-2-2-2-2-22-2-2222-2-222-2-2-2-22222-220000-2-2000022-2-222000000000000000000000000000000
χ352222-2-22-2-2-222-2222-2-2-2-22-200200-2-2222222-2-2-2-2000000000000000000000000000000000022-2-2-2200000000
χ362222-2-22-2-2-222-2222-2-2-2-22-200200-2-2222222-2-2-2-20000000000000000000000000000000000-2-2222-200000000
χ372222-2-2-1222-2-22-1-1-1-1-1-1-12-222-2-2-2111111-1-111-1-1-22000011000011-1-1-1-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000
χ382222-2-2-1222-2-22-1-1-1-1-1-1-12-222-2-2-2111111-1-111-1-1-22000011000011-1-1-1-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000
χ392222-2-2-1222-2-22-1-1-1-1-1-1-12-2-2-2-222111111-1-111-1-12-20000-1-10000-1-11111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000
χ402222-2-2-1222-2-22-1-1-1-1-1-1-12-2-2-2-222111111-1-111-1-12-20000-1-10000-1-11111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000
χ412222-2-2-1-2-22-2-22-1-1-11111-22222-2-211-1-11111-1-1-1-12-20000-1-1000011-1-111−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000
χ422222-2-2-1-2-22-2-22-1-1-11111-22222-2-211-1-11111-1-1-1-12-20000-1-1000011-1-111i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000
χ432222-2-2-1-2-22-2-22-1-1-11111-22-2-222211-1-11111-1-1-1-1-220000110000-1-111-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000
χ442222-2-2-1-2-22-2-22-1-1-11111-22-2-222211-1-11111-1-1-1-1-220000110000-1-111-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000
χ4522-2-22-2200-22-22-22-20000002i−2i02i−2i2-2002-200002-200002i−2i00002-22i−2i2i−2i0000002i−2i2i−2i00002-22-200000000000000
χ4622-2-22-2200-22-22-22-20000002i−2i02i−2i2-2002-200002-20000−2i2i0000-222i−2i2i−2i000000−2i2i−2i2i0000-22-2200000000000000
χ4722-2-22-2200-22-22-22-2000000−2i2i0−2i2i2-2002-200002-200002i−2i0000-22−2i2i−2i2i0000002i−2i2i−2i0000-22-2200000000000000
χ4822-2-22-2200-22-22-22-2000000−2i2i0−2i2i2-2002-200002-20000−2i2i00002-2−2i2i−2i2i000000−2i2i−2i2i00002-22-200000000000000
χ4922-2-22-2-100-22-221-1133−3−3002i−2i02i−2i-113−3-113−33−3-1100002i−2i−i3i3002-2−ii−ii−i3i3−i3i3−i3i3−ii−ii3−33−3-11-1100000000000000
χ5022-2-22-2-100-22-221-1133−3−3002i−2i02i−2i-113−3-113−33−3-110000−2i2i−i3i300-22−ii−ii−i3i3i3−i3i3−i3i−ii−i−33−331-11-100000000000000
χ5122-2-22-2-100-22-221-1133−3−300−2i2i0−2i2i-113−3-113−33−3-1100002i−2ii3−i300-22i−ii−ii3−i3−i3i3−i3i3−ii−ii−33−331-11-100000000000000
χ5222-2-22-2-100-22-221-1133−3−300−2i2i0−2i2i-113−3-113−33−3-110000−2i2ii3−i3002-2i−ii−ii3−i3i3−i3i3−i3i−ii−i3−33−3-11-1100000000000000
χ5322-2-22-2-100-22-221-11−3−333002i−2i02i−2i-11−33-11−33−33-1100002i−2ii3−i3002-2−ii−iii3−i3i3−i3i3−i3−ii−ii−33−33-11-1100000000000000
χ5422-2-22-2-100-22-221-11−3−333002i−2i02i−2i-11−33-11−33−33-110000−2i2ii3−i300-22−ii−iii3−i3−i3i3−i3i3i−ii−i3−33−31-11-100000000000000
χ5522-2-22-2-100-22-221-11−3−33300−2i2i0−2i2i-11−33-11−33−33-1100002i−2i−i3i300-22i−ii−i−i3i3i3−i3i3−i3−ii−ii3−33−31-11-100000000000000
χ5622-2-22-2-100-22-221-11−3−33300−2i2i0−2i2i-11−33-11−33−33-110000−2i2i−i3i3002-2i−ii−i−i3i3−i3i3−i3i3i−ii−i−33−33-11-1100000000000000
χ5722-2-2-22200-2-222-22-20000002i−2i0−2i2i-2200-2200002-2002-200002i−2i00−2i2i2i−2i002-2-2200002i−2i−2i2i000000000000000000
χ5822-2-2-22200-2-222-22-20000002i−2i0−2i2i-2200-2200002-200-220000−2i2i00−2i2i2i−2i00-222-20000−2i2i2i−2i000000000000000000
