Finite Group Databasebeta

← Group #10713872

Character table — Group #10713872

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size111122222244444444668888888888888888121212161616161616161616161616162424242424242424484848
order12222236664444446644448888121212121212121212124444881212242424242424242444448888488
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1
χ311111111111111111111-1-111111111-1-1-1-111111-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1
χ411111111111111111111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-1-1-1111111-1-1-1-1-1-1-111
χ5111111111111111111-1-11111111111111111-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111-1-111-1-1-1-11111111111-1-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ7111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-11111111-1-1
χ9111111111111-1-1-1-1111111ii−i−i11-1-11111-1-11-1-1-1i−i-1-1ii−i−iii−i−i1-111ii−i−i-1i−i
χ10111111111111-1-1-1-1111111−i−iii11-1-11111-1-11-1-1-1−ii-1-1−i−iii−i−iii1-111−i−iii-1−ii
χ11111111111111-1-1-1-11111-1-1ii−i−i11-1-1-1-1-1-1-1-11-1-11−ii11ii−i−i−i−iii1-1-1-1ii−i−i1−ii
χ12111111111111-1-1-1-11111-1-1−i−iii11-1-1-1-1-1-1-1-11-1-11i−i11−i−iiiii−i−i1-1-1-1−i−iii1i−i
χ13111111111111-1-1-1-111-1-111ii−i−i11-1-11111-1-1-111-1i−i-1-1ii−i−iii−i−i-11-1-1−i−iii1−ii
χ14111111111111-1-1-1-111-1-111−i−iii11-1-11111-1-1-111-1−ii-1-1−i−iii−i−iii-11-1-1ii−i−i1i−i
χ15111111111111-1-1-1-111-1-1-1-1ii−i−i11-1-1-1-1-1-1-1-1-1111−ii11ii−i−i−i−iii-1111−i−iii-1i−i
χ16111111111111-1-1-1-111-1-1-1-1−i−iii11-1-1-1-1-1-1-1-1-1111i−i11−i−iiiii−i−i-1111ii−i−i-1−ii
χ172222222222-2-22-2-222222000000-2-22-200002-22-2-20000000000000-22000000000
χ182222222222-2-22-2-2222-2-2000000-2-22-200002-2-22200000000000002-2000000000
χ192222222222-2-2-222-22222000000-2-2-220000-222220000000000000-2-2000000000
χ202222222222-2-2-222-222-2-2000000-2-2-220000-22-2-2-2000000000000022000000000
χ21222222-1-1-1-1222222-1-100222222-1-1-1-1-1-1-1-1-1-1000222-1-1-1-1-1-1-1-1-1-100000000000
χ22222222-1-1-1-1222222-1-10022-2-2-2-2-1-1-1-1-1-1-1-1-1-10002-2-2-1-11111111100000000000
χ23222222-1-1-1-1222222-1-100-2-22222-1-1-1-11111-1-1000-2-2-211-1-1-1-1111100000000000
χ24222222-1-1-1-1222222-1-100-2-2-2-2-2-2-1-1-1-11111-1-1000-222111111-1-1-1-100000000000
χ25222222-1-1-1-122-2-2-2-2-1-100222i2i−2i−2i-1-111-1-1-1-111000-22i−2i11−i−iii−i−iii00000000000
χ26222222-1-1-1-122-2-2-2-2-1-10022−2i−2i2i2i-1-111-1-1-1-111000-2−2i2i11ii−i−iii−i−i00000000000
χ27222222-1-1-1-122-2-2-2-2-1-100-2-22i2i−2i−2i-1-1111111110002−2i2i-1-1−i−iiiii−i−i00000000000
χ28222222-1-1-1-122-2-2-2-2-1-100-2-2−2i−2i2i2i-1-11111111100022i−2i-1-1ii−i−i−i−iii00000000000
χ2922-2-22-22-2-222-222-2-22-200002-22-22-22-20000-22000000002-22-2000000000000000
χ3022-2-22-22-2-222-222-2-22-20000-22-222-22-20000-2200000000-22-22000000000000000
