Finite Group Databasebeta

← Group #10909575

Character table — Group #10909575

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1111222222222244444444888888888888888888888888812121616161616161616242424242424242424484848
order12222234444666668812121212222224446666666681212121224242424884681212122424244488888448
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-111-111-1-1-1-1-1-1111-1-1111111-11-1-1-11-1-1-1-111-1-1111-1-11
χ4111111111111111111111111-1-1-111-111-1-1-1-1-1-1111-1-11111-1-1-11-1-1-11-1-111-1-111-1-1-111-1
χ51111111111111111111111-1-111-1-1-1-1-1-11111-1-11-1-1-1-11111111-1-111-1-1-1-1-111-1-11-1-111-1
χ61111111111111111111111-1-111-1-1-1-1-1-11111-1-11-1-1-1-11111-1-11-1-111-1-1-111-1-111-111-1-11
χ71111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1111-1-111111111-1-11-1-1-1111111111-1-1-1-1-1
χ81111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1111-1-1111111-1-1-1-11-1-1-111-1-1-1-1-1-1-111111
χ91111111111111111-1-111111-11111-1111111111-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11-1-11-11
χ101111111111111111-1-111111-11111-1111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-11-1
χ111111111111111111-1-111111-1-1-1-11-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1111-1111-111-1-1-1-1111-1-1-111
χ121111111111111111-1-111111-1-1-1-11-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1111-1111111-1-1-1111-1-1
χ131111111111111111-1-11111-1111-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-111-1-1111-1-1-1-1111111-1-1
χ141111111111111111-1-11111-1111-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-1-1-1-1-111
χ151111111111111111-1-11111-11-1-11-111-1-1-1-1-1-111-1-1-111-1-1-1-11111-1111-1-111-1-1-1-1111-11-1
χ161111111111111111-1-11111-11-1-11-111-1-1-1-1-1-111-1-1-111-1-1-1-1-1-111-1111-1-1-1-11111-1-1-11-11
χ17222222-12222-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-12-1-1-1-1-1-1-1-1002-12-1-1-1-1-1000000000000
χ18222222-12222-1-1-1-1-122-1-1-1-122-2-2-222-2-1-11111112-1-111-1-1-1-100-2-1-211-111000000000000
χ19222222-12222-1-1-1-1-122-1-1-1-1-2-222-2-2-2-211-1-1-1-11121111-1-1-1-10021-2-1-1111000000000000
χ20222222-12222-1-1-1-1-122-1-1-1-1-2-2-2-22-2-22111111-1-1211-1-1-1-1-1-100-212111-1-1000000000000
χ21222222-12222-1-1-1-1-1-2-2-1-1-1-12-22222-22-1-1-1-1-1-1-1-1-2-1-1-1-1111100-21-211111000000000000
χ22222222-12222-1-1-1-1-1-2-2-1-1-1-12-2-2-2-22-2-2-1-1111111-2-1-111111100212-1-11-1-1000000000000
χ23222222-12222-1-1-1-1-1-2-2-1-1-1-1-2222-2-22-211-1-1-1-111-21111111100-2-1211-1-1-1000000000000
χ24222222-12222-1-1-1-1-1-2-2-1-1-1-1-22-2-22-222111111-1-1-211-1-11111002-1-2-1-1-111000000000000
χ252222-2-222-22-2222-2-222-2-22222000-2-2022000000-2-2-20022-2-20002000-200000000000000
χ262222-2-222-22-2222-2-222-2-222-2-2000220-2-2000000-2220022-2-2000-2000200000000000000
χ272222-2-222-22-2222-2-2-2-2-2-2222-2000-220220000002-2-200-2-222000-2000200000000000000
χ282222-2-222-22-2222-2-2-2-2-2-222-220002-20-2-200000022200-2-2220002000-200000000000000
χ292222-2-22-22-22222-2-20022-2-20000200-200000022000-2-200002200000000-220000-200000
χ302222-2-22-22-22222-2-20022-2-20000200-200000022000-2-20000-2-2000000002-20000200000
χ312222-2-22-22-22222-2-20022-2-20000-2002000000-2-200022000022000000002-20000-200000
χ322222-2-22-22-22222-2-20022-2-20000-2002000000-2-2000220000-2-200000000-220000200000
χ332222-2-2-12-22-2-1-1-1112211-1-122000-2-20-1-1−i3−i3i3i3−i3i3-211−i3i3-1-111000-10−i3i31−i3i3000000000000