χ5922-2-2-22200-2-222-22-2000000−2i2i02i−2i-2200-2200002-2002-20000−2i2i002i−2i−2i2i002-2-220000−2i2i2i−2i000000000000000000
χ6022-2-2-22200-2-222-22-2000000−2i2i02i−2i-2200-2200002-200-2200002i−2i002i−2i−2i2i00-222-200002i−2i−2i2i000000000000000000
χ6122-2-2-22-100-2-2221-1133−3−3002i−2i0−2i2i1-1−331-13−3−33-11002-200i3−i32i−2i00i−i−ii−i3i3-111-13−3−33−iii−i−i3i3i3−i300000000000000
χ6222-2-2-22-100-2-2221-1133−3−3002i−2i0−2i2i1-1−331-13−3−33-1100-2200i3−i3−2i2i00i−i−ii−i3i31-1-11−333−3i−i−iii3−i3−i3i300000000000000
χ6322-2-2-22-100-2-2221-1133−3−300−2i2i02i−2i1-1−331-13−3−33-11002-200−i3i3−2i2i00−iii−ii3−i3-111-13−3−33i−i−iii3−i3−i3i300000000000000
χ6422-2-2-22-100-2-2221-1133−3−300−2i2i02i−2i1-1−331-13−3−33-1100-2200−i3i32i−2i00−iii−ii3−i31-1-11−333−3−iii−i−i3i3i3−i300000000000000
χ6522-2-2-22-100-2-2221-11−3−333002i−2i0−2i2i1-13−31-1−333−3-11002-200−i3i32i−2i00i−i−iii3−i3-111-1−333−3−iii−ii3−i3−i3i300000000000000
χ6622-2-2-22-100-2-2221-11−3−333002i−2i0−2i2i1-13−31-1−333−3-1100-2200−i3i3−2i2i00i−i−iii3−i31-1-113−3−33i−i−ii−i3i3i3−i300000000000000
χ6722-2-2-22-100-2-2221-11−3−33300−2i2i02i−2i1-13−31-1−333−3-11002-200i3−i3−2i2i00−iii−i−i3i3-111-1−333−3i−i−ii−i3i3i3−i300000000000000
χ6822-2-2-22-100-2-2221-11−3−33300−2i2i02i−2i1-13−31-1−333−3-1100-2200i3−i32i−2i00−iii−i−i3i31-1-113−3−33−iii−ii3−i3−i3i300000000000000
χ69444444-244-4-4-4-4-2-2-2-2-2-2-2-4-400400-2-2-2-222222222000000000000000000000000000000000000000000000000
χ70444444-2-4-4-4-4-4-4-2-2-222224400-400-2-22222-2-2-2-222000000000000000000000000000000000000000000000000
χ714444-4-4-244-444-4-2-2-2-2-2-2-2-4400-4002222-2-222-2-222000000000000000000000000000000000000000000000000
χ724444-4-4-2-4-4-444-4-2-2-222224-40040022-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ7344-4-44-44004-44-4-44-4000000000004-400-440000-44000000000000000000000000000000000000000000000000
χ7444-4-44-4-2004-44-42-222323−23−230000000-2223−232-2−2323−23232-2000000000000000000000000000000000000000000000000
χ7544-4-44-4-2004-44-42-22−23−2323230000000-22−23232-223−2323−232-2000000000000000000000000000000000000000000000000
χ7644-4-4-4440044-4-4-44-400000000000-44004-40000-44000000000000000000000000000000000000000000000000
χ7744-4-4-44-20044-4-42-222323−23−2300000002-2−2323-22−232323−232-2000000000000000000000000000000000000000000000000
χ7844-4-4-44-20044-4-42-22−23−23232300000002-223−23-2223−23−23232-2000000000000000000000000000000000000000000000000
χ794-4-440044-400004-4-44-44-400000000000000000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ804-4-440044-400004-4-44-44-4000000000000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ814-4-44004-4400004-4-4-44-4400000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ824-4-44004-4400004-4-4-44-44000000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ838-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000
χ848-88-800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000
χ858-88-800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000
χ868-8-8800-48-80000-444-44-440000000000000000000000000000000000000000000000000000000000000000000
χ878-8-8800-4-880000-4444-44-40000000000000000000000000000000000000000000000000000000000000000000

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