Finite Group Databasebeta

← Group #10710657

Character table — Group #10710657

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222244444444444444444488888888888812121212121212121616161616161616161616162424242448484848
order12222234444666222244446612121212121212122466666612121212222244448888242424242424242444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111111111ii−i−iiiii−i−i−i−i-1-1-1-1ii−i−i
χ61111111111111111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-111111111−i−iii−i−i−i−iiiii-1-1-1-1−i−iii
χ71111111111111111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−i1111−i−iii
χ81111111111111111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii1111ii−i−i
χ91111111-1-1-1-11111111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-11-11-1
χ101111111-1-1-1-11111111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-11111-1-1-11-11
χ111111111-1-1-1-11111111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111-11-111-1-111-1-1-1-111-11-11
χ121111111-1-1-1-11111111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-11-1-111-1-111-1-1111-11-1
χ131111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1i−i−iiii−i−i−i−iii-1-111i−i−ii
χ141111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1−iii−i−i−iiiii−i−i-1-111−iii−i
χ151111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111i−i−iiii−i−i−i−iii11-1-1−iii−i
χ161111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111−iii−i−i−iiiii−i−i11-1-1i−i−ii
χ1722222222222222-2-222-2-2-2-2222222-2-2-2-2-22-2-222-2-2-2-2220000000000000000000000000000
χ1822222222222222-2-2-2-2-2-22222222222222-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ192222222-2-2-2-2222-2-22222-2-222-2-2-2-2-2-2-2-22-2-2-2222222-2-20000000000000000000000000000
χ202222222-2-2-2-2222-2-2-2-2222222-2-2-2-22222-22-2-2-2-2-2-222220000000000000000000000000000
χ21222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ22222222-12222-1-1-122222222-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ23222222-12222-1-1-122-2-222-2-2-1-1-1-1-1-11111-2-2-1-11111-1-111000000002i2i−2i−2i−i−i−i−iiiii00000000
χ24222222-12222-1-1-122-2-222-2-2-1-1-1-1-1-11111-2-2-1-11111-1-11100000000−2i−2i2i2iiiii−i−i−i−i00000000
χ25222222-12222-1-1-1-2-222-2-2-2-2-1-1-1-1-1-11111-2211-1-11111-1-10000000000003−33−33−33−300000000
χ26222222-12222-1-1-1-2-222-2-2-2-2-1-1-1-1-1-11111-2211-1-11111-1-1000000000000−33−33−33−3300000000
χ27222222-12222-1-1-1-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-12-21111-1-11111000000000000−i3i3−i3i3i3−i3i3−i300000000
χ28222222-12222-1-1-1-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-12-21111-1-11111000000000000i3−i3i3−i3−i3i3−i3i300000000
χ29222222-1-2-2-2-2-1-1-12222-2-222-1-11111-1-1-1-1-2-2-1-1-1-1111111000000002-22-2-1-111-1-11100000000
χ30222222-1-2-2-2-2-1-1-12222-2-222-1-11111-1-1-1-1-2-2-1-1-1-111111100000000-22-2211-1-111-1-100000000
χ31222222-1-2-2-2-2-1-1-122-2-2-2-2-2-2-1-11111111122-1-111-1-111-1-1000000002i−2i−2i2i−i−iiiii−i−i00000000
χ32222222-1-2-2-2-2-1-1-122-2-2-2-2-2-2-1-11111111122-1-111-1-111-1-100000000−2i2i2i−2iii−i−i−i−iii00000000
χ33222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-1111111112-211-1-1-1-1-1-1110000000000003−3−333−3−3300000000
χ34222222-1-2-2-2-2-1-1-1-2-22222-2-2-1-1111111112-211-1-1-1-1-1-111000000000000−333−3−333−300000000
χ35222222-1-2-2-2-2-1-1-1-2-2-2-22222-1-11111-1-1-1-1-22111111-1-1-1-1000000000000−i3i3i3−i3i3−i3−i3i300000000
