Finite Group Databasebeta

← Group #10769080

Character table — Group #10769080

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222444444444444444444448888888888888888888888888888888888242424242424242448484848
order1222223444466612121212222244446666661212121212122244444444666666121212121212121212121212121212121212888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111-1-11-1-11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11-1-11-1-11-11-11111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11-1-11-1-11-11-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-11-1-11-1-11-1111-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111
χ811111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-11-1-11-1-11-1111-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1
χ91111111-1-1-1-1111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1111-1-1-111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-111-1-111-1-11-11-1
χ101111111-1-1-1-1111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1111-1-1-111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-111-1-111-11-11
χ111111111-1-1-1-1111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-111-1-1-1-111-1-11111111111-1-111-1-1-11-11
χ121111111-1-1-1-1111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-111-1-1111-11-1
χ131111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-1111-1-11-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1111-1-11
χ141111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-1111-1-11-1-111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-111-1
χ151111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-11-11-111-1-1-1-1-111-1-111-1-11111-1-11111-1-111-1-1-1-111-111-1
χ161111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-11-11-11-111-1-1-1-1-111-1-111-1-11111-1-11111-1-1-1-11111-1-11-1-11
χ17222222222222222222-2-22222-2-222222222222200-200-20000-2-20000-2-2-2-200000000-2-20000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-20020020000-2-20000222200000000-2-20000000000000000
χ192222222-2-2-2-2222-2-2-2-22222-2-2-2-2222222-2-2-2-2-2-200-20020000220000-2-22200000000-2-20000000000000000
χ202222222-2-2-2-2222-2-2-2-222-2-222-2-222-2-2-2-2-2-2222200200-2000022000022-2-200000000-2-20000000000000000
χ21222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-22-2-22-2-2-2-2-1-11111-1-1-1-111111111-1-11111000000000000
χ23222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-11111-1-111112-2-22-2-22-22-2-1-1-1-1111111-1-1-1-11111-1-1-1-111000000000000
χ24222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-11111-1-11111-22-2-22-2-22-22-1-111-1-111111111-1-1-1-1-1-111-1-1000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-100-200-2000011−i3i3−i3i31111−i3i3−i3i3−i3i3−i3i311−i3i3−i3i3000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-1-1-1-1-1-1-1-100-200-2000011i3−i3i3−i31111i3−i3i3−i3i3−i3i3−i311i3−i3i3−i3000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-11111002002000011−i3i3i3−i3-1-1-1-1−i3i3−i3i3i3−i3i3−i311−i3i3i3−i3000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111-1-11111002002000011i3−i3−i3i3-1-1-1-1i3−i3i3−i3−i3i3−i3i311i3−i3−i3i3000000000000
χ29222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-111111100-20020000-1-1−i3i3−i3i311-1-1−i3i3i3−i3−i3i3i3−i311i3−i3i3−i3000000000000
