Finite Group Databasebeta

← Group #10849690

Character table — Group #10849690

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11112222222222224444444444444444444444444888888888888888888888888888888882424242424242424242424244848
order122222344444466644444446612121212121212121212121212121212222244444466666666121212121212121212121212121244448888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-1
χ81111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ91111111-1-11111111-1-1-11111111111-1-1-1-111111111-1-11-11-11-11-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-11-1
χ101111111-1-11111111-1-1-11111111111-1-1-1-111111111-1-11-11-11-11-1-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-111-1-111-1-111-11
χ111111111-1-11111111-1-1-11111111111-1-1-1-111111111-1-1-11-11-11-11-1-1-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1111-1
χ121111111-1-11111111-1-1-11111111111-1-1-1-111111111-1-1-11-11-11-11-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-111-1-1-11
χ131111111-1-11111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-11-11111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-11
χ141111111-1-11111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-11-11111111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-11-1
χ151111111-1-11111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-11-111-11-11111-1-111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-11
χ161111111-1-11111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-11-111-11-11111-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1111-1
χ17222222222-2-2-2-2222-2-2222-2-222-2-2-2-222222222-2-2-2-22-20000000022-2-20000-2-200000000000000000000000000
χ18222222222-2-2-2-2222-2-22-2-22222-2-2-2-22222-2-2-2-22222-2200000000-2-2220000-2-200000000000000000000000000
χ192222222-2-2-2-2-2-222222-222-2-222-2-2-2-2-2-2-2-22222-2-2-2-2-2200000000-2-22200002200000000000000000000000000
χ202222222-2-2-2-2-2-222222-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-222222-20000000022-2-200002200000000000000000000000000
χ21222222-1222222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222222-1222222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-11111-1-111111111111100000000000000
χ23222222-1222222-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-22222-2-2-2-21111-1-1-1-1-1-1-1-1-1-11111111100000000000000
χ24222222-1222222-1-1-1222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2-2-2222211111111-1-11111-1-1-1-1-1-1-1-100000000000000
χ25222222-122-2-2-2-2-1-1-1-2-2222-2-2-1-11111-1-1-1-1-1-1-1-111112-200000000-1-111−i3i3−i3i311−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300000000000000
χ26222222-122-2-2-2-2-1-1-1-2-2222-2-2-1-11111-1-1-1-1-1-1-1-111112-200000000-1-111i3−i3i3−i311i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300000000000000
χ27222222-122-2-2-2-2-1-1-1-2-22-2-222-1-11111-1-1-1-11111-1-1-1-1-220000000011-1-1−i3i3−i3i311−i3i3−i3i3i3−i3i3−i3i3−i3i3−i300000000000000
χ28222222-122-2-2-2-2-1-1-1-2-22-2-222-1-11111-1-1-1-11111-1-1-1-1-220000000011-1-1i3−i3i3−i311i3−i3i3−i3−i3i3−i3i3−i3i3−i3i300000000000000
χ29222222-1-2-22222-1-1-1-2-2-22222-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-22-22-22-22-21111-1-11111-1-111-1-111-1-11100000000000000
χ30222222-1-2-22222-1-1-1-2-2-22222-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-22-22-22-22111111-1-11111-1-111-1-111-1-100000000000000