χ342222-2-2-12-22-2-1-1-1112211-1-122000-2-20-1-1i3i3−i3−i3i3−i3-211i3−i3-1-111000-10i3−i31i3−i3000000000000
χ352222-2-2-12-22-2-1-1-1112211-1-1-2-200022011−i3−i3i3i3i3−i3-2-1-1i3−i3-1-11100010−i3i3-1i3−i3000000000000
χ362222-2-2-12-22-2-1-1-1112211-1-1-2-200022011i3i3−i3−i3−i3i3-2-1-1−i3i3-1-11100010i3−i3-1−i3i3000000000000
χ372222-2-2-12-22-2-1-1-111-2-211-1-12-2000-220-1-1−i3−i3i3i3−i3i3211−i3i311-1-100010i3−i3-1i3−i3000000000000
χ382222-2-2-12-22-2-1-1-111-2-211-1-12-2000-220-1-1i3i3−i3−i3i3−i3211i3−i311-1-100010−i3i3-1−i3i3000000000000
χ392222-2-2-12-22-2-1-1-111-2-211-1-1-220002-2011−i3−i3i3i3i3−i32-1-1i3−i311-1-1000-10i3−i31−i3i3000000000000
χ402222-2-2-12-22-2-1-1-111-2-211-1-1-220002-2011i3i3−i3−i3−i3i32-1-1−i3i311-1-1000-10−i3i31i3−i3000000000000
χ412-22-22-2222-2-2-2-222-2002-22-2002-20000002-22-200000000000000000000000002i−2i02i−2i000
χ422-22-22-2222-2-2-2-222-2002-22-2002-20000002-22-20000000000000000000000000−2i2i0−2i2i000
χ432-22-22-2222-2-2-2-222-2002-22-200-22000000-22-2200000000000000000000000002i−2i0−2i2i000
χ442-22-22-2222-2-2-2-222-2002-22-200-22000000-22-220000000000000000000000000−2i2i02i−2i000
χ454444444-4-4-4-44444400-4-4-4-400000000000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-2-200222200000000000000−2i32i30002i3−2i300000000000000000000000000
χ47444444-2-4-4-4-4-2-2-2-2-2002222000000000000002i3−2i3000−2i32i300000000000000000000000000
χ484444-4-4-2-44-44-2-2-22200-2-2220000400-4000000-2-20002200000000000000000000000000
χ494444-4-4-2-44-44-2-2-22200-2-2220000-400400000022000-2-200000000000000000000000000
χ5044-4-40040000-44-40022−22000000000000000000000000022−2200−2i22i200000000002i−2i00000000
χ5144-4-40040000-44-40022−22000000000000000000000000022−22002i2−2i20000000000−2i2i00000000
χ5244-4-40040000-44-400−22220000000000000000000000000−222200−2i22i20000000000−2i2i00000000
χ5344-4-40040000-44-400−22220000000000000000000000000−2222002i2−2i200000000002i−2i00000000
χ544-44-44-44-4-444-4-444-400-44-4400000000000000000000000000000000000000000000000
χ554-44-44-4-244-4-422-2-2200-22-22004-4000000-22-22000000000000000000000000000000000
χ564-44-44-4-244-4-422-2-2200-22-2200-440000002-22-2000000000000000000000000000000000
χ574-44-44-4-2-4-44422-2-22002-22-200000000−2i32i30000000−2i32i30000000000000000000000000000
χ584-44-44-4-2-4-44422-2-22002-22-2000000002i3−2i300000002i3−2i30000000000000000000000000000
χ594-44-4-4444-4-44-4-44-4400-444-400000000000000000000000000000000000000000000000
χ604-44-4-444-444-4-4-44-44004-4-4400000000000000000000000000000000000000000000000
χ614-44-4-44-24-4-4422-22-2002-2-220000000000−2i32i32i3−2i3000000000000000000000000000000000
χ624-44-4-44-24-4-4422-22-2002-2-2200000000002i3−2i3−2i32i3000000000000000000000000000000000
χ634-44-4-44-2-444-422-22-200-222-200000000−2i32i300000002i3−2i30000000000000000000000000000
χ644-44-4-44-2-444-422-22-200-222-2000000002i3−2i30000000−2i32i30000000000000000000000000000
χ6588-8-800-400004-440042−420000000000000000000000000−2222000000000000000000000000
χ6688-8-800-400004-4400−4242000000000000000000000000022−22000000000000000000000000
χ678-8-8800800008-8-80000000000000000000000000000000000000000000000000000000
χ688-8-8800-40000-444000000000000000000000000000000026−260000000000000000000000
χ698-8-8800-40000-4440000000000000000000000000000000−26260000000000000000000000

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