χ30222222-1-2-2-2-2-1-1-111112222-2-2-2-2-1-1-1-1-1-111111100-20020000-1-1i3−i3i3−i311-1-1i3−i3−i3i3i3−i3−i3i311−i3i3−i3i3000000000000
χ31222222-1-2-2-2-2-1-1-1111122-2-222-2-2-1-1111111-1-1-1-100200-20000-1-1−i3i3i3−i3-1-111−i3i3i3−i3i3−i3−i3i311i3−i3−i3i3000000000000
χ32222222-1-2-2-2-2-1-1-1111122-2-222-2-2-1-1111111-1-1-1-100200-20000-1-1i3−i3−i3i3-1-111i3−i3−i3i3−i3i3i3−i311−i3i3i3−i3000000000000
χ33222222-1-2-2-2-2-1-1-11111-2-222-2-222-1-1-1-1-1-1111111222-2-2-222-2-211-1-1-1-1-1-111-1-111-1-111-1-11111000000000000
χ34222222-1-2-2-2-2-1-1-11111-2-222-2-222-1-1-1-1-1-1111111-2-2222-2-2-222111111-1-11111-1-111-1-1-1-1-1-1-1-1000000000000
χ35222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-12-2-2-2222-2-2211-1-11111-1-1-1-11111-1-1-1-111-1-1000000000000
χ36222222-1-2-2-2-2-1-1-11111-2-2-2-22222-1-1111111-1-1-1-1-22-22-22-222-21111-1-111-1-111-1-1-1-111-1-1-1-111000000000000
χ372222-2-2222-2-222222222-200002-2-2-20000-2-200000200-200-2022-2002200000000-2-2-2-22-20022000000000000
χ382222-2-2222-2-222222222-200002-2-2-20000-2-200000-20020020-22-200-2-20000000022222-200-2-2000000000000
χ392222-2-2222-2-22222222-220000-22-2-20000-2-20000200-200-2020-2222000000-2-2-2-20000-222200000000000000
χ402222-2-2222-2-22222222-220000-22-2-20000-2-20000-20020020-20-22-2-200000022220000-22-2-200000000000000
χ412222-2-22-2-222222-2-2-2-22-20000-22-2-20000220000200200-20-202-222000000-2-2220000-22-2-200000000000000
χ422222-2-22-2-222222-2-2-2-22-20000-22-2-20000220000-200-20020202-2-2-200000022-2-20000-222200000000000000
χ432222-2-22-2-222222-2-2-2-2-2200002-2-2-200002200000200200-20-2-22002200000000-2-2222-200-2-2000000000000
χ442222-2-22-2-222222-2-2-2-2-2200002-2-2-200002200000-200-200202-2200-2-20000000022-2-22-20022000000000000
χ452222-2-2-122-2-2-1-1-1-1-1-1-12-200002-211−i3−i3i3i311−i3−i3i3i30200-200-202-11−i3i3-1-1−i3i3−i3i3i3−i3i3−i31111-11−i3i3-1-1000000000000
χ462222-2-2-122-2-2-1-1-1-1-1-1-12-200002-211−i3−i3i3i311−i3−i3i3i30-20020020-2-11i3−i311−i3i3−i3i3−i3i3−i3i3-1-1-1-1-11i3−i311000000000000
χ472222-2-2-122-2-2-1-1-1-1-1-1-12-200002-211i3i3−i3−i311i3i3−i3−i30200-200-202-11i3−i3-1-1i3−i3i3−i3−i3i3−i3i31111-11i3−i3-1-1000000000000
χ482222-2-2-122-2-2-1-1-1-1-1-1-12-200002-211i3i3−i3−i311i3i3−i3−i30-20020020-2-11−i3i311i3−i3i3−i3i3−i3i3−i3-1-1-1-1-11−i3i311000000000000
χ492222-2-2-122-2-2-1-1-1-1-1-1-1-220000-2211−i3−i3i3i311−i3−i3i3i3200-200-20201-1-1-1−i3i3i3−i3i3−i31111i3−i3i3−i31-1-1-1−i3i3000000000000
χ502222-2-2-122-2-2-1-1-1-1-1-1-1-220000-2211−i3−i3i3i311−i3−i3i3i3-20020020-201-111i3−i3i3−i3i3−i3-1-1-1-1−i3i3−i3i31-111i3−i3000000000000
χ512222-2-2-122-2-2-1-1-1-1-1-1-1-220000-2211i3i3−i3−i311i3i3−i3−i3200-200-20201-1-1-1i3−i3−i3i3−i3i31111−i3i3−i3i31-1-1-1i3−i3000000000000
χ522222-2-2-122-2-2-1-1-1-1-1-1-1-220000-2211i3i3−i3−i311i3i3−i3−i3-20020020-201-111−i3i3−i3i3−i3i3-1-1-1-1i3−i3i3−i31-111−i3i3000000000000
χ532222-2-2-1-2-222-1-1-111112-20000-2211−i3−i3i3i3-1-1i3i3−i3−i3200200-20-20-11-1-1−i3i3i3−i3−i3i311-1-1i3−i3−i3i31-111i3−i3000000000000
χ542222-2-2-1-2-222-1-1-111112-20000-2211−i3−i3i3i3-1-1i3i3−i3−i3-200-2002020-1111i3−i3i3−i3−i3i3-1-111−i3i3i3−i31-1-1-1−i3i3000000000000
χ552222-2-2-1-2-222-1-1-111112-20000-2211i3i3−i3−i3-1-1−i3−i3i3i3200200-20-20-11-1-1i3−i3−i3i3i3−i311-1-1−i3i3i3−i31-111−i3i3000000000000
χ562222-2-2-1-2-222-1-1-111112-20000-2211i3i3−i3−i3-1-1−i3−i3i3i3-200-2002020-1111−i3i3−i3i3i3−i3-1-111i3−i3−i3i31-1-1-1i3−i3000000000000