χ31222222-1-2-22222-1-1-1-2-2-2-2-2-2-2-1-1-1-1-1-1111111111111222-22-2-22-22-1-1-1-1-1-11111-1-11111-1-111-1-100000000000000
χ32222222-1-2-22222-1-1-1-2-2-2-2-2-2-2-1-1-1-1-1-111111111111122-22-222-22-2-1-1-1-111-1-11111-1-1-1-111-1-11100000000000000
χ33222222-1-2-2-2-2-2-2-1-1-122-222-2-2-1-111111111-1-1-1-11111-220000000011-1-1−i3i3i3−i3-1-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000
χ34222222-1-2-2-2-2-2-2-1-1-122-222-2-2-1-111111111-1-1-1-11111-220000000011-1-1i3−i3−i3i3-1-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000
χ35222222-1-2-2-2-2-2-2-1-1-122-2-2-222-1-1111111111111-1-1-1-12-200000000-1-111−i3i3i3−i3-1-1−i3i3i3−i3i3−i3−i3i3i3−i3−i3i300000000000000
χ36222222-1-2-2-2-2-2-2-1-1-122-2-2-222-1-1111111111111-1-1-1-12-200000000-1-111i3−i3−i3i3-1-1i3−i3−i3i3−i3i3i3−i3−i3i3i3−i300000000000000
χ372222-2-222222-2-22222-2-20000-2-222-2-222-2-20000000000000022-2-2000000002-200002222-2-2-2-200000000000000
χ382222-2-222222-2-22222-2-20000-2-222-2-222-2-200000000000000-2-222000000002-20000-2-2-2-2222200000000000000
χ392222-2-2222-2-222222-22-20000-2-2-2-22222-2-2000000000022-2-2000000002222-22-2-2-2-20000000000000000000000
χ402222-2-2222-2-222222-22-20000-2-2-2-22222-2-20000000000-2-22200000000-2-2-2-2-2222220000000000000000000000
χ412222-2-22-2-222-2-2222-2220000-2-222-2-2-2-222000000000000002-2-2200000000-22000022-2-2-2-22200000000000000
χ422222-2-22-2-222-2-2222-2220000-2-222-2-2-2-22200000000000000-222-200000000-220000-2-22222-2-200000000000000
χ432222-2-22-2-2-2-2222222-220000-2-2-2-222-2-22200000000002-2-220000000022-2-22-2-2-2220000000000000000000000
χ442222-2-22-2-2-2-2222222-220000-2-2-2-222-2-2220000000000-222-200000000-2-2222-222-2-20000000000000000000000
χ452222-2-2-12222-2-2-1-1-12-2-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i300000022-2-2−i3i3−i3i3−i3i3−i3i3-11i3−i3i3−i3-1-1-1-1111100000000000000
χ462222-2-2-12222-2-2-1-1-12-2-2000011-1-111-1-111−i3−i3i3i3−i3−i3i3i3000000-2-222−i3i3−i3i3i3−i3i3−i3-11−i3i3−i3i31111-1-1-1-100000000000000
χ472222-2-2-12222-2-2-1-1-12-2-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i300000022-2-2i3−i3i3−i3i3−i3i3−i3-11−i3i3−i3i3-1-1-1-1111100000000000000
χ482222-2-2-12222-2-2-1-1-12-2-2000011-1-111-1-111i3i3−i3−i3i3i3−i3−i3000000-2-222i3−i3i3−i3−i3i3−i3i3-11i3−i3i3−i31111-1-1-1-100000000000000
χ492222-2-2-122-2-222-1-1-1-22-200001111-1-1-1-111−i3−i3i3i3i3i3−i3−i30022-2-20000−i3i3i3−i3-1-1-1-11-11111−i3i3−i3i3i3−i3i3−i300000000000000
χ502222-2-2-122-2-222-1-1-1-22-200001111-1-1-1-111−i3−i3i3i3i3i3−i3−i300-2-2220000−i3i3i3−i311111-1-1-1-1-1i3−i3i3−i3−i3i3−i3i300000000000000
χ512222-2-2-122-2-222-1-1-1-22-200001111-1-1-1-111i3i3−i3−i3−i3−i3i3i30022-2-20000i3−i3−i3i3-1-1-1-11-11111i3−i3i3−i3−i3i3−i3i300000000000000
χ522222-2-2-122-2-222-1-1-1-22-200001111-1-1-1-111i3i3−i3−i3−i3−i3i3i300-2-2220000i3−i3−i3i311111-1-1-1-1-1−i3i3−i3i3i3−i3i3−i300000000000000
χ532222-2-2-1-2-222-2-2-1-1-1-222000011-1-11111-1-1−i3−i3i3i3−i3−i3i3i30000002-2-22i3−i3i3−i3−i3i3i3−i31-1i3−i3−i3i3-1-11111-1-100000000000000
χ542222-2-2-1-2-222-2-2-1-1-1-222000011-1-11111-1-1−i3−i3i3i3−i3−i3i3i3000000-222-2i3−i3i3−i3i3−i3−i3i31-1−i3i3i3−i311-1-1-1-11100000000000000
χ552222-2-2-1-2-222-2-2-1-1-1-222000011-1-11111-1-1i3i3−i3−i3i3i3−i3−i30000002-2-22−i3i3−i3i3i3−i3−i3i31-1−i3i3i3−i3-1-11111-1-100000000000000
χ562222-2-2-1-2-222-2-2-1-1-1-222000011-1-11111-1-1i3i3−i3−i3i3i3−i3−i3000000-222-2−i3i3−i3i3−i3i3i3−i31-1i3−i3−i3i311-1-1-1-11100000000000000
