Finite Group Databasebeta

← Group #10691599

Character table — Group #10691599

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444444444444444444444488888888888888888888888888242424242424242448484848
order12222234444446661212121244444446688881212121212121212121212121212242424242424242444888888121212121212242424242424242424242424888888882288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ61111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111111-11-1-1-11111-1-1-1-11-111-1-1-111ii−i−i-1-111-1-11111-1-1-1-1iiii−i−i−i−i1-1i−iii−i−i1-111-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i1-1i−i
χ101111111-11-1-1-11111-1-1-1-11-111-1-1-111ii−i−i-1-111-1-11111-1-1-1-1iiii−i−i−i−i1-1i−iii−i−i1-111-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-11−ii
χ111111111-11-1-1-11111-1-1-1-11-111-1-1-111−i−iii-1-111-1-11111-1-1-1-1−i−i−i−iiiii1-1−ii−i−iii1-111-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii1-1−ii
χ121111111-11-1-1-11111-1-1-1-11-111-1-1-111−i−iii-1-111-1-11111-1-1-1-1−i−i−i−iiiii1-1−ii−i−iii1-111-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-11i−i
χ131111111-11-1-1-11111-1-1-1-11-1-1-111-111ii−i−i-1-111-1-1-1-1-1-11111iiii−i−i−i−i-11i−i−i−iii1-1-1-111ii−i−i−i−i−i−iiiii11-1-1ii−i−i-11−ii
χ141111111-11-1-1-11111-1-1-1-11-1-1-111-111ii−i−i-1-111-1-1-1-1-1-11111iiii−i−i−i−i-11i−i−i−iii1-1-1-111ii−i−i−i−i−i−iiiii-1-111−i−iii1-1i−i
χ151111111-11-1-1-11111-1-1-1-11-1-1-111-111−i−iii-1-111-1-1-1-1-1-11111−i−i−i−iiiii-11−iiii−i−i1-1-1-111−i−iiiiiii−i−i−i−i11-1-1−i−iii-11i−i
χ161111111-11-1-1-11111-1-1-1-11-1-1-111-111−i−iii-1-111-1-1-1-1-1-11111−i−i−i−iiiii-11−iiii−i−i1-1-1-111−i−iiiiiii−i−i−i−i-1-111ii−i−i1-1−ii
χ1722222222-2222-22222222-2-20000-222222222-2-2-2-2000000002222222200-2-20000-2-20000-2-2-2-200000000000000000000
χ1822222222-2222-22222222-2-20000-222-2-2-2-222-2-2-2-200000000-2-2-2-2-2-2-2-200220000-2-20000222200000000000000000000
χ192222222-2-2-2-2-2-2222-2-2-2-2-2200002222i2i−2i−2i-2-2-2-222000000002i2i2i2i−2i−2i−2i−2i00−2i2i0000-220000−2i−2i2i2i00000000000000000000
χ202222222-2-2-2-2-2-2222-2-2-2-2-220000222−2i−2i2i2i-2-2-2-22200000000−2i−2i−2i−2i2i2i2i2i002i−2i0000-2200002i2i−2i−2i00000000000000000000
χ21222222-1222222-1-1-1-1-1-1-12222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-1222222-1-1-1-1-1-1-12222222-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000
χ23222222-1222222-1-1-1-1-1-1-122-2-2-2-22-1-12222-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-11111-1-1-1-111111111000000000000
χ24222222-1222222-1-1-1-1-1-1-122-2-2-2-22-1-1-2-2-2-2-1-1-1-1-1-11111111111111111-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000
χ25222222-12-2222-2-1-1-1-1-1-1-1-2-20000-2-1-12222-1-11111−i3−i3i3i3−i3−i3i3i3-1-1-1-1-1-1-1-100-2-2000011−i3i3−i3i31111−i3−i3i3i3−i3−i3i3i3000000000000
χ26222222-12-2222-2-1-1-1-1-1-1-1-2-20000-2-1-12222-1-11111i3i3−i3−i3i3i3−i3−i3-1-1-1-1-1-1-1-100-2-2000011i3−i3i3−i31111i3i3−i3−i3i3i3−i3−i3000000000000
