Finite Group Databasebeta

← Group #270116

Character table — Group #270116

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-11111111111111111-1-11-1-1-1-1-1-1-1-1-111-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-11111-1-11
χ51111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-11111-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ101111111111111111-1-1-1-11111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1
χ111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1111-11111-1-1-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111-1-11-1-1-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-111-1111-1-111-1-111-1
χ17222222222-2-22-222-22222-2-2000000002200-2-2-2-222000000000000-2000000000000
χ18222222222-2-22-222-22222-2-200000000-2-200-2-222-2-20000000000002000000000000
χ19222222222-2-22-222-2-2-2-2-2-2-20000000022002222-2-2000000000000-2000000000000
χ20222222222-2-22-222-2-2-2-2-2-2-200000000-2-20022-2-2220000000000002000000000000
χ2122222222-222-22-2-220000-2-2222222-2-200-2-2000000-2-200000000000002000000000
χ2222222222-222-22-2-220000-2-22222-2-2220022000000-2-20000000000000-2000000000
χ2322222222-222-22-2-220000-2-2-2-2-2-222-2-20022000000220000000000000-2000000000
χ2422222222-222-22-2-220000-2-2-2-2-2-2-2-22200-2-20000002200000000000002000000000
χ2522-2-222-2-2200-20-22022-2-200i2i2−i2−i200002-20000002-2i2−i2i2i2−i2−i2i2i2−i2−i2000000000000i2−i20
χ2622-2-222-2-2200-20-22022-2-200i2i2−i2−i20000-22000000-22i2−i2i2i2−i2−i2−i2−i2i2i2000000000000−i2i20
χ2722-2-222-2-2200-20-22022-2-200−i2−i2i2i200002-20000002-2−i2i2−i2−i2i2i2−i2−i2i2i2000000000000−i2i20
χ2822-2-222-2-2200-20-22022-2-200−i2−i2i2i20000-22000000-22−i2i2−i2−i2i2i2i2i2−i2−i2000000000000i2−i20
χ2922-2-222-2-2200-20-220-2-22200i2i2−i2−i200002-2000000-22i2−i2−i2−i2i2i2−i2−i2i2i2000000000000i2−i20
χ3022-2-222-2-2200-20-220-2-22200i2i2−i2−i20000-220000002-2i2−i2−i2−i2i2i2i2i2−i2−i2000000000000−i2i20
χ3122-2-222-2-2200-20-220-2-22200−i2−i2i2i200002-2000000-22−i2i2i2i2−i2−i2i2i2−i2−i2000000000000−i2i20
χ3222-2-222-2-2200-20-220-2-22200−i2−i2i2i20000-220000002-2−i2i2i2i2−i2−i2−i2−i2i2i2000000000000i2−i20
χ332-2-2-22-222222-2-22-2-22-22-22-20000000000002-2000000000000000002i−2i000002i−2i000
χ342-2-2-22-222222-2-22-2-22-22-22-20000000000002-200000000000000000−2i2i00000−2i2i000
χ352-2-2-22-222222-2-22-2-2-22-222-2000000000000-22000000000000000002i−2i00000−2i2i000
χ362-2-2-22-222222-2-22-2-2-22-222-2000000000000-2200000000000000000−2i2i000002i−2i000
χ372-2-2-22-2222-2-2-222-222-22-2-2200002-22-20000-22000000000000002-20000000000000
χ382-2-2-22-2222-2-2-222-222-22-2-220000-22-220000-2200000000000000-220000000000000
χ392-2-2-22-2222-2-2-222-22-22-22-2200002-22-200002-200000000000000-220000000000000
χ402-2-2-22-2222-2-2-222-22-22-22-220000-22-2200002-2000000000000002-20000000000000
χ412-2-2-22-222-2-2-222-22200002-200002-2-220000000000002-22-200000000002-20000000
χ422-2-2-22-222-2-2-222-22200002-200002-2-22000000000000-22-220000000000-220000000
χ432-2-2-22-222-2-2-222-22200002-20000-222-20000000000002-22-20000000000-220000000
χ442-2-2-22-222-2-2-222-22200002-20000-222-2000000000000-22-2200000000002-20000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-44-404-40400-400000000000000000000000000000022−2222−22000000000000000
χ47444-4-4-44-404-40400-4000000000000000000000000000000−2222−2222000000000000000
χ48444-4-4-44-40-440-40040000004i−4i4i−4i000000000000000000000000000000000000000
χ49444-4-4-44-40-440-4004000000−4i4i−4i4i000000000000000000000000000000000000000
χ5044-44-4-4-440000000000000022−22−222200000000002i2−2i2000000002i−2i−2i2i000000000000000
χ5144-44-4-4-440000000000000022−22−22220000000000−2i22i200000000−2i2i2i−2i000000000000000
χ5244-44-4-4-4400000000000000−222222−2200000000002i2−2i200000000−2i2i2i−2i000000000000000
χ5344-44-4-4-4400000000000000−222222−220000000000−2i22i2000000002i−2i−2i2i000000000000000
χ5444-4-444-4-4-400404-400000002i22i2−2i2−2i200000000000000−2i22i200000000000000000000000
χ5544-4-444-4-4-400404-40000000−2i2−2i22i22i2000000000000002i2−2i200000000000000000000000
χ564-4444-4-4-440040-4-404-4-44000000000000000000000000000000000000000000000
χ574-4444-4-4-440040-4-40-444-4000000000000000000000000000000000000000000000
χ584-4444-4-4-4-400-40440000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ594-4444-4-4-4-400-4044000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ604-4-44-444-404-40-400400000000000000004-40000000000000000000000000000000
χ614-4-44-444-404-40-40040000000000000000-440000000000000000000000000000000
χ624-4-44-444-40-440400-40000000000000000000000000000000000000000002i2−2i200000
χ634-4-44-444-40-440400-4000000000000000000000000000000000000000000−2i22i200000
χ644-4-4-44-444-4444-4-44-40000-440000000000000000000000000000000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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