Finite Group Databasebeta

← Group #10828063

Character table — Group #10828063

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222222222444444444444444444488888888888888888888888888888888882424242424242424242424244848
order1222222234444666666622244446666121212121212121224444466668888121212121212121212121212242424242424242422244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-111-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-11111-1-1
χ6111111111111111111111-1-111-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111
χ7111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-111
χ8111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-111111-1-1
χ91111-1-111111111-1-1-1-111-111-1-11111-1-1111-1-1-1-11-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-1
χ101111-1-111111111-1-1-1-111-111-1-11111-1-1111-1-1-1-11-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-11
χ111111-1-111111111-1-1-1-111-111-1-11111-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-11
χ121111-1-111111111-1-1-1-111-111-1-11111-1-1111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11-1
χ131111-1-111111111-1-1-1-111-1-1-1-1-1-1-111-1-1111-1-1-1-111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-1111-1-1-11
χ141111-1-111111111-1-1-1-111-1-1-1-1-1-1-111-1-1111-1-1-1-111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-111-111-1-1-1111-1
χ151111-1-111111111-1-1-1-111-1-1-1-1-1-1-111-1-1111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11-1-11-1-1111-1
χ161111-1-111111111-1-1-1-111-1-1-1-1-1-1-111-1-1111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-111-111-1-1-11
χ17222222222-2-2-2-22222222200-2-2002222-2-2-2-2-2-2-2-200000000000000000000000000000000002-20002-20000000
χ18222222222-2-2-2-22222222200-2-2002222-2-2-2-2-2-2-2-20000000000000000000000000000000000-22000-220000000
χ1922222222-12222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2022222222-12222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-2-2-2-2-1-1-1-1111111111111111100000000000000
χ2122222222-12222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-222221111-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000000000
χ2222222222-12222-1-1-1-1-1-1-12-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-211112222111111111111-1-1-1-1-1-1-1-100000000000000
χ23222222-2-2222-2-22222222-2222-2-2-2-2-2-2-22-2-222-2-222-2000022220000-2-2-2-2000000000000000000000000000000
χ24222222-2-2222-2-22222222-2-2-22-222-2-2-2-22-2-222-2-22-220000-2-2-2-200002222000000000000000000000000000000
χ25222222-2-22-2-2222222222-200-2200-2-2-2-2-222-2-222-20000000000000000000000000000000000002-2-2002000000
χ26222222-2-22-2-2222222222-200-2200-2-2-2-2-222-2-222-2000000000000000000000000000000000000-22200-2000000
χ27222222-2-2-122-2-2-1-1-1-1-1-1-1-2222-2-2-21111-111-1-111-12-20000-1-1-1-100001111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000
χ28222222-2-2-122-2-2-1-1-1-1-1-1-1-2222-2-2-21111-111-1-111-12-20000-1-1-1-100001111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000
χ29222222-2-2-122-2-2-1-1-1-1-1-1-1-2-2-22-2221111-111-1-111-1-22000011110000-1-1-1-1−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000
χ30222222-2-2-122-2-2-1-1-1-1-1-1-1-2-2-22-2221111-111-1-111-1-22000011110000-1-1-1-1i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000
χ312222-2-2222-2-2-2-22-2-2-2-222-200220022-2-2-2-2-22222-200000000000000000000000000000000002-2000-220000000