χ27222222-12-2222-2-1-1-1-1-1-1-1-2-20000-2-1-1-2-2-2-2-1-11111−i3−i3i3i3−i3−i3i3i3111111110022000011−i3i3−i3i3-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000
χ28222222-12-2222-2-1-1-1-1-1-1-1-2-20000-2-1-1-2-2-2-2-1-11111i3i3−i3−i3i3i3−i3−i3111111110022000011i3−i3i3−i3-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000
χ29222222-1-22-2-2-22-1-1-111112-222-2-2-2-1-12i2i−2i−2i11-1-111-1-1-1-11111−i−i−i−iiiii2-22i−2i2i2i−2i−2i-11-1-111−i−iii−i−i−i−iiiii000000000000
χ30222222-1-22-2-2-22-1-1-111112-222-2-2-2-1-1−2i−2i2i2i11-1-111-1-1-1-11111iiii−i−i−i−i2-2−2i2i−2i−2i2i2i-11-1-111ii−i−iiiii−i−i−i−i000000000000
χ31222222-1-22-2-2-22-1-1-111112-2-2-222-2-1-12i2i−2i−2i11-1-1111111-1-1-1-1−i−i−i−iiiii-222i−2i−2i−2i2i2i-1111-1-1−i−iiiiiii−i−i−i−i000000000000
χ32222222-1-22-2-2-22-1-1-111112-2-2-222-2-1-1−2i−2i2i2i11-1-1111111-1-1-1-1iiii−i−i−i−i-22−2i2i2i2i−2i−2i-1111-1-1ii−i−i−i−i−i−iiiii000000000000
χ33222222-1-2-2-2-2-2-2-1-1-11111-2200002-1-12i2i−2i−2i1111-1-1−i3−i3i3i3i3i3−i3−i3−i−i−i−iiiii00−2i2i00001-1−i3i3i3−i3ii−i−i33−3−3−3−333000000000000
χ34222222-1-2-2-2-2-2-2-1-1-11111-2200002-1-12i2i−2i−2i1111-1-1i3i3−i3−i3−i3−i3i3i3−i−i−i−iiiii00−2i2i00001-1i3−i3−i3i3ii−i−i−3−33333−3−3000000000000
χ35222222-1-2-2-2-2-2-2-1-1-11111-2200002-1-1−2i−2i2i2i1111-1-1−i3−i3i3i3i3i3−i3−i3iiii−i−i−i−i002i−2i00001-1−i3i3i3−i3−i−iii−3−33333−3−3000000000000
χ36222222-1-2-2-2-2-2-2-1-1-11111-2200002-1-1−2i−2i2i2i1111-1-1i3i3−i3−i3−i3−i3i3i3iiii−i−i−i−i002i−2i00001-1i3−i3−i3i3−i−iii33−3−3−3−333000000000000
χ372222-2-2222-2-222222-2-2-2-2-2-222-2-22-2-200002222-2-22222-2-2-2-200000000-22000000-22-2-222000000000000000000000000
χ382222-2-2222-2-222222-2-2-2-2-2-2-2-2222-2-200002222-2-2-2-2-2-22222000000002-2000000-2222-2-2000000000000000000000000
χ392222-2-222-2-2-22-2222-2-2-2-2220000-2-2-2000022-2-222000000000000000000002i−2i2i−2i2-2000000002i−2i2i−2i2i−2i2i−2i000000000000
χ402222-2-222-2-2-22-2222-2-2-2-2220000-2-2-2000022-2-22200000000000000000000−2i2i−2i2i2-200000000−2i2i−2i2i−2i2i−2i2i000000000000
χ412222-2-22-2222-222222222-222222-2-2-20000-2-222222222222200000000-2-2000000-2-2-2-2-2-2000000000000000000000000
χ422222-2-22-2222-222222222-22-2-2-2-2-2-2-20000-2-22222-2-2-2-2-2-2-2-20000000022000000-2-22222000000000000000000000000
χ432222-2-22-2-222-2-222222222-200002-2-20000-2-2-2-2-2-2000000000000000000002-2-2222000000002-22-2-22-22000000000000
χ442222-2-22-2-222-2-222222222-200002-2-20000-2-2-2-2-2-200000000000000000000-222-22200000000-22-222-22-2000000000000
χ452222-2-2-122-2-222-1-1-11111-2-222-2-22110000-1-1-1-111-1-1-1-1111133−3−333−3−3-220000001-111-1-13−33−33−3−333−3−33000000000000
χ462222-2-2-122-2-222-1-1-11111-2-222-2-22110000-1-1-1-111-1-1-1-11111−3−333−3−333-220000001-111-1-1−33−33−333−3−333−3000000000000
χ472222-2-2-122-2-222-1-1-11111-2-2-2-2222110000-1-1-1-1111111-1-1-1-133−3−333−3−32-20000001-1-1-1113−33−3−333−3−333−3000000000000
