Finite Group Databasebeta

← Group #10828709

Character table — Group #10828709

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222224444444444444444444444444888888888888888888888888888888882424242424242424242424244848
order122222223444466624444446666121212121212121212121212121224444444446661212121212121212121212121212121212121244444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-11-1-1-1-1-1-11-11-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111-11-1-1-1-1-1-11-11-1-111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11-111-1-1-1-1-11111-1-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ61111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11-111-1-1-1-1-11111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ81111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ91111-1-11111111111-1-1-1111111-1-111111111-1-111111-11-111-1-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-111-1-11-1
χ101111-1-11111111111-1-1-1111111-1-111111111-1-111111-11-111-1-1-1-1-111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-11
χ111111-1-11111111111-1-1-1111111-1-111111111-1-11111-1-1-11-1-111-11-1-1-1-1-111-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-11
χ121111-1-11111111111-1-1-1111111-1-111111111-1-11111-1-1-11-1-111-11-1-1-1-1-111-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1111-1
χ131111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1111-1-11111-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-1111-1
χ141111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1111-1-11111-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-11
χ151111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1111-1-111-1-1-11111-111-1-1111111-1-1-1-111-1-111-1-1-1-111-11
χ161111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-11-1111-1-111-1-1-11111-111-1-1111111-1-1-1-1-1-111-1-11111-1-11-1
χ17222222222-2-2-2-22222-2-2000022220000-2-2-2-2-2-2000000002-22-2002000000-200000022-2-222-2-200000000000000
χ18222222222-2-2-2-22222-2-2000022220000-2-2-2-2-2-200000000-22-22002000000-2000000-2-222-2-22200000000000000
χ1922222222-12222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2022222222-12222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22-2-2-2-2-2-22-2-111-1-111-1-1-111111111111100000000000000
χ2122222222-12222-1-1-1222-2-2-2-2-1-1-1-11111-1-1-1-1-1-111112-222-2-2-2-2-22-1-1-111-1-1-111-1-1-1-11111111100000000000000
χ2222222222-12222-1-1-1222-2-2-2-2-1-1-1-11111-1-1-1-1-1-11111-2-2-2-22222-2-2-1111111-1111111-1-1-1-1-1-1-1-100000000000000
χ2322222222-1-2-2-2-2-1-1-12-2-20000-1-1-1-1−i3−i3i3i3111111−i3−i3i3i300002-22-200-1−i3i3−i3i3−i3i31−i3i3−i3i3−i3i3-1-111-1-11100000000000000
χ2422222222-1-2-2-2-2-1-1-12-2-20000-1-1-1-1−i3−i3i3i3111111−i3−i3i3i30000-22-2200-1i3−i3−i3i3i3−i31−i3i3i3−i3i3−i311-1-111-1-100000000000000
χ2522222222-1-2-2-2-2-1-1-12-2-20000-1-1-1-1i3i3−i3−i3111111i3i3−i3−i300002-22-200-1i3−i3i3−i3i3−i31i3−i3i3−i3i3−i3-1-111-1-11100000000000000
χ2622222222-1-2-2-2-2-1-1-12-2-20000-1-1-1-1i3i3−i3−i3111111i3i3−i3−i30000-22-2200-1−i3i3i3−i3−i3i31i3−i3−i3i3−i3i311-1-111-1-100000000000000
χ27222222-2-222-2-22222-22-222-2-2-2-222-2-2-2-222-2-2-2-2222202000000-20-200-2-20022200000000000000000000000000
χ28222222-2-222-2-22222-22-2-2-222-2-222222222-2-2-2-2-2-2-2-20-200000020-20022002-2-200000000000000000000000000
χ29222222-2-22-222-2222-2-220000-2-2220000-2-22222000020-2-2000002-2220022-200-2-2-2-20000000000000000000000
χ30222222-2-22-222-2222-2-220000-2-2220000-2-222220000-202200000-2-2-2-200-2-2-20022220000000000000000000000
