Finite Group Databasebeta

← Group #10846238

Character table — Group #10846238

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222444444446688888888888881212121212121212121616161616161616161616161616242424242424244848
order1222223444466666881212121244244488888242424244448888884681212121212242424242424244488828
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1111-1-111111111111111-11-1-1-11-1-111-1-1-1-111-1-1-1-11-1-1
χ3111111111111111111111111-111-1-1-1-1-11111111111-1-1-1-11-1-111-111-1-1-1-1-1-1-1-111-1-111-1
χ4111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-1111-11
χ51111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-11-1-1111-1-111111-1-1-1-1-1-1-1-1-1-11-1-1-11-1-111-1-1-1-1-1-11111-111
χ71111111111111111111111-1-1-111-1-1-1-1-111111-1-1-1-1-111111-1-111-111-1-1-1-1-1-111-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-11111-1-11-1-1-1-1-1-1-111111111-1-1-11-1
χ91111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111111-1-1-1-111-1-11111-1-1-1-11
χ101111111111111111-1-11111111-1-11-1-111-1-1-1-1-1111-1-1-1-1-1-111-1-1-1111-1-1-1-11111-1-111-11-1
χ111111111111111111-1-1111111-111-11111-1-1-1-1-1111-1-11111-1-1-111-1-1-111-1-111-1-11111-1-1-1
χ121111111111111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1111-1-111111-11-1-1-1111111-1-1-1-1-1-1-1-1-111
χ131111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-111111-1-1-1-111-1-1-1-1-1-11111-1
χ141111111111111111-1-11111-1-11-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1111-1-1-1-111-1-111-1-11-11
χ151111111111111111-1-11111-1-1-111-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-1111
χ161111111111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11-1-1-1111111-1-11111111-1-1
χ172222222-2-2-2-22222200-2-2-2-22200002i−2i00000002-2-2002i2i−2i−2i000000002i−2i0000000000000
χ182222222-2-2-2-22222200-2-2-2-2220000−2i2i00000002-2-200−2i−2i2i2i00000000−2i2i0000000000000
χ192222222-2-2-2-22222200-2-2-2-2-2-200002i−2i0000000-22200−2i−2i2i2i000000002i−2i0000000000000
χ202222222-2-2-2-22222200-2-2-2-2-2-20000−2i2i0000000-222002i2i−2i−2i00000000−2i2i0000000000000
χ21222222-12222-1-1-1-1-122-1-1-1-100222222222-1-1-1-10000000002-12-1-1-1-1-1-1-1-1-1-1-1000000000
χ22222222-12222-1-1-1-1-122-1-1-1-1002-2-2222-2-22-1-1-1-1000000000-2-1-211-111-1-11111000000000
χ23222222-12222-1-1-1-1-122-1-1-1-100-222-2-2-2-2-22-1-1-1-100000000021-2-1-11-1-1111111000000000
χ24222222-12222-1-1-1-1-122-1-1-1-100-2-2-2-2-2-2222-1-1-1-1000000000-2121111111-1-1-1-1000000000
χ25222222-12222-1-1-1-1-1-2-2-1-1-1-1002222-2-2-2-2-21111000000000-2-12-1-1-11111-1-111000000000
χ26222222-12222-1-1-1-1-1-2-2-1-1-1-1002-2-22-2-222-211110000000002-1-211-1-1-11111-1-1000000000
χ27222222-12222-1-1-1-1-1-2-2-1-1-1-100-222-22222-21111000000000-21-2-1-1111-1-111-1-1000000000
χ28222222-12222-1-1-1-1-1-2-2-1-1-1-100-2-2-2-222-2-2-21111000000000212111-1-1-1-1-1-111000000000
χ292222-2-222-2-22222-2-222-222-22200000000-222-2-2-22-222000000000000000000000000-200
χ302222-2-222-2-22222-2-222-222-2-2-200000000-222-2-22-22-2-2000000000000000000000000200
χ312222-2-222-2-22222-2-2-2-2-222-222000000002-2-222-22-2-2-2000000000000000000000000200
χ322222-2-222-2-22222-2-2-2-2-222-2-2-2000000002-2-2222-2222000000000000000000000000-200