χ322222-2-2222-2-2-2-22-2-2-2-222-200220022-2-2-2-2-22222-20000000000000000000000000000000000-220002-20000000
χ332222-2-222-12222-11111-1-1-222-2-222-1-111-1-1-11111-1-2-222-2-2-1-11122-2-2-1-111-1-1-1-11111-1-1-1-1111100000000000000
χ342222-2-222-12222-11111-1-1-222-2-222-1-111-1-1-11111-1-2-2-2-222-1-111-2-222-1-1111111-1-1-1-11111-1-1-1-100000000000000
χ352222-2-222-12222-11111-1-1-2-2-2-2-2-2-2-1-111-1-1-11111-12222-2-211-1-1-2-22211-1-1-1-1-1-111111111-1-1-1-100000000000000
χ362222-2-222-12222-11111-1-1-2-2-2-2-2-2-2-1-111-1-1-11111-122-2-22211-1-122-2-211-1-11111-1-1-1-1-1-1-1-1111100000000000000
χ372222-2-2-2-2222-2-22-2-2-2-222222-22-2-2-2-2222-2-2-2-2222-22000022-2-20000-2-222000000000000000000000000000000
χ382222-2-2-2-2222-2-22-2-2-2-2222-2-2-2222-2-2222-2-2-2-22222-20000-2-222000022-2-2000000000000000000000000000000
χ392222-2-2-2-22-2-2222-2-2-2-2222002-200-2-222-22222-2-2-20000000000000000000000000000000000002-2200-2000000
χ402222-2-2-2-22-2-2222-2-2-2-2222002-200-2-222-22222-2-2-2000000000000000000000000000000000000-22-2002000000
χ412222-2-2-2-2-122-2-2-11111-1-1222-22-2-211-1-1-11111-1-1-1-220000-1-111000011-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000
χ422222-2-2-2-2-122-2-2-11111-1-1222-22-2-211-1-1-11111-1-1-1-220000-1-111000011-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000
χ432222-2-2-2-2-122-2-2-11111-1-12-2-2-222211-1-1-11111-1-1-12-2000011-1-10000-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000
χ442222-2-2-2-2-122-2-2-11111-1-12-2-2-222211-1-1-11111-1-1-12-2000011-1-10000-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000
χ4522-2-2002-222-22-2-200002-202-2002-22-20022-20000-200002i−2i2-200002i−2i2-20000002i−2i2i−2i00002i−2i2i−2i00000000000000
χ4622-2-2002-222-22-2-200002-202-2002-22-20022-20000-20000−2i2i2-20000−2i2i2-2000000−2i2i−2i2i0000−2i2i−2i2i00000000000000
χ4722-2-2002-222-22-2-200002-20-2200-222-20022-20000-200002i−2i-220000−2i2i-220000002i−2i2i−2i0000−2i2i−2i2i00000000000000
χ4822-2-2002-222-22-2-200002-20-2200-222-20022-20000-20000−2i2i-2200002i−2i-22000000−2i2i−2i2i00002i−2i2i−2i00000000000000
χ4922-2-2002-2-12-22-21−i3−i3i3i3-1102-2002-2-11−i3i3-1-11−i3i3−i3i3100002i−2i-11−i3i3002i−2i-11−i3i33−33−3−ii−ii3−33−3−ii−ii00000000000000
χ5022-2-2002-2-12-22-21−i3−i3i3i3-1102-2002-2-11−i3i3-1-11−i3i3−i3i310000−2i2i-11−i3i300−2i2i-11−i3i3−33−33i−ii−i−33−33i−ii−i00000000000000
χ5122-2-2002-2-12-22-21−i3−i3i3i3-110-2200-22-11−i3i3-1-11−i3i3−i3i3100002i−2i1-1i3−i300−2i2i1-1i3−i33−33−3−ii−ii−33−33i−ii−i00000000000000
χ5222-2-2002-2-12-22-21−i3−i3i3i3-110-2200-22-11−i3i3-1-11−i3i3−i3i310000−2i2i1-1i3−i3002i−2i1-1i3−i3−33−33i−ii−i3−33−3−ii−ii00000000000000
χ5322-2-2002-2-12-22-21i3i3−i3−i3-1102-2002-2-11i3−i3-1-11i3−i3i3−i3100002i−2i-11i3−i3002i−2i-11i3−i3−33−33−ii−ii−33−33−ii−ii00000000000000
χ5422-2-2002-2-12-22-21i3i3−i3−i3-1102-2002-2-11i3−i3-1-11i3−i3i3−i310000−2i2i-11i3−i300−2i2i-11i3−i33−33−3i−ii−i3−33−3i−ii−i00000000000000
χ5522-2-2002-2-12-22-21i3i3−i3−i3-110-2200-22-11i3−i3-1-11i3−i3i3−i3100002i−2i1-1−i3i300−2i2i1-1−i3i3−33−33−ii−ii3−33−3i−ii−i00000000000000
χ5622-2-2002-2-12-22-21i3i3−i3−i3-110-2200-22-11i3−i3-1-11i3−i3i3−i310000−2i2i1-1−i3i3002i−2i1-1−i3i33−33−3i−ii−i−33−33−ii−ii00000000000000
χ5722-2-200-2222-2-22-200002-202-200-22-22002-220000-2002i−2i002-2002i−2i00-22002i−2i−2i2i00002i−2i−2i2i000000000000000000
χ5822-2-200-2222-2-22-200002-202-200-22-22002-220000-200−2i2i002-200−2i2i00-2200−2i2i2i−2i0000−2i2i2i−2i000000000000000000