χ31222222-2-2-12-2-22-1-1-1-22-222-2-211-1-11111-1-11111-1-1-1-102000000-201−i3i311−i3i3-1-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i300000000000000
χ32222222-2-2-12-2-22-1-1-1-22-222-2-211-1-11111-1-11111-1-1-1-102000000-201i3−i311i3−i3-1-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i300000000000000
χ33222222-2-2-12-2-22-1-1-1-22-2-2-22211-1-1-1-1-1-1-1-1111111110-2000000201−i3i3-1-1−i3i3-111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300000000000000
χ34222222-2-2-12-2-22-1-1-1-22-2-2-22211-1-1-1-1-1-1-1-1111111110-2000000201i3−i3-1-1i3−i3-111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300000000000000
χ35222222-2-2-1-222-2-1-1-1-2-22000011-1-1−i3−i3i3i311-1-1-1-1i3i3−i3−i320-2-20000021-1-1−i3i3-1-11i3−i31111i3−i3−i3i3i3−i3−i3i300000000000000
χ36222222-2-2-1-222-2-1-1-1-2-22000011-1-1−i3−i3i3i311-1-1-1-1i3i3−i3−i3-202200000-2111−i3i3111i3−i3-1-1-1-1−i3i3i3−i3−i3i3i3−i300000000000000
χ37222222-2-2-1-222-2-1-1-1-2-22000011-1-1i3i3−i3−i311-1-1-1-1−i3−i3i3i320-2-20000021-1-1i3−i3-1-11−i3i31111−i3i3i3−i3−i3i3i3−i300000000000000
χ38222222-2-2-1-222-2-1-1-1-2-22000011-1-1i3i3−i3−i311-1-1-1-1−i3−i3i3i3-202200000-2111i3−i3111−i3i3-1-1-1-1i3−i3−i3i3i3−i3−i3i300000000000000
χ392222-2-2222-2-2-2-2222-222000022-2-20000-2-2-2-222000000002-2-2200-2000000200000022-2-2-2-22200000000000000
χ402222-2-2222-2-2-2-2222-222000022-2-20000-2-2-2-22200000000-222-200-20000002000000-2-22222-2-200000000000000
χ412222-2-222-12222-1-1-1-2-2-22222-1-111-1-1-1-1-1-1-1-111-1-1-1-12-22-222-2-2-2-21-1-11111111-1-111-1-1-1-1111100000000000000
χ422222-2-222-12222-1-1-1-2-2-22222-1-111-1-1-1-1-1-1-1-111-1-1-1-1-2-2-22-2-222-2211111-1-111111-1-11111-1-1-1-100000000000000
χ432222-2-222-12222-1-1-1-2-2-2-2-2-2-2-1-1111111-1-1-1-1111111222-2-2-2222-21-1-1-1-1111-1-1-1-1111111-1-1-1-100000000000000
χ442222-2-222-12222-1-1-1-2-2-2-2-2-2-2-1-1111111-1-1-1-1111111-22-2222-2-222111-1-1-1-11-1-111-1-1-1-1-1-1111100000000000000
χ452222-2-222-1-2-2-2-2-1-1-1-2220000-1-111−i3−i3i3i31111-1-1−i3−i3i3i300002-2-22001−i3i3i3−i3i3−i3-1i3−i3−i3i3i3−i3-1-11111-1-100000000000000
χ462222-2-222-1-2-2-2-2-1-1-1-2220000-1-111−i3−i3i3i31111-1-1−i3−i3i3i30000-222-2001i3−i3i3−i3−i3i3-1i3−i3i3−i3−i3i311-1-1-1-11100000000000000
χ472222-2-222-1-2-2-2-2-1-1-1-2220000-1-111i3i3−i3−i31111-1-1i3i3−i3−i300002-2-22001i3−i3−i3i3−i3i3-1−i3i3i3−i3−i3i3-1-11111-1-100000000000000
χ482222-2-222-1-2-2-2-2-1-1-1-2220000-1-111i3i3−i3−i31111-1-1i3i3−i3−i30000-222-2001−i3i3−i3i3i3−i3-1−i3i3−i3i3i3−i311-1-1-1-11100000000000000
χ492222-2-2-2-222-2-222222-2222-2-2-2-2-2-2-2-2-2-222-2-22222220-2000000202002200-2-2-200000000000000000000000000
χ502222-2-2-2-222-2-222222-22-2-222-2-2-2-2222222-2-222-2-2-2-202000000-20200-2-200-22200000000000000000000000000
χ512222-2-2-2-22-222-222222-20000-2-2-2-20000-2-222-2-2000020-2200000-222200-2-2200-2-2220000000000000000000000
χ522222-2-2-2-22-222-222222-20000-2-2-2-20000-2-222-2-20000-202-20000022-2-2002220022-2-20000000000000000000000
χ532222-2-2-2-2-12-2-22-1-1-12-2222-2-211111111-1-111-1-1-1-1-1-10-200000020-1−i3i3-1-1i3−i3111i3−i3−i3i3−i3i3−i3i3i3−i3i3−i300000000000000
χ542222-2-2-2-2-12-2-22-1-1-12-2222-2-211111111-1-111-1-1-1-1-1-10-200000020-1i3−i3-1-1−i3i3111−i3i3i3−i3i3−i3i3−i3−i3i3−i3i300000000000000
χ552222-2-2-2-2-12-2-22-1-1-12-22-2-2221111-1-1-1-1-1-111-1-1111102000000-20-1−i3i311i3−i31-1-1i3−i3−i3i3i3−i3i3−i3−i3i3−i3i300000000000000
χ562222-2-2-2-2-12-2-22-1-1-12-22-2-2221111-1-1-1-1-1-111-1-1111102000000-20-1i3−i311−i3i31-1-1−i3i3i3−i3−i3i3−i3i3i3−i3i3−i300000000000000