χ3122-2-22-22-2-222-2-2-2222-200002i−2i−2i2i2-2-2200002-2000000002i−2i−2i2i000000000000000
χ3222-2-22-22-2-222-2-2-2222-20000−2i2i2i−2i2-2-2200002-200000000−2i2i2i−2i000000000000000
χ3322-2-22-22-2-22-222-22-22-200000000-22220000-2-2000000000000000000002-22-2000
χ3422-2-22-22-2-22-222-22-22-200000000-22220000-2-200000000000000000000-22-22000
χ3522-2-22-22-2-22-22-22-222-200000000-22-2-2000022000000000000000000002i−2i−2i2i000
χ3622-2-22-22-2-22-22-22-222-200000000-22-2-200002200000000000000000000−2i2i2i−2i000
χ3722-2-22-2-111-12-222-2-2-1100002-22-2-11-1133−3−31-10000003−3-11-113−33−300000000000
χ3822-2-22-2-111-12-222-2-2-1100002-22-2-11-11−3−3331-1000000−33-11-11−33−3300000000000
χ3922-2-22-2-111-12-222-2-2-110000-22-22-11-1133−3−31-10000003−31-11-1−33−3300000000000
χ4022-2-22-2-111-12-222-2-2-110000-22-22-11-11−3−3331-1000000−331-11-13−33−300000000000
χ4122-2-22-2-111-12-2-2-222-1100002i−2i−2i2i-111-133−3−3-11000000−33−iii−ii3−i3−i3i300000000000
χ4222-2-22-2-111-12-2-2-222-1100002i−2i−2i2i-111-1−3−333-110000003−3−iii−i−i3i3i3−i300000000000
χ4322-2-22-2-111-12-2-2-222-110000−2i2i2i−2i-111-133−3−3-11000000−33i−i−ii−i3i3i3−i300000000000
χ4422-2-22-2-111-12-2-2-222-110000−2i2i2i−2i-111-1−3−333-110000003−3i−i−iii3−i3−i3i300000000000
χ45444444-2-2-2-2-4-44-4-44-2-20000000022-220000-22000000000000000000000000000
χ46444444-2-2-2-2-4-4-444-4-2-200000000222-200002-2000000000000000000000000000
χ474444-4-44444000000-4-4440000000000000000-400000000000000000000000000
χ484444-4-44444000000-4-4-4-40000000000000000400000000000000000000000000
χ4944-4-44-4-222-2-444-44-4-22000000002-2-2-2000022000000000000000000000000000
χ5044-4-44-4-222-2-44-44-44-22000000002-2220000-2-2000000000000000000000000000
χ5144-4-4-444-4-44000000-4400000000000000000004i−4i000000000000000000000000
χ5244-4-4-444-4-44000000-440000000000000000000−4i4i000000000000000000000000
χ534-44-40044-4-4000000004-42-2000000002-22-2000000000000000000002-20000000
χ544-44-40044-4-4000000004-4-2200000000-22-2200000000000000000000-220000000
χ554-44-40044-4-400000000-442-2000000002-22-200000000000000000000-220000000
χ564-44-40044-4-400000000-44-2200000000-22-22000000000000000000002-20000000
χ578888-8-8-4-4-4-400000044000000000000000000000000000000000000000000000
χ5888-8-8-88-444-40000004-4000000000000000000000000000000000000000000000
χ598-88-800-4-44400000000004-400000000-22-2200000000000000000000000000000
χ608-88-800-4-4440000000000-44000000002-22-200000000000000000000000000000
χ618-8-88008-88-800000000000000000000000000000000000000000000000000000
χ628-8-8800-44-440000000000000000000023−23−232300000000000000000000000000000
χ638-8-8800-44-4400000000000000000000−232323−2300000000000000000000000000000

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