Finite Group Databasebeta

← Group #310539

Character table — Group #310539

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111111-1-1-1-11111-1-1-1-11-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-111111111111111-11-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-11111-1-111-1
χ71111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11
χ91111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11
χ101111111111111111-1-1-1-111111111-1-1-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-111111111-1-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1111-1-111-1-111-1-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-1111
χ17222222222-22-2-222-20000-2-2222222000022-2-2-2-2000000000000-200000000000000
χ18222222222-22-2-222-20000-2-22222-2-20000-2-222-2-2000000000000200000000000000
χ19222222222-22-2-222-20000-2-2-2-2-2-2220000-2-22222000000000000-200000000000000
χ20222222222-22-2-222-20000-2-2-2-2-2-2-2-2000022-2-222000000000000200000000000000
χ2122222222-22-222-2-222222-2-200000022-2-200000022-2-2000000000-20000000000000
χ2222222222-22-222-2-222222-2-2000000-2-2-2-2000000-2-22200000000020000000000000
χ2322222222-22-222-2-22-2-2-2-2-2-20000002222000000-2-222000000000-20000000000000
χ2422222222-22-222-2-22-2-2-2-2-2-2000000-2-22200000022-2-200000000020000000000000
χ2522-22-2-2-2222-2-2-22-2200002-200000000002i−2i2i−2i00000022-2-20000002i−2i00000000000
χ2622-22-2-2-2222-2-2-22-2200002-200000000002i−2i2i−2i000000-2-222000000−2i2i00000000000
χ2722-22-2-2-2222-2-2-22-2200002-20000000000−2i2i−2i2i00000022-2-2000000−2i2i00000000000
χ2822-22-2-2-2222-2-2-22-2200002-20000000000−2i2i−2i2i000000-2-2220000002i−2i00000000000
χ2922-22-2-2-222-2-2222-2-22i2i−2i−2i-22000000002i−2i2i−2i−2i2i0000000000000000002-2000000000
χ3022-22-2-2-222-2-2222-2-22i2i−2i−2i-22000000002i−2i−2i2i2i−2i000000000000000000-22000000000
χ3122-22-2-2-222-2-2222-2-2−2i−2i2i2i-2200000000−2i2i2i−2i−2i2i000000000000000000-22000000000
χ3222-22-2-2-222-2-2222-2-2−2i−2i2i2i-2200000000−2i2i−2i2i2i−2i0000000000000000002-2000000000
χ3322-22-2-2-22-2-2222-22-22i2i−2i−2i2-200000000−2i2i0000000000000000000000002-200002i−2i0
χ3422-22-2-2-22-2-2222-22-22i2i−2i−2i2-200000000−2i2i000000000000000000000000-220000−2i2i0
χ3522-22-2-2-22-2-2222-22-2−2i−2i2i2i2-2000000002i−2i0000000000000000000000002-20000−2i2i0
χ3622-22-2-2-22-2-2222-22-2−2i−2i2i2i2-2000000002i−2i000000000000000000000000-2200002i−2i0
χ372-2-2222-2-20-202-20022i−2i2i−2i0022−2−2002i−2i0000002−22-200i2−i2i2−i222−2−200000000i2−i200000
χ382-2-2222-2-20-202-20022i−2i2i−2i0022−2−200−2i2i0000002−2-2200i2−i2i2−i2−2−22200000000−i2i200000
χ392-2-2222-2-20-202-20022i−2i2i−2i00−2−222002i−2i000000−222-200−i2i2−i2i2−2−22200000000−i2i200000
χ402-2-2222-2-20-202-20022i−2i2i−2i00−2−22200−2i2i000000−22-2200−i2i2−i2i222−2−200000000i2−i200000
χ412-2-2222-2-20-202-2002−2i2i−2i2i0022−2−2002i−2i0000002−2-2200−i2i2−i2i2−2−22200000000i2−i200000
χ422-2-2222-2-20-202-2002−2i2i−2i2i0022−2−200−2i2i0000002−22-200−i2i2−i2i222−2−200000000−i2i200000
χ432-2-2222-2-20-202-2002−2i2i−2i2i00−2−222002i−2i000000−22-2200i2−i2i2−i222−2−200000000−i2i200000
χ442-2-2222-2-20-202-2002−2i2i−2i2i00−2−22200−2i2i000000−222-200i2−i2i2−i2−2−22200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-440-400-4400000004-44-4000000000000000000000000000000000000000
χ47444-44-4-4-440-400-440000000-44-44000000000000000000000000000000000000000
χ48444-44-4-4-4-404004-4000000000000000000000000000000022−2222−22000000000000000
χ49444-44-4-4-4-404004-40000000000000000000000000000000−2222−2222000000000000000
χ5044-44-4-4-44-444-4-4-4440000-440000000000000000000000000000000000000000000
χ5144-4-4-444-440400-4-4000000000004-40000000000000000000000000000000000000
χ5244-4-4-444-440400-4-400000000000-440000000000000000000000000000000000000
χ5344-4-4-444-4-40-400440000000000000000000000000000000000000000000002i2−2i2000
χ5444-4-4-444-4-40-40044000000000000000000000000000000000000000000000−2i22i2000
χ554-444-4-44-40404-400-44-4-44000000000000000000000000000000000000000000000
χ564-444-4-44-40404-400-4-444-4000000000000000000000000000000000000000000000
χ574-444-4-44-40-40-44004000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ584-444-4-44-40-40-4400400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ594-4-4444-4-4040-4400-40000002222−22−220000000000−2222000000000000000000000000000
χ604-4-4444-4-4040-4400-4000000−22−222222000000000022−22000000000000000000000000000
χ614-4-4-44-4440000000000000022−22−22220000000000000022−2200002-2-22000000000000000
χ624-4-4-44-4440000000000000022−22−222200000000000000−22220000-222-2000000000000000
χ634-4-4-44-44400000000000000−222222−220000000000000022−220000-222-2000000000000000
χ644-4-4-44-44400000000000000−222222−2200000000000000−222200002-2-22000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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