χ482222-2-2-122-2-222-1-1-11111-2-2-2-2222110000-1-1-1-1111111-1-1-1-1−3−333−3−3332-20000001-1-1-111−33−333−3−333−3−33000000000000
χ492222-2-2-12-2-2-22-2-1-1-11111220000-2110000-1-111-1-1−i3−i3i3i3i3i3−i3−i333−3−333−3−300002i−2i2i−2i-11i3−i3−i3i3−33−33−ii−ii−ii−ii000000000000
χ502222-2-2-12-2-2-22-2-1-1-11111220000-2110000-1-111-1-1−i3−i3i3i3i3i3−i3−i3−3−333−3−3330000−2i2i−2i2i-11i3−i3−i3i33−33−3i−ii−ii−ii−i000000000000
χ512222-2-2-12-2-2-22-2-1-1-11111220000-2110000-1-111-1-1i3i3−i3−i3−i3−i3i3i333−3−333−3−30000−2i2i−2i2i-11−i3i3i3−i3−33−33i−ii−ii−ii−i000000000000
χ522222-2-2-12-2-2-22-2-1-1-11111220000-2110000-1-111-1-1i3i3−i3−i3−i3−i3i3i3−3−333−3−33300002i−2i2i−2i-11−i3i3i3−i33−33−3−ii−ii−ii−ii000000000000
χ532222-2-2-1-2222-22-1-1-1-1-1-1-1-222222-211000011-1-1-1-1-1-1-1-1-1-1-1-1−i3−i3i3i3i3i3−i3−i3-2-2000000111111−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3000000000000
χ542222-2-2-1-2222-22-1-1-1-1-1-1-1-222222-211000011-1-1-1-1-1-1-1-1-1-1-1-1i3i3−i3−i3−i3−i3i3i3-2-2000000111111i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3000000000000
χ552222-2-2-1-2222-22-1-1-1-1-1-1-1-22-2-2-2-2-211000011-1-1-1-111111111−i3−i3i3i3i3i3−i3−i32200000011-1-1-1-1−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3000000000000
χ562222-2-2-1-2222-22-1-1-1-1-1-1-1-22-2-2-2-2-211000011-1-1-1-111111111i3i3−i3−i3−i3−i3i3i32200000011-1-1-1-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3000000000000
χ572222-2-2-1-2-222-2-2-1-1-1-1-1-1-12-200002110000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300002-2-22-1-1i3−i3i3−i3i3−i3−i3i3-11-111-11-1000000000000
χ582222-2-2-1-2-222-2-2-1-1-1-1-1-1-12-200002110000111111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000-222-2-1-1i3−i3i3−i3−i3i3i3−i31-11-1-11-11000000000000
χ592222-2-2-1-2-222-2-2-1-1-1-1-1-1-12-200002110000111111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000-222-2-1-1−i3i3−i3i3i3−i3−i3i31-11-1-11-11000000000000
χ602222-2-2-1-2-222-2-2-1-1-1-1-1-1-12-200002110000111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300002-2-22-1-1−i3i3−i3i3−i3i3i3−i3-11-111-11-1000000000000
χ6122-2-22-2220-22-202-2-2-2-22200000002-22i−2i2i−2i2-20000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000−i2i2−i2i22−22−20000
χ6222-2-22-2220-22-202-2-2-2-22200000002-22i−2i2i−2i2-20000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000i2−i2i2−i2−22−220000
χ6322-2-22-2220-22-202-2-2-2-22200000002-2−2i2i−2i2i2-2000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−i2i2−i2i2−22−220000
χ6422-2-22-2220-22-202-2-2-2-22200000002-2−2i2i−2i2i2-2000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000i2−i2i2−i22−22−20000
χ6522-2-22-22-202-2202-2-222-2-200000002-22-2-22-220000000000002-22-2-22-2200000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ6622-2-22-22-202-2202-2-222-2-200000002-22-2-22-220000000000002-22-2-22-2200000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ6722-2-22-22-202-2202-2-222-2-200000002-2-222-2-22000000000000-22-222-22-200000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ6822-2-22-22-202-2202-2-222-2-200000002-2-222-2-22000000000000-22-222-22-200000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ6944-4-44-4-240-44-40-22222-2-20000000-224i−4i4i−4i-22000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000