χ572222-2-2-2-2-1-222-2-1-1-122-200001111−i3−i3i3i311-1-111i3i3−i3−i320-2200000-2-1-1-1i3−i311-1−i3i311-1-1i3−i3−i3i3−i3i3i3−i300000000000000
χ582222-2-2-2-2-1-222-2-1-1-122-200001111−i3−i3i3i311-1-111i3i3−i3−i3-202-2000002-111i3−i3-1-1-1−i3i3-1-111−i3i3i3−i3i3−i3−i3i300000000000000
χ592222-2-2-2-2-1-222-2-1-1-122-200001111i3i3−i3−i311-1-111−i3−i3i3i320-2200000-2-1-1-1−i3i311-1i3−i311-1-1−i3i3i3−i3i3−i3−i3i300000000000000
χ602222-2-2-2-2-1-222-2-1-1-122-200001111i3i3−i3−i311-1-111−i3−i3i3i3-202-2000002-111−i3i3-1-1-1i3−i3-1-111i3−i3−i3i3−i3i3i3−i300000000000000
χ6122-2-2002-22-22-22-22-20002i−2i2i−2i2-2002i−2i2i−2i2-22-2002i−2i2i−2i00000000000000000000000000000000002i−2i0000002-200
χ6222-2-2002-22-22-22-22-20002i−2i2i−2i2-2002i−2i2i−2i2-22-2002i−2i2i−2i0000000000000000000000000000000000−2i2i000000-2200
χ6322-2-2002-22-22-22-22-2000−2i2i−2i2i2-200−2i2i−2i2i2-22-200−2i2i−2i2i00000000000000000000000000000000002i−2i000000-2200
χ6422-2-2002-22-22-22-22-2000−2i2i−2i2i2-200−2i2i−2i2i2-22-200−2i2i−2i2i0000000000000000000000000000000000−2i2i0000002-200
χ6522-2-200-222-2-222-22-20002i−2i−2i2i-2200−2i2i−2i2i2-2-22002i−2i2i−2i000000000000000000000000000000002i−2i0000002-20000
χ6622-2-200-222-2-222-22-20002i−2i−2i2i-2200−2i2i−2i2i2-2-22002i−2i2i−2i00000000000000000000000000000000−2i2i000000-220000
χ6722-2-200-222-2-222-22-2000−2i2i2i−2i-22002i−2i2i−2i2-2-2200−2i2i−2i2i000000000000000000000000000000002i−2i000000-220000
χ6822-2-200-222-2-222-22-2000−2i2i2i−2i-22002i−2i2i−2i2-2-2200−2i2i−2i2i00000000000000000000000000000000−2i2i0000002-20000
χ6944-4-4004-444-44-4-44-400000004-4000000-44-440000000000000000000000000000000000000000000000000000
χ7044-4-4004-4-24-44-42-220000000-220023−23−23232-22-20023−23−23230000000000000000000000000000000000000000000000
χ7144-4-4004-4-24-44-42-220000000-2200−232323−232-22-200−232323−230000000000000000000000000000000000000000000000
χ7244-4-4004-4-2-44-442-220004i−4i4i−4i-2200−2i2i−2i2i-22-2200−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7344-4-4004-4-2-44-442-22000−4i4i−4i4i-22002i−2i2i−2i-22-22002i−2i2i−2i0000000000000000000000000000000000000000000000
χ7444-4-400-44444-4-4-44-40000000-44000000-444-40000000000000000000000000000000000000000000000000000
χ7544-4-400-44-244-4-42-2200000002-20023−23−23232-2-2200−232323−230000000000000000000000000000000000000000000000
χ7644-4-400-44-244-4-42-2200000002-200−232323−232-2-220023−23−23230000000000000000000000000000000000000000000000
χ7744-4-400-44-2-4-4442-220004i−4i−4i4i2-2002i−2i2i−2i-222-200−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7844-4-400-44-2-4-4442-22000−4i4i4i−4i2-200−2i2i−2i2i-222-2002i−2i2i−2i0000000000000000000000000000000000000000000000
χ794-4-444-400400004-4-40000000004-4000000000000000000000000000000000000000000000000002i−2i2i−2i000000
χ804-4-444-400400004-4-40000000004-400000000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ814-4-44-4400400004-4-4000000000-44000000000000000000000000000000000000000000000000002i−2i−2i2i000000
χ824-4-44-4400400004-4-4000000000-4400000000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ838-88-8000080000-8-8800000000000000000000000000000000000000000000000000000000000000000000000
χ848-88-80000-4000044-4000000000000000000043−4300000000000000000000000000000000000000000000000000
χ858-88-80000-4000044-40000000000000000000−434300000000000000000000000000000000000000000000000000
χ868-8-888-800-40000-444000000000-44000000000000000000000000000000000000000000000000000000000000
χ878-8-88-8800-40000-4440000000004-4000000000000000000000000000000000000000000000000000000000000

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