χ572222-2-2-1-2-222-1-1-11111-2200002-211−i3−i3i3i3-1-1i3i3−i3−i30200200-20-21-1−i3i3-1-1−i3i3i3−i3i3−i3−i3i311-1-1-11i3−i311000000000000
χ582222-2-2-1-2-222-1-1-11111-2200002-211−i3−i3i3i3-1-1i3i3−i3−i30-200-2002021-1i3−i311−i3i3i3−i3−i3i3i3−i3-1-111-11−i3i3-1-1000000000000
χ592222-2-2-1-2-222-1-1-11111-2200002-211i3i3−i3−i3-1-1−i3−i3i3i30200200-20-21-1i3−i3-1-1i3−i3−i3i3−i3i3i3−i311-1-1-11−i3i311000000000000
χ602222-2-2-1-2-222-1-1-11111-2200002-211i3i3−i3−i3-1-1−i3−i3i3i30-200-2002021-1−i3i311i3−i3−i3i3i3−i3−i3i3-1-111-11i3−i3-1-1000000000000
χ612-22-22-222i−2i2i−2i2-2-22i2i−2i−2i002-22i−2i002-22-22-22i−2i2i−2i2i−2i00000000000000000000000000000000002−2−i2i22−2−i2i20000
χ622-22-22-222i−2i2i−2i2-2-22i2i−2i−2i002-22i−2i002-22-22-22i−2i2i−2i2i−2i0000000000000000000000000000000000−22i2−i2−22i2−i20000
χ632-22-22-222i−2i2i−2i2-2-22i2i−2i−2i00-22−2i2i002-2-22-222i−2i−2i2i−2i2i00000000000000000000000000000000002−2−i2i2−22i2−i20000
χ642-22-22-222i−2i2i−2i2-2-22i2i−2i−2i00-22−2i2i002-2-22-222i−2i−2i2i−2i2i0000000000000000000000000000000000−22i2−i22−2−i2i20000
χ652-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i002-2−2i2i002-22-22-2−2i2i−2i2i−2i2i00000000000000000000000000000000002−2i2−i22−2i2−i20000
χ662-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i002-2−2i2i002-22-22-2−2i2i−2i2i−2i2i0000000000000000000000000000000000−22−i2i2−22−i2i20000
χ672-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i00-222i−2i002-2-22-22−2i2i2i−2i2i−2i00000000000000000000000000000000002−2i2−i2−22−i2i20000
χ682-22-22-22−2i2i−2i2i2-2-2−2i−2i2i2i00-222i−2i002-2-22-22−2i2i2i−2i2i−2i0000000000000000000000000000000000−22−i2i22−2i2−i20000
χ694-44-44-4-24i−4i4i−4i-222−2i−2i2i2i004-44i−4i00-22-22-22−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ704-44-44-4-24i−4i4i−4i-222−2i−2i2i2i00-44−4i4i00-222-22-2−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ714-44-44-4-2−4i4i−4i4i-2222i2i−2i−2i004-4−4i4i00-22-22-222i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000
χ724-44-44-4-2−4i4i−4i4i-2222i2i−2i−2i00-444i−4i00-222-22-22i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000
χ734-44-4-4444i−4i−4i4i4-4-44i4i−4i−4i00000000-440000−4i4i00000000000000000000000000000000000000000000000000
χ744-44-4-444−4i4i4i−4i4-4-4−4i−4i4i4i00000000-4400004i−4i00000000000000000000000000000000000000000000000000
χ754-44-4-44-24i−4i−4i4i-222−2i−2i2i2i000000002-2−2i32i32i3−2i32i−2i23−23−23230000000000000000000000000000000000000000000000
χ764-44-4-44-24i−4i−4i4i-222−2i−2i2i2i000000002-22i3−2i3−2i32i32i−2i−232323−230000000000000000000000000000000000000000000000
χ774-44-4-44-2−4i4i4i−4i-2222i2i−2i−2i000000002-2−2i32i32i3−2i3−2i2i−232323−230000000000000000000000000000000000000000000000
χ784-44-4-44-2−4i4i4i−4i-2222i2i−2i−2i000000002-22i3−2i3−2i32i3−2i2i23−23−23230000000000000000000000000000000000000000000000
χ7988-8-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-400004-4443−4343−43000000000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-400004-44−4343−4343000000000000000000000000000000000000000000000000000000000000000000
χ828-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000
χ838-8-8800-4000044-4−4i34i34i3−4i3000000000000000000000000000000000000000000000000000000000000000000
χ848-8-8800-4000044-44i3−4i3−4i34i3000000000000000000000000000000000000000000000000000000000000000000

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