χ7044-4-44-4-240-44-40-22222-2-20000000-22−4i4i−4i4i-220000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000
χ7144-4-44-4-2-404-440-222-2-2220000000-224-4-442-2000000000000-22-222-22-200000000000000000000000000000000000000
χ7244-4-44-4-2-404-440-222-2-2220000000-22-444-42-20000000000002-22-2-22-2200000000000000000000000000000000000000
χ7344-4-4-444404-4-404-4-444-4-40000000-4400004-40000000000000000000000000000000000000000000000000000000000
χ7444-4-4-444-40-44404-4-4-4-4440000000-440000-440000000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-2404-4-40-222-2-22200000002-20000-22000000000000−2i32i32i3−2i3−2i32i32i3−2i300000000000000000000000000000000000000
χ7644-4-4-44-2404-4-40-222-2-22200000002-20000-220000000000002i3−2i3−2i32i32i3−2i3−2i32i300000000000000000000000000000000000000
χ7744-4-4-44-2-40-4440-22222-2-200000002-200002-200000000000023−23−2323−232323−2300000000000000000000000000000000000000
χ7844-4-4-44-2-40-4440-22222-2-200000002-200002-2000000000000−232323−2323−23−232300000000000000000000000000000000000000
χ794-44-400404000-4-44-4000000004i−4i0000000004-40000004i−4i4i−4i0000000000000000000000000000000000000000000000
χ804-44-400404000-4-44-400000000−4i4i0000000004-4000000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ814-44-40040-40004-44-40000004-400000000000-44004-44-400000000000000000000000000000000000000000000000000
χ824-44-40040-40004-44-4000000-4400000000000-4400-44-4400000000000000000000000000000000000000000000000000
χ834-44-400-204000-42-2223−2323−2300004i−4i000000000-2223−23−2i32i32i3−2i3−2i2i−2i2i0000000000000000000000000000000000000000000000
χ844-44-400-204000-42-2223−2323−230000−4i4i000000000-2223−232i3−2i3−2i32i32i−2i2i−2i0000000000000000000000000000000000000000000000
χ854-44-400-204000-42-22−2323−232300004i−4i000000000-22−23232i3−2i3−2i32i3−2i2i−2i2i0000000000000000000000000000000000000000000000
χ864-44-400-204000-42-22−2323−23230000−4i4i000000000-22−2323−2i32i32i3−2i32i−2i2i−2i0000000000000000000000000000000000000000000000
χ874-44-400-20-400042-2223−2323−23004-4000000000002-2−2323-22-2223−23−23230000000000000000000000000000000000000000000000
χ884-44-400-20-400042-2223−2323−2300-44000000000002-2−23232-22-2−232323−230000000000000000000000000000000000000000000000
χ894-44-400-20-400042-22−2323−2323004-4000000000002-223−23-22-22−232323−230000000000000000000000000000000000000000000000
χ904-44-400-20-400042-22−2323−232300-44000000000002-223−232-22-223−23−23230000000000000000000000000000000000000000000000
χ918-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000000000
χ938-8-8800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000000000

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