χ572222-2-2-1-2-2-2-222-1-1-12-2200001111-1-111-1-1−i3−i3i3i3i3i3−i3−i3002-2-220000i3−i3−i3i3-1-111-1111-1-1−i3i3i3−i3i3−i3−i3i300000000000000
χ582222-2-2-1-2-2-2-222-1-1-12-2200001111-1-111-1-1−i3−i3i3i3i3i3−i3−i300-222-20000i3−i3−i3i311-1-1-11-1-111i3−i3−i3i3−i3i3i3−i300000000000000
χ592222-2-2-1-2-2-2-222-1-1-12-2200001111-1-111-1-1i3i3−i3−i3−i3−i3i3i3002-2-220000−i3i3i3−i3-1-111-1111-1-1i3−i3−i3i3−i3i3i3−i300000000000000
χ602222-2-2-1-2-2-2-222-1-1-12-2200001111-1-111-1-1i3i3−i3−i3−i3−i3i3i300-222-20000−i3i3i3−i311-1-1-11-1-111−i3i3i3−i3i3−i3−i3i300000000000000
χ6122-2-2-222002-22-22-2-20002i−2i2i−2i2-22-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000002-2002i−2i00
χ6222-2-2-222002-22-22-2-20002i−2i2i−2i2-22-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000-2200−2i2i00
χ6322-2-2-222002-22-22-2-2000−2i2i−2i2i2-22-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000002-200−2i2i00
χ6422-2-2-222002-22-22-2-2000−2i2i−2i2i2-22-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000-22002i−2i00
χ6522-2-2-22200-22-222-2-20002i−2i−2i2i2-2-22-2200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000002-2002i−2i0000
χ6622-2-2-22200-22-222-2-20002i−2i−2i2i2-2-22-2200002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000-2200−2i2i0000
χ6722-2-2-22200-22-222-2-2000−2i2i2i−2i2-2-22-220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000002-200−2i2i0000
χ6822-2-2-22200-22-222-2-2000−2i2i2i−2i2-2-22-220000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000-22002i−2i0000
χ6944-4-44-44004-4-444-4-40000000-444-4-440000000000000000000000000000000000000000000000000000000000
χ7044-4-44-4400-444-44-4-40000000-44-444-40000000000000000000000000000000000000000000000000000000000
χ7144-4-44-4-2004-4-44-22200000002-2-222-2000023−23−232323−23−23230000000000000000000000000000000000000000000000
χ7244-4-44-4-2004-4-44-22200000002-2-222-20000−232323−23−232323−230000000000000000000000000000000000000000000000
χ7344-4-44-4-200-444-4-22200000002-22-2-22000023−23−2323−232323−230000000000000000000000000000000000000000000000
χ7444-4-44-4-200-444-4-22200000002-22-2-220000−232323−2323−23−23230000000000000000000000000000000000000000000000
χ7544-4-4-44-2004-44-4-2220004i−4i4i−4i-22-22-220000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ7644-4-4-44-2004-44-4-222000−4i4i−4i4i-22-22-2200002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7744-4-4-44-200-44-44-2220004i−4i−4i4i-222-22-20000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ7844-4-4-44-200-44-44-222000−4i4i4i−4i-222-22-200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ794-4-440044-40000-4-4400000000000004-40000000000000000000000000000000000000000002-22-20000000000
χ804-4-440044-40000-4-4400000000000004-4000000000000000000000000000000000000000000-22-220000000000
χ814-4-44004-440000-4-440000000000000-440000000000000000000000000000000000000000002-2-220000000000
χ824-4-44004-440000-4-440000000000000-44000000000000000000000000000000000000000000-222-20000000000
χ838-88-8008000000-88-800000000000000000000000000000000000000000000000000000000000000000000000
χ848-88-800-40000004-4400000000000000043−43000000000000000000000000000000000000000000000000000000
χ858-88-800-40000004-44000000000000000−4343000000000000000000000000000000000000000000000000000000
χ868-8-8800-48-8000044-40000000000000-4400000000000000000000000000000000000000000000000000000000
χ878-8-8800-4-88000044-400000000000004-400000000000000000000000000000000000000000000000000000000

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