Finite Group Databasebeta

← Group #10697136

Character table — Group #10697136

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212888812122424242424242424888888884444121212121212121288884488
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
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-111-1-1
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111
χ9222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-200002-200000000000000000000000000000000002i−2i
χ10222222222-2-2-2-2-2-22222-22222-2-2-2-2-2-200002-20000000000000000000000000000000000−2i2i
χ112222222-2-2222-2-22222-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ122222222-2-2222-2-22222-2-222-2-2-2-22222-2-222-2-2-2-2-2-222220000000000000000000000000000
χ132222222-2-2-2-2-222-2222-2222-2-222-2-2-2-20000-22000000000000000000000000000000002-200
χ142222222-2-2-2-2-222-2222-2222-2-222-2-2-2-20000-2200000000000000000000000000000000-2200
χ15222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000
χ16222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000
χ17222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-2-2-1-1-1-1111100000000
χ18222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2221111-1-1-1-100000000
χ19222222-1-2-2222-2-22-1-1-1-2-2-1-11111-1-1-1-122-2-211-1-1-1-11111000000000000−i3−i3i3i3−i3−i3i3i300000000
χ20222222-1-2-2222-2-22-1-1-1-2-2-1-11111-1-1-1-122-2-211-1-1-1-11111000000000000i3i3−i3−i3i3i3−i3−i300000000
χ21222222-1-2-2222-2-22-1-1-1-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-1000000000000−i3−i3i3i3i3i3−i3−i300000000
χ22222222-1-2-2222-2-22-1-1-1-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-1000000000000i3i3−i3−i3−i3−i3i3i300000000
χ232222-2-22222-2-2-2-22222-22-2-222-2-222-2-20000-22000000002222-2-2-2-200000000000000000000
χ242222-2-22222-2-2-2-22222-22-2-222-2-222-2-20000-2200000000-2-2-2-2222200000000000000000000
χ252222-2-2222-22222-2222-2-2-2-22222-2-2220000-2-200000000000000002-2002-22-2000000000000
χ262222-2-2222-22222-2222-2-2-2-22222-2-2220000-2-20000000000000000-2200-22-22000000000000
χ272222-2-22-2-22-2-22222222-2-2-2-2-22222-2-200002-2000000000000000000000000000022-2-20000
χ282222-2-22-2-22-2-22222222-2-2-2-2-22222-2-200002-20000000000000000000000000000-2-2220000
χ292222-2-22-2-2-222-2-2-222222-2-2-2-2-2-2-2-2220000220000000000000000002-200002-22-200000000
χ302222-2-22-2-2-222-2-2-222222-2-2-2-2-2-2-2-222000022000000000000000000-220000-22-2200000000
χ312222-2-2-122-22222-2-1-1-1-2-211-1-1-1-111-1-1000011−i3−i3i3i3−i3−i3i3i3000000002-200-11-11−i3i3i3−i300000000
χ322222-2-2-122-22222-2-1-1-1-2-211-1-1-1-111-1-1000011−i3−i3i3i3−i3−i3i3i300000000-22001-11-1i3−i3−i3i300000000
χ332222-2-2-122-22222-2-1-1-1-2-211-1-1-1-111-1-1000011i3i3−i3−i3i3i3−i3−i3000000002-200-11-11i3−i3−i3i300000000
χ342222-2-2-122-22222-2-1-1-1-2-211-1-1-1-111-1-1000011i3i3−i3−i3i3i3−i3−i300000000-22001-11-1−i3i3i3−i300000000
χ352222-2-2-1-2-2-222-2-2-2-1-1-12211111111-1-10000-1-1−i3−i3i3i3i3i3−i3−i300000000002-2−i3i3i3−i3-11-1100000000
χ362222-2-2-1-2-2-222-2-2-2-1-1-12211111111-1-10000-1-1−i3−i3i3i3i3i3−i3−i30000000000-22i3−i3−i3i31-11-100000000
χ372222-2-2-1-2-2-222-2-2-2-1-1-12211111111-1-10000-1-1i3i3−i3−i3−i3−i3i3i300000000002-2i3−i3−i3i3-11-1100000000