χ5922-2-200-2222-2-22-200002-20-22002-2-22002-220000-2002i−2i00-2200−2i2i002-2002i−2i−2i2i0000−2i2i2i−2i000000000000000000
χ6022-2-200-2222-2-22-200002-20-22002-2-22002-220000-200−2i2i00-22002i−2i002-200−2i2i2i−2i00002i−2i−2i2i000000000000000000
χ6122-2-200-22-12-2-221−i3−i3i3i3-1102-200-221-1i3−i3-11-1−i3i3i3−i31002i−2i00-11−i3i32i−2i001-1i3−i3−iii−i3−3−33−iii−i3−3−3300000000000000
χ6222-2-200-22-12-2-221−i3−i3i3i3-1102-200-221-1i3−i3-11-1−i3i3i3−i3100−2i2i00-11−i3i3−2i2i001-1i3−i3i−i−ii−333−3i−i−ii−333−300000000000000
χ6322-2-200-22-12-2-221−i3−i3i3i3-110-22002-21-1i3−i3-11-1−i3i3i3−i31002i−2i001-1i3−i3−2i2i00-11−i3i3−iii−i3−3−33i−i−ii−333−300000000000000
χ6422-2-200-22-12-2-221−i3−i3i3i3-110-22002-21-1i3−i3-11-1−i3i3i3−i3100−2i2i001-1i3−i32i−2i00-11−i3i3i−i−ii−333−3−iii−i3−3−3300000000000000
χ6522-2-200-22-12-2-221i3i3−i3−i3-1102-200-221-1−i3i3-11-1i3−i3−i3i31002i−2i00-11i3−i32i−2i001-1−i3i3−iii−i−333−3−iii−i−333−300000000000000
χ6622-2-200-22-12-2-221i3i3−i3−i3-1102-200-221-1−i3i3-11-1i3−i3−i3i3100−2i2i00-11i3−i3−2i2i001-1−i3i3i−i−ii3−3−33i−i−ii3−3−3300000000000000
χ6722-2-200-22-12-2-221i3i3−i3−i3-110-22002-21-1−i3i3-11-1i3−i3−i3i31002i−2i001-1−i3i3−2i2i00-11i3−i3−iii−i−333−3i−i−ii3−3−3300000000000000
χ6822-2-200-22-12-2-221i3i3−i3−i3-110-22002-21-1−i3i3-11-1i3−i3−i3i3100−2i2i001-1−i3i32i−2i00-11i3−i3i−i−ii3−3−33−iii−i−333−300000000000000
χ6944444444-2-4-4-4-4-2-2-2-2-2-2-2400-4-400-2-2-2-222222222000000000000000000000000000000000000000000000000
χ70444444-4-4-2-4-444-2-2-2-2-2-2-2-400-440022222-2-222-2-22000000000000000000000000000000000000000000000000
χ714444-4-444-2-4-4-4-4-22222-2-2-4004400-2-222222-2-2-2-22000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-2-4-444-22222-2-24004-40022-2-22-2-2-2-2222000000000000000000000000000000000000000000000000
χ7344-4-4004-44-44-44-400004-400000004-400-4-4400004000000000000000000000000000000000000000000000000
χ7444-4-4004-4-2-44-442−2i3−2i32i32i3-220000000-22−2i32i322-22i3−2i32i3−2i3-2000000000000000000000000000000000000000000000000
χ7544-4-4004-4-2-44-4422i32i3−2i3−2i3-220000000-222i3−2i322-2−2i32i3−2i32i3-2000000000000000000000000000000000000000000000000
χ7644-4-400-444-444-4-400004-40000000-4400-44-400004000000000000000000000000000000000000000000000000
χ7744-4-400-44-2-444-42−2i3−2i32i32i3-2200000002-22i3−2i32-222i3−2i3−2i32i3-2000000000000000000000000000000000000000000000000
χ7844-4-400-44-2-444-422i32i3−2i3−2i3-2200000002-2−2i32i32-22−2i32i32i3−2i3-2000000000000000000000000000000000000000000000000
χ794-4-444-4004000044-44-4-4-400000000000000000000000000000000000000000000000000000000000002i−2i2i−2i00
χ804-4-444-4004000044-44-4-4-40000000000000000000000000000000000000000000000000000000000000−2i2i−2i2i00
χ814-4-44-4400400004-44-44-4-400000000000000000000000000000000000000000000000000000000000002i−2i−2i2i00
χ824-4-44-4400400004-44-44-4-40000000000000000000000000000000000000000000000000000000000000−2i2i2i−2i00
χ838-88-8000080000-80000-880000000000000000000000000000000000000000000000000000000000000000000
χ848-88-80000-400004−4i34i34i3−4i34-40000000000000000000000000000000000000000000000000000000000000000000
χ858-88-80000-4000044i3−4i3−4i34i34-40000000000000000000000000000000000000000000000000000000000000000000
χ868-8-888-800-40000-4-44-44440000000000000000000000000000000000000000000000000000000000000000000
χ878-8-88-8800-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000000

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