χ332222-2-22-222-2222-2-2002-2-2222200-2000000000-2-2200000002000-200000000-220000000
χ342222-2-22-222-2222-2-2002-2-2222-2002000000000-2-220000000-20002000000002-20000000
χ352222-2-22-222-2222-2-2002-2-22-2-2200-200000000022-200000002000-2000000002-20000000
χ362222-2-22-222-2222-2-2002-2-22-2-2-200200000000022-20000000-2000200000000-220000000
χ372-2-222-2222-2-2-2-222-20022-2-20002i−2i0000000000000002i−2i2i−2i0002i−2i00000000000002-2000
χ382-2-222-2222-2-2-2-222-20022-2-20002i−2i000000000000000−2i2i−2i2i0002i−2i0000000000000-22000
χ392-2-222-2222-2-2-2-222-20022-2-2000−2i2i0000000000000002i−2i2i−2i000−2i2i0000000000000-22000
χ402-2-222-2222-2-2-2-222-20022-2-2000−2i2i000000000000000−2i2i−2i2i000−2i2i00000000000002-2000
χ412-2-222-22-2-222-2-222-200-2-222000000002-200000000002-2-220000000000002-2002-200000
χ422-2-222-22-2-222-2-222-200-2-222000000002-20000000000-222-20000000000002-200-2200000
χ432-2-222-22-2-222-2-222-200-2-22200000000-2200000000002-2-22000000000000-2200-2200000
χ442-2-222-22-2-222-2-222-200-2-22200000000-220000000000-222-2000000000000-22002-200000
χ45444444-2-4-4-4-4-2-2-2-2-20022220000004i−4i000000000000000000000000−2i2i0000000000000
χ46444444-2-4-4-4-4-2-2-2-2-2002222000000−4i4i0000000000000000000000002i−2i0000000000000
χ474444-4-4-24-4-44-2-2-222442-2-220000000000-4-2-22200000000000000000000000000000000
χ484444-4-4-24-4-44-2-2-222-4-42-2-220000000000422-2-200000000000000000000000000000000
χ494444-4-4-2-444-4-2-2-22200-222-200400-40000000000000000000-2000200000000000000000
χ504444-4-4-2-444-4-2-2-22200-222-200-400400000000000000000002000-200000000000000000
χ514-44-40040000-44-400−2i22i200004i−4i000000000−2i22i20000022−22000000000000000000000000000
χ524-44-40040000-44-400−2i22i20000−4i4i000000000−2i22i200000−2222000000000000000000000000000
χ534-44-40040000-44-4002i2−2i200004i−4i0000000002i2−2i200000−2222000000000000000000000000000
χ544-44-40040000-44-4002i2−2i20000−4i4i0000000002i2−2i20000022−22000000000000000000000000000
χ554-4-444-4-244-4-422-2-2200-2-2220004i−4i0000000000000000000000−2i2i000000000000000000
χ564-4-444-4-244-4-422-2-2200-2-222000−4i4i00000000000000000000002i−2i000000000000000000
χ574-4-444-4-2-4-44422-2-220022-2-2000000004-400000000000000000000000000-22000000000
χ584-4-444-4-2-4-44422-2-220022-2-200000000-44000000000000000000000000002-2000000000
χ594-4-44-4444-44-4-4-44-4400-44-4400000000000000000000000000000000000000000000000
χ604-4-44-444-44-44-4-44-44004-44-400000000000000000000000000000000000000000000000
χ614-4-44-44-24-44-422-22-2002-22-2000000000000000000000000000000−2i32i3000000000000000
χ624-4-44-44-24-44-422-22-2002-22-20000000000000000000000000000002i3−2i3000000000000000
χ634-4-44-44-2-44-4422-22-200-22-22000000000000000000000000000000000023−2300000000000
χ644-4-44-44-2-44-4422-22-200-22-220000000000000000000000000000000000−232300000000000
χ6588-8-800800008-8-80000000000000000000000000000000000000000000000000000000
χ6688-8-800-40000-4440000000000000000000002i6−2i600000000000000000000000000000000
χ6788-8-800-40000-444000000000000000000000−2i62i600000000000000000000000000000000
χ688-88-800-400004-4400−4i24i20000000000000002i2−2i20000000000000000000000000000000000
χ698-88-800-400004-44004i2−4i2000000000000000−2i22i20000000000000000000000000000000000

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