Finite Group Databasebeta

← Group #310259

Character table — Group #310259

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111111111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-111-1
χ411111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-1-1
χ61111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-1111111-1-111-1
χ91111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111
χ101111111111111111-1-1-1-111111111-1-1-1-11111111111-1-1-1-11111-11-1-1-1-1-1-11111-1-1-1
χ111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1111111-1
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
χ131111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-111-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1111
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1111-1-111-1-11111-1
χ17222222222-22-2-222-22222-2-200000022-2-2000000-2-22200000000-200000000000000
χ18222222222-22-2-222-22222-2-2000000-2-2-2-200000022-2-200000000200000000000000
χ19222222222-22-2-222-2-2-2-2-2-2-2000000222200000022-2-200000000-200000000000000
χ20222222222-22-2-222-2-2-2-2-2-2-2000000-2-222000000-2-22200000000200000000000000
χ2122222222-22-222-2-220000-2-22222220000-2-2-2-2-2-2000000000000020000000000000
χ2222222222-22-222-2-220000-2-22222-2-200002222-2-20000000000000-20000000000000
χ2322222222-22-222-2-220000-2-2-2-2-2-2220000-2-222220000000000000-20000000000000
χ2422222222-22-222-2-220000-2-2-2-2-2-2-2-2000022-2-222000000000000020000000000000
χ252-2-22-222-222-2-2-22-222i2i−2i−2i2-2000000002i−2i0000000000000000000000002i−2i2-200000
χ262-2-22-222-222-2-2-22-222i2i−2i−2i2-2000000002i−2i000000000000000000000000−2i2i-2200000
χ272-2-22-222-222-2-2-22-22−2i−2i2i2i2-200000000−2i2i0000000000000000000000002i−2i-2200000
χ282-2-22-222-222-2-2-22-22−2i−2i2i2i2-200000000−2i2i000000000000000000000000−2i2i2-200000
χ292-2-22-222-22-2-2222-2-22i2i−2i−2i-2200002i−2i00−2i2i2i−2i0000000000000000002-200000000000
χ302-2-22-222-22-2-2222-2-22i2i−2i−2i-220000−2i2i00−2i2i−2i2i000000000000000000-2200000000000
χ312-2-22-222-22-2-2222-2-2−2i−2i2i2i-2200002i−2i002i−2i2i−2i000000000000000000-2200000000000
χ322-2-22-222-22-2-2222-2-2−2i−2i2i2i-220000−2i2i002i−2i−2i2i0000000000000000002-200000000000
χ332-2-22-222-2-2-2222-22-200002-200002i−2i0000−2i2i000000002i2i−2i−2i000000002-2000000000
χ342-2-22-222-2-2-2222-22-200002-200002i−2i0000−2i2i00000000−2i−2i2i2i00000000-22000000000
χ352-2-22-222-2-2-2222-22-200002-20000−2i2i00002i−2i000000002i2i−2i−2i00000000-22000000000
χ362-2-22-222-2-2-2222-22-200002-20000−2i2i00002i−2i00000000−2i−2i2i2i000000002-2000000000
χ372-2-2-222-2220200-2-202i−2i2i−2i0022−2−2002-20000002−2002i−2ii2−i2i2−i2i2i2−i2−i20000000000002−20
χ382-2-2-222-2220200-2-202i−2i2i−2i0022−2−200-220000002−200−2i2ii2−i2i2−i2−i2−i2i2i2000000000000−220
χ392-2-2-222-2220200-2-202i−2i2i−2i00−2−222002-2000000−22002i−2i−i2i2−i2i2−i2−i2i2i2000000000000−220
χ402-2-2-222-2220200-2-202i−2i2i−2i00−2−22200-22000000−2200−2i2i−i2i2−i2i2i2i2−i2−i20000000000002−20
χ412-2-2-222-2220200-2-20−2i2i−2i2i0022−2−2002-20000002−200−2i2i−i2i2−i2i2−i2−i2i2i20000000000002−20
χ422-2-2-222-2220200-2-20−2i2i−2i2i0022−2−200-220000002−2002i−2i−i2i2−i2i2i2i2−i2−i2000000000000−220
χ432-2-2-222-2220200-2-20−2i2i−2i2i00−2−222002-2000000−2200−2i2ii2−i2i2−i2i2i2−i2−i2000000000000−220
χ442-2-2-222-2220200-2-20−2i2i−2i2i00−2−22200-22000000−22002i−2ii2−i2i2−i2−i2−i2i2i20000000000002−20
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-44-4-440-400-4404-4-44000000000000000000000000000000000000000000000
χ47444-4-44-4-440-400-440-444-4000000000000000000000000000000000000000000000
χ48444-4-44-4-4-404004-400000000000000000000000000022−22−22220000000000000000000
χ49444-4-44-4-4-404004-4000000000000000000000000000−222222−220000000000000000000
χ5044-4-44-44-40404-400-40000004-44-4000000000000000000000000000000000000000
χ5144-4-44-44-40404-400-4000000-44-44000000000000000000000000000000000000000
χ5244-4-44-44-40-40-440040000000000000000000000000000002i2−2i22i2−2i2000000000000000
χ5344-4-44-44-40-40-44004000000000000000000000000000000−2i22i2−2i22i2000000000000000
χ544-4444-4-4-40000000000000022−22−222200000000000022−220000002-2-22000000000000000
χ554-4444-4-4-40000000000000022−22−2222000000000000−2222000000-222-2000000000000000
χ564-4444-4-4-400000000000000−222222−2200000000000022−22000000-222-2000000000000000
χ574-4444-4-4-400000000000000−222222−22000000000000−22220000002-2-22000000000000000
χ584-44-4-4-444040-4400-4000000000000000000000000000000000000000000002i2−2i2000
χ594-44-4-4-444040-4400-400000000000000000000000000000000000000000000−2i22i2000
χ604-44-4-4-4440-404-40040000000000000000004-400000000000000000000000000000
χ614-44-4-4-4440-404-4004000000000000000000-4400000000000000000000000000000
χ624-4-44-444-4-444-4-4-4440000-440000000000000000000000000000000000000000000
χ634-4-4-444-44-40-4004400000002222−22−220000000000−2222000000000000000000000000000
χ644-4-4-444-44-40-400440000000−22−222222000000000022−22000000000000000000000000000
χ6588-88-8-8-88000000000000000000000000000000000000000000000000000000000

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