Finite Group Databasebeta

← Group #274298

Character table — Group #274298

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444244444444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-11111111111-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11-1
χ1011111111-1-1-1-11111111111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-111-11
χ1111111111-1-1-1-11111111111-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-11111-11
χ1211111111-1-1-1-11111111111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-111-1-111-1-11-1
χ1311111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-111-1-111-1-111-1-1-11
χ1411111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111111-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1111111-1-1-1-1-11
χ172222222222222-2-222-2-22-2-222-2-2-222-2-222-2-2000000000000000000000000000000
χ182222222222222-2-222-2-22-2-222-2-2-2-2-222-2-222000000000000000000000000000000
χ19222222222222-222-2-222-2-2-2-2-222-20000000022220000-2-2-2-2000000000000000000
χ20222222222222-222-2-222-2-2-2-2-222-200000000-2-2-2-200002222000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-220000000000000000000000000000002i−2i2i−2i0000
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-22000000000000000000000000000000−2i2i−2i2i0000
χ2322222222-2-2-2-22-2-222-2-22-2-2-2-222222-2-2-2-222000000000000000000000000000000
χ2422222222-2-2-2-22-2-222-2-22-2-2-2-2222-2-22222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-222-2-222-2-2-222-2-220000000022-2-20000-2-222000000000000000000
χ2622222222-2-2-2-2-222-2-222-2-2-222-2-2200000000-2-222000022-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-20000000000000000000000000000002i−2i−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2000000000000000000000000000000−2i2i2i−2i0000
χ2922-2-2-222-22i2i−2i−2i02-2002-2000002i−2i000000000000022−2−22i−2i2-2i2i2−i2−i20000i2−i200002−200
χ3022-2-2-222-22i2i−2i−2i02-2002-2000002i−2i000000000000022−2−2−2i2i-22i2i2−i2−i20000−i2i20000−2200
χ3122-2-2-222-22i2i−2i−2i02-2002-2000002i−2i0000000000000−2−2222i−2i2-2−i2−i2i2i20000−i2i20000−2200
χ3222-2-2-222-22i2i−2i−2i02-2002-2000002i−2i0000000000000−2−222−2i2i-22−i2−i2i2i20000i2−i200002−200
χ3322-2-2-222-2−2i−2i2i2i02-2002-200000−2i2i000000000000022−2−22i−2i-22−i2−i2i2i20000i2−i20000−2200
χ3422-2-2-222-2−2i−2i2i2i02-2002-200000−2i2i000000000000022−2−2−2i2i2-2−i2−i2i2i20000−i2i200002−200
χ3522-2-2-222-2−2i−2i2i2i02-2002-200000−2i2i0000000000000−2−2222i−2i-22i2i2−i2−i20000−i2i200002−200
χ3622-2-2-222-2−2i−2i2i2i02-2002-200000−2i2i0000000000000−2−222−2i2i2-2i2i2−i2−i20000i2−i20000−2200
χ372-22-2-22-22000022-22-2-22-22-2000002i−2i2i−2i00000000000000002i−2i2i−2i2-2000000000000
χ382-22-2-22-22000022-22-2-22-22-2000002i−2i2i−2i0000000000000000−2i2i−2i2i-22000000000000
χ392-22-2-22-22000022-22-2-22-22-200000−2i2i−2i2i00000000000000002i−2i2i−2i-22000000000000
χ402-22-2-22-22000022-22-2-22-22-200000−2i2i−2i2i0000000000000000−2i2i−2i2i2-2000000000000
χ412-22-2-22-2200002-222-22-2-2-22000002i−2i−2i2i000000002i−2i2i−2i00000000002-20000000000
χ422-22-2-22-2200002-222-22-2-2-22000002i−2i−2i2i00000000−2i2i−2i2i0000000000-220000000000
χ432-22-2-22-2200002-222-22-2-2-2200000−2i2i2i−2i000000002i−2i2i−2i0000000000-220000000000
χ442-22-2-22-2200002-222-22-2-2-2200000−2i2i2i−2i00000000−2i2i−2i2i00000000002-20000000000
χ454444-4-4-4-44-44-40000000000000000000000022−2222−2200000000000000000000000000
χ464444-4-4-4-44-44-400000000000000000000000−2222−222200000000000000000000000000
χ474444-4-4-4-4-44-440000000000000000000000022−22−222200000000000000000000000000
χ484444-4-4-4-4-44-4400000000000000000000000−222222−2200000000000000000000000000
χ4944-4-44-4-444i−4i−4i4i400-4-4004004i−4i00000000000000000000000000000000000000000
χ5044-4-44-4-444i−4i−4i4i-4004400-400−4i4i00000000000000000000000000000000000000000
χ5144-4-44-4-44−4i4i4i−4i400-4-400400−4i4i00000000000000000000000000000000000000000
χ5244-4-44-4-44−4i4i4i−4i-4004400-4004i−4i00000000000000000000000000000000000000000
χ5344-4-4-444-44i4i−4i−4i0-4400-4400000−4i4i000000000000000000000000000000000000000
χ5444-4-4-444-4−4i−4i4i4i0-4400-44000004i−4i000000000000000000000000000000000000000
χ554-44-4-44-440000-44-4-44-444-440000000000000000000000000000000000000000000
χ564-44-4-44-440000-4-44-444-444-40000000000000000000000000000000000000000000
χ574-4-4444-4-4000004400-4-4000000000000000000000000000022−22−222200000000000000
χ584-4-4444-4-4000004400-4-40000000000000000000000000000−222222−2200000000000000
χ594-4-4444-4-400000-4-40044000000000000000000002i2−2i2−2i22i20000000000000000000000
χ604-4-4444-4-400000-4-4004400000000000000000000−2i22i22i2−2i20000000000000000000000
χ614-4-44-4-4440000400-4400-4000000000004i−4i00000000000000000000000000000000
χ624-4-44-4-4440000400-4400-400000000000−4i4i00000000000000000000000000000000
χ634-4-44-4-4440000-4004-400400000000000004-4000000000000000000000000000000
χ644-4-44-4-4440000-4004-40040000000000000-44000000000000000000000000000000
χ658-88-88-88-8000000000000000000000000000000000000000000000000000000000

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