Finite Group Databasebeta

← Group #270197

Character table — Group #270197

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-11-1-1-1-1-1-1-111-1
χ31111111111111111111111111111-1-111111111-1-1-1-11111-1-1-1-11111-1-1-11-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-11111-1-11
χ51111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-1111-1-1-1-11
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-11111-1
χ91111111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111
χ101111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-111-1-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111111111-1-1111-111-1-1-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1111-1-11-1-111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111111
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-111111-1-111-1
χ17222222222-2-22-222-22222-2-20000-2-2220000000022-2-2000000000000-20000000000
χ18222222222-2-22-222-22222-2-20000-2-2-2-200000000-2-22200000000000020000000000
χ19222222222-2-22-222-2-2-2-2-2-2-20000222200000000-2-222000000000000-20000000000
χ20222222222-2-22-222-2-2-2-2-2-2-2000022-2-20000000022-2-200000000000020000000000
χ2122222222-222-22-2-220000-2-22222000022-2-2-2-2-2-2000000000000000000020000000
χ2222222222-222-22-2-220000-2-222220000-2-22222-2-20000000000000000000-20000000
χ2322222222-222-22-2-220000-2-2-2-2-2-200002222-2-2220000000000000000000-20000000
χ2422222222-222-22-2-220000-2-2-2-2-2-20000-2-2-2-22222000000000000000000020000000
χ2522-222-2-2-2-200-202202i2i−2i−2i0022−2−2002-20000002−22i−2i00i2i2−i2−i2i2i2−i2−i20000000000002−20
χ2622-222-2-2-2-200-202202i2i−2i−2i0022−2−200-220000002−2−2i2i00i2i2−i2−i2−i2−i2i2i2000000000000−220
χ2722-222-2-2-2-200-202202i2i−2i−2i00−2−222002-2000000−222i−2i00−i2−i2i2i2−i2−i2i2i2000000000000−220
χ2822-222-2-2-2-200-202202i2i−2i−2i00−2−22200-22000000−22−2i2i00−i2−i2i2i2i2i2−i2−i20000000000002−20
χ2922-222-2-2-2-200-20220−2i−2i2i2i0022−2−2002-20000002−2−2i2i00−i2−i2i2i2−i2−i2i2i20000000000002−20
χ3022-222-2-2-2-200-20220−2i−2i2i2i0022−2−200-220000002−22i−2i00−i2−i2i2i2i2i2−i2−i2000000000000−220
χ3122-222-2-2-2-200-20220−2i−2i2i2i00−2−222002-2000000−22−2i2i00i2i2−i2−i2i2i2−i2−i2000000000000−220
χ3222-222-2-2-2-200-20220−2i−2i2i2i00−2−22200-22000000−222i−2i00i2i2−i2−i2−i2−i2i2i20000000000002−20
χ332-2-2-22-222222-2-22-2-22-22-22-200002-20000000000000000000000000002i−2i0002i−2i000
χ342-2-2-22-222222-2-22-2-22-22-22-200002-2000000000000000000000000000−2i2i000−2i2i000
χ352-2-2-22-222222-2-22-2-2-22-222-20000-220000000000000000000000000002i−2i000−2i2i000
χ362-2-2-22-222222-2-22-2-2-22-222-20000-22000000000000000000000000000−2i2i0002i−2i000
χ372-2-2-22-2222-2-2-222-222-22-2-220000-22002-2002-200000000000000002-200000000000
χ382-2-2-22-2222-2-2-222-222-22-2-220000-2200-2200-220000000000000000-2200000000000
χ392-2-2-22-2222-2-2-222-22-22-22-2200002-2002-2002-20000000000000000-2200000000000
χ402-2-2-22-2222-2-2-222-22-22-22-2200002-200-2200-2200000000000000002-200000000000
χ412-2-2-22-222-2-2-222-22200002-2000000002-200-220000002-22-200002-20000000000000
χ422-2-2-22-222-2-2-222-22200002-2000000002-200-22000000-22-220000-220000000000000
χ432-2-2-22-222-2-2-222-22200002-200000000-22002-20000002-22-20000-220000000000000
χ442-2-2-22-222-2-2-222-22200002-200000000-22002-2000000-22-2200002-20000000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-44-404-40400-400000000000000004-40000000000000000000000000000000
χ47444-4-4-44-404-40400-40000000000000000-440000000000000000000000000000000
χ48444-4-4-44-40-440-40040000000000000000000000000000000000000000002i2−2i200000
χ49444-4-4-44-40-440-4004000000000000000000000000000000000000000000−2i22i200000
χ5044-444-4-4-440040-4-400000002222−22−220000000000−2222000000000000000000000000000
χ5144-444-4-4-440040-4-40000000−22−222222000000000022−22000000000000000000000000000
χ524-444-4-4-44000000000000002i2−2i22i2−2i20000000000000022−2200002i−2i2i−2i000000000000000
χ534-444-4-4-44000000000000002i2−2i22i2−2i200000000000000−22220000−2i2i−2i2i000000000000000
χ544-444-4-4-4400000000000000−2i22i2−2i22i20000000000000022−220000−2i2i−2i2i000000000000000
χ554-444-4-4-4400000000000000−2i22i2−2i22i200000000000000−222200002i−2i2i−2i000000000000000
χ564-44-444-4-4400-40-440000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ574-44-444-4-4400-40-44000000000000000000000000000−2i22i22i2−2i20000000000000000000
χ584-44-444-4-4-400404-404i−4i−4i4i000000000000000000000000000000000000000000000
χ594-44-444-4-4-400404-40−4i4i4i−4i000000000000000000000000000000000000000000000
χ604-4-44-444-404-40-400400000000000000000000000000000022−22−2222000000000000000
χ614-4-44-444-404-40-4004000000000000000000000000000000−222222−22000000000000000
χ624-4-44-444-40-440400-40000004i−4i−4i4i000000000000000000000000000000000000000
χ634-4-44-444-40-440400-4000000−4i4i4i−4i000000000000000000000000000000000000000
χ644-4-4-44-444-4444-4-44-40000-440000000000000000000000000000000000000000000
χ6588-8-8-88-88000000000000000000000000000000000000000000000000000000000

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