Finite Group Databasebeta

← Group #308155

Character table — Group #308155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888224444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-11111111111111111-1-1-1-1-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-111-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111-1-11-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1111111-1-1-1
χ91111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-111111-1-1-1-11
χ101111111111111111-1-1-1-11111111111-1-111-1-111-1-1-1-1111111111-1-1-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-11111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-111-1-1111-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-111-1-1-1-1-111-1-1-1-1-11111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111-1-1111-1-1-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-11-1-111-11111-1-111-1
χ17222222222-2-22-222-20000-2-2222222-2-200-2-200000000-2-2000000200000000000000
χ18222222222-2-22-222-20000-2-22222-2-222002200000000-2-2000000-200000000000000
χ19222222222-2-22-222-20000-2-2-2-2-2-222-2-200220000000022000000-200000000000000
χ20222222222-2-22-222-20000-2-2-2-2-2-2-2-22200-2-20000000022000000200000000000000
χ2122222222-222-22-2-222222-2-200000000-2-20022-2-200000022000000000-2000000000
χ2222222222-222-22-2-222222-2-200000000-2-200-2-222000000-2-20000000002000000000
χ2322222222-222-22-2-22-2-2-2-2-2-20000000022002222000000-2-2000000000-2000000000
χ2422222222-222-22-2-22-2-2-2-2-2-2000000002200-2-2-2-2000000220000000002000000000
χ2522-22-22-2-2222-2-22-2-200002-200002-22-20000000022-2-20000000002-2000000000000
χ2622-22-22-2-2222-2-22-2-200002-200002-22-200000000-2-222000000000-22000000000000
χ2722-22-22-2-2222-2-22-2-200002-20000-22-220000000022-2-2000000000-22000000000000
χ2822-22-22-2-2222-2-22-2-200002-20000-22-2200000000-2-2220000000002-2000000000000
χ2922-22-22-2-22-2-2-222-222i2i−2i−2i-2200002-2-222i−2i0000000000000000000002i−2i0000000000
χ3022-22-22-2-22-2-2-222-222i2i−2i−2i-220000-222-22i−2i000000000000000000000−2i2i0000000000
χ3122-22-22-2-22-2-2-222-22−2i−2i2i2i-2200002-2-22−2i2i000000000000000000000−2i2i0000000000
χ3222-22-22-2-22-2-2-222-22−2i−2i2i2i-220000-222-2−2i2i0000000000000000000002i−2i0000000000
χ3322-22-22-2-2-2-2-222-2222i2i−2i−2i2-200000000−2i2i0000000000000000000000002i−2i002-2000
χ3422-22-22-2-2-2-2-222-2222i2i−2i−2i2-200000000−2i2i000000000000000000000000−2i2i00-22000
χ3522-22-22-2-2-2-2-222-222−2i−2i2i2i2-2000000002i−2i0000000000000000000000002i−2i00-22000
χ3622-22-22-2-2-2-2-222-222−2i−2i2i2i2-2000000002i−2i000000000000000000000000−2i2i002-2000
χ372-2-222-2-2202-20200-22i−2i2i−2i0022−2−2000000002-200i2−i2i2−i22−22i−2ii2i2−i2−i2000000002−200000
χ382-2-222-2-2202-20200-22i−2i2i−2i0022−2−200000000-2200i2−i2i2−i22−2−2i2i−i2−i2i2i200000000−2200000
χ392-2-222-2-2202-20200-22i−2i2i−2i00−2−222000000002-200−i2i2−i2i2−222i−2i−i2−i2i2i200000000−2200000
χ402-2-222-2-2202-20200-22i−2i2i−2i00−2−22200000000-2200−i2i2−i2i2−22−2i2ii2i2−i2−i2000000002−200000
χ412-2-222-2-2202-20200-2−2i2i−2i2i0022−2−2000000002-200−i2i2−i2i22−2−2i2i−i2−i2i2i2000000002−200000
χ422-2-222-2-2202-20200-2−2i2i−2i2i0022−2−200000000-2200−i2i2−i2i22−22i−2ii2i2−i2−i200000000−2200000
χ432-2-222-2-2202-20200-2−2i2i−2i2i00−2−222000000002-200i2−i2i2−i2−22−2i2ii2i2−i2−i200000000−2200000
χ442-2-222-2-2202-20200-2−2i2i−2i2i00−2−22200000000-2200i2−i2i2−i2−222i−2i−i2−i2i2i2000000002−200000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-4400-40-44000000000000000000000000000000022−2222−22000000000000000
χ47444-44-4-4-4400-40-440000000000000000000000000000000−2222−2222000000000000000
χ48444-44-4-4-4-400404-400000004-44-4000000000000000000000000000000000000000
χ49444-44-4-4-4-400404-40000000-44-44000000000000000000000000000000000000000
χ5044-44-44-4-4-4444-4-44-40000-440000000000000000000000000000000000000000000
χ5144-4-4-4-44440040-4-4000000000000000000000000000000000000000000000002i2−2i20
χ5244-4-4-4-44440040-4-400000000000000000000000000000000000000000000000−2i22i20
χ5344-4-4-4-444-400-4044000000000000000004-40000000000000000000000000000000
χ5444-4-4-4-444-400-404400000000000000000-440000000000000000000000000000000
χ554-444-4-44-404-40-400400000000000000000000002i2−2i2−2i22i200000000000000000000000
χ564-444-4-44-404-40-40040000000000000000000000−2i22i22i2−2i200000000000000000000000
χ574-444-4-44-40-440400-44-4-44000000000000000000000000000000000000000000000
χ584-444-4-44-40-440400-4-444-4000000000000000000000000000000000000000000000
χ594-4-444-4-440-440-40040000002222−22−220000000000000000−2222000000000000000000000
χ604-4-444-4-440-440-4004000000−22−222222000000000000000022−22000000000000000000000
χ614-4-4-4444-40000000000000022−22−222200000000002i2−2i2000000002i−2i−2i2i000000000000000
χ624-4-4-4444-40000000000000022−22−22220000000000−2i22i200000000−2i2i2i−2i000000000000000
χ634-4-4-4444-400000000000000−222222−2200000000002i2−2i200000000−2i2i2i−2i000000000000000
χ644-4-4-4444-400000000000000−222222−220000000000−2i22i2000000002i−2i−2i2i000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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