χ36222222-1-2-2-2-2-1-1-1-2-2-2-22222-1-11111-1-1-1-1-22111111-1-1-1-1000000000000i3−i3−i3i3−i3i3i3−i300000000
χ372-2-22-2220000-2-222-22-2002-22-2000022-2-2002-22-2000000000022-2-2000000000000002-20000
χ382-2-22-2220000-2-222-22-2002-22-2000022-2-2002-22-20000000000-2-22200000000000000-220000
χ392-2-22-2220000-2-222-2-2200-222-20000-2-222002-2-22000000000022-2-200000000000000-220000
χ402-2-22-2220000-2-222-2-2200-222-20000-2-222002-2-220000000000-2-222000000000000002-20000
χ412-2-22-2220000-2-22-222-200-222-20000-2-22200-222-200000022-2-200000000000000002-2000000
χ422-2-22-2220000-2-22-222-200-222-20000-2-22200-222-2000000-2-2220000000000000000-22000000
χ432-2-22-2220000-2-22-22-22002-22-2000022-2-200-22-2200000022-2-20000000000000000-22000000
χ442-2-22-2220000-2-22-22-22002-22-2000022-2-200-22-22000000-2-22200000000000000002-2000000
χ454444-4-4444-4-444400000000-4-444-4-400000000000000000000000000000000000000000000
χ464444-4-44-4-44444400000000-4-4-4-44400000000000000000000000000000000000000000000
χ474444-4-4-244-4-4-2-2-20000000022-2-222−2i32i3−2i32i3000000−2i32i300000000000000000000000000000000
χ484444-4-4-244-4-4-2-2-20000000022-2-2222i3−2i32i3−2i30000002i3−2i300000000000000000000000000000000
χ494444-4-4-2-4-444-2-2-2000000002222-2-2−2i32i3−2i32i30000002i3−2i300000000000000000000000000000000
χ504444-4-4-2-4-444-2-2-2000000002222-2-22i3−2i32i3−2i3000000−2i32i300000000000000000000000000000000
χ5144-4-4004004i−4i4-4-40000000000004i−4i00000000000000002-22-22i−2i2i−2i00000000000000000000
χ5244-4-4004004i−4i4-4-40000000000004i−4i0000000000000000-22-22−2i2i−2i2i00000000000000000000
χ5344-4-400400−4i4i4-4-4000000000000−4i4i00000000000000002-22-2−2i2i−2i2i00000000000000000000
χ5444-4-400400−4i4i4-4-4000000000000−4i4i0000000000000000-22-222i−2i2i−2i00000000000000000000
χ554-44-40044i−4i00-44-400000000004i−4i0000000000000000002-2-222i−2i−2i2i00000000000000000000
χ564-44-40044i−4i00-44-400000000004i−4i000000000000000000-222-2−2i2i2i−2i00000000000000000000
χ574-44-4004−4i4i00-44-40000000000−4i4i0000000000000000002-2-22−2i2i2i−2i00000000000000000000
χ584-44-4004−4i4i00-44-40000000000−4i4i000000000000000000-222-22i−2i−2i2i00000000000000000000
χ594-4-444-440000-4-4400004-400-4400000000000000004-4000000000000000000000000000000
χ604-4-444-440000-4-440000-4400-440000000000000000-44000000000000000000000000000000
χ614-4-444-4-2000022-200004-4002-20000−2i32i32i3−2i300000000-22−2i32i30000000000000000000000000000
χ624-4-444-4-2000022-200004-4002-200002i3−2i3−2i32i300000000-222i3−2i30000000000000000000000000000
χ634-4-444-4-2000022-20000-44002-20000−2i32i32i3−2i3000000002-22i3−2i30000000000000000000000000000
χ644-4-444-4-2000022-20000-44002-200002i3−2i3−2i32i3000000002-2−2i32i30000000000000000000000000000
χ654-4-44-44-2000022-24-44-4004-4-220000-2-22200-22-220000000000000000000000000000000000
χ664-4-44-44-2000022-24-4-4400-44-22000022-2-200-222-20000000000000000000000000000000000
χ674-4-44-44-2000022-2-444-400-44-22000022-2-2002-2-220000000000000000000000000000000000
χ684-4-44-44-2000022-2-44-44004-4-220000-2-222002-22-20000000000000000000000000000000000
χ6988-8-800-4008i−8i-444000000000000−4i4i00000000000000000000000000000000000000000000
χ7088-8-800-400−8i8i-4440000000000004i−4i00000000000000000000000000000000000000000000
χ718-88-800-48i−8i004-440000000000−4i4i0000000000000000000000000000000000000000000000
χ728-88-800-4−8i8i004-4400000000004i−4i0000000000000000000000000000000000000000000000

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