χ382222-2-2-1-2-2-222-2-2-2-1-1-12211111111-1-10000-1-1i3i3−i3−i3−i3−i3i3i30000000000-22−i3i3i3−i31-11-100000000
χ392-2-222-220022-200-2-2-22002-200002-22-2002i−2i0000002i−2i2i−2i22−2−222−2−2000000000000−i2i2−i2i20000
χ402-2-222-220022-200-2-2-22002-200002-22-2002i−2i0000002i−2i2i−2i−2−222−2−222000000000000i2−i2i2−i20000
χ412-2-222-220022-200-2-2-22002-200002-22-200−2i2i000000−2i2i−2i2i22−2−222−2−2000000000000i2−i2i2−i20000
χ422-2-222-220022-200-2-2-22002-200002-22-200−2i2i000000−2i2i−2i2i−2−222−2−222000000000000−i2i2−i2i20000
χ432-2-22-222002-2200-2-2-2200-2200002-2-222i−2i00002i−2i2i−2i000022−2−2−2−222000000000000−i2i2i2−i20000
χ442-2-22-222002-2200-2-2-2200-2200002-2-222i−2i00002i−2i2i−2i0000−2−22222−2−2000000000000i2−i2−i2i20000
χ452-2-22-222002-2200-2-2-2200-2200002-2-22−2i2i0000−2i2i−2i2i000022−2−2−2−222000000000000i2−i2−i2i20000
χ462-2-22-222002-2200-2-2-2200-2200002-2-22−2i2i0000−2i2i−2i2i0000−2−22222−2−2000000000000−i2i2i2−i20000
χ47444444-244-4-4-4-4-4-4-2-2-24-4-2-2-2-22222220000-22000000000000000000000000000000000000
χ48444444-2-4-4-4-4-444-4-2-2-2-44-2-222-2-2222200002-2000000000000000000000000000000000000
χ494444-4-4-2444-4-4-4-44-2-2-2-4422-2-222-2-22200002-2000000000000000000000000000000000000
χ504444-4-4-2-4-44-4-4444-2-2-24-42222-2-2-2-2220000-22000000000000000000000000000000000000
χ5144-4-4004000004-404-4-40000004-40000000000000000002-22-22-22-200000000000000000000
χ5244-4-4004000004-404-4-40000004-4000000000000000000-22-22-22-2200000000000000000000
χ5344-4-400400000-4404-4-4000000-440000000000000000002-22-2-22-2200000000000000000000
χ5444-4-400400000-4404-4-4000000-44000000000000000000-22-222-22-200000000000000000000
χ554-44-40044-4000000-44-400004-400000000000000000000000022−22−222200000000000000000000
χ564-44-40044-4000000-44-400004-4000000000000000000000000−222222−2200000000000000000000
χ574-44-4004-44000000-44-40000-440000000000000000000022−22−2222000000000000000000000000
χ584-44-4004-44000000-44-40000-4400000000000000000000−222222−22000000000000000000000000
χ594-4-444-4400-4-44004-4-44004-40000-44-44000000000000000000000000000000000000000000
χ604-4-444-4-20044-400-422-200-220000-22-22004i−4i000000−2i2i−2i2i0000000000000000000000000000
χ614-4-444-4-20044-400-422-200-220000-22-2200−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ624-4-444-4-200-4-4400422-200-2200002-22-200000023−23−232300000000000000000000000000000000
χ634-4-444-4-200-4-4400422-200-2200002-22-2000000−232323−2300000000000000000000000000000000
χ644-4-44-44400-44-4004-4-4400-440000-444-4000000000000000000000000000000000000000000
χ654-4-44-44-2004-4400-422-2002-20000-222-24i−4i0000−2i2i−2i2i00000000000000000000000000000000
χ664-4-44-44-2004-4400-422-2002-20000-222-2−4i4i00002i−2i2i−2i00000000000000000000000000000000
χ674-4-44-44-200-44-400422-2002-200002-2-22000000000023−23−23230000000000000000000000000000
χ684-4-44-44-200-44-400422-2002-200002-2-220000000000−232323−230000000000000000000000000000
χ6988-8-800-4000008-80-444000000-440000000000000000000000000000000000000000000000
χ7088-8-800-400000-880-4440000004-40000000000000000000000000000000000000000000000
χ718-88-800-48-80000004-440000-44000000000000000000000000000000000000000000000000
χ728-88-800-4-880000004-4400004-4000000000000000000000000000000000000000000000000

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