Finite Group Databasebeta

← Group #309022

Character table — Group #309022

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-11-111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-11-1-1-1-1-11-1-1-1-111-1-1
χ411111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-1-1-111111-1
χ71111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111-11-1-111-1-11-1
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-111-1-111-1-111-11
χ91111111111111111-1-1-1-111111111-1-111111111-1-1-1-111111-1-1-1-1-11-11111-1-1-1-1
χ101111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-111-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11-111-1-1-1-1-1-11111-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1111-1-1-1-11-1
χ172222222222-2-2-222-22222-2-2000000-2-2000022-2-2000000000200000-200000000
χ182222222222-2-2-222-22222-2-2000000-2-20000-2-222000000000-200000200000000
χ192222222222-2-2-222-2-2-2-2-2-2-200000022000022-2-2000000000-200000200000000
χ202222222222-2-2-222-2-2-2-2-2-2-2000000220000-2-222000000000200000-200000000
χ2122222222-2-2222-2-220000-2-22222220022-2-2000000000000-200000-2000000000
χ2222222222-2-2222-2-220000-2-22222-2-200-2-2-2-20000000000002000002000000000
χ2322222222-2-2222-2-220000-2-2-2-2-2-22200-2-222000000000000200000-2000000000
χ2422222222-2-2222-2-220000-2-2-2-2-2-2-2-2002222000000000000-2000002000000000
χ2522-2-2-222-222-222-2-2-200002-222-2-20000002-2000000000000002-22-20000000000
χ2622-2-2-222-222-222-2-2-200002-222-2-20000002-200000000000000-22-220000000000
χ2722-2-2-222-222-222-2-2-200002-2-2-222000000-22000000000000002-2-220000000000
χ2822-2-2-222-222-222-2-2-200002-2-2-222000000-2200000000000000-222-20000000000
χ2922-2-2-222-2-2-22-2-22222i2i−2i−2i2-20000002i−2i0000000000002i2i−2i−2i0000000000002-200
χ3022-2-2-222-2-2-22-2-22222i2i−2i−2i2-20000002i−2i000000000000−2i−2i2i2i000000000000-2200
χ3122-2-2-222-2-2-22-2-2222−2i−2i2i2i2-2000000−2i2i0000000000002i2i−2i−2i000000000000-2200
χ3222-2-2-222-2-2-22-2-2222−2i−2i2i2i2-2000000−2i2i000000000000−2i−2i2i2i0000000000002-200
χ3322-2-2-222-2-2-2-22222-22i2i−2i−2i-2222-2-200−2i2i00-2200002i2i−2i−2i00000000000000000000
χ3422-2-2-222-2-2-2-22222-22i2i−2i−2i-22-2-22200−2i2i002-20000−2i−2i2i2i00000000000000000000
χ3522-2-2-222-2-2-2-22222-2−2i−2i2i2i-2222-2-2002i−2i00-220000−2i−2i2i2i00000000000000000000
χ3622-2-2-222-2-2-2-22222-2−2i−2i2i2i-22-2-222002i−2i002-200002i2i−2i−2i00000000000000000000
χ372-222-22-2-200-22-20020000002i−2i2i−2i2-2002i−2i002−22−20000i2−i2i2−i2000000002−2i2−i20000
χ382-222-22-2-200-22-20020000002i−2i2i−2i2-2002i−2i00−22−220000−i2i2−i2i200000000−22−i2i20000
χ392-222-22-2-200-22-20020000002i−2i2i−2i-2200−2i2i002−22−20000i2−i2i2−i200000000−22−i2i20000
χ402-222-22-2-200-22-20020000002i−2i2i−2i-2200−2i2i00−22−220000−i2i2−i2i2000000002−2i2−i20000
χ412-222-22-2-200-22-2002000000−2i2i−2i2i2-200−2i2i002−22−20000−i2i2−i2i2000000002−2−i2i20000
χ422-222-22-2-200-22-2002000000−2i2i−2i2i2-200−2i2i00−22−220000i2−i2i2−i200000000−22i2−i20000
χ432-222-22-2-200-22-2002000000−2i2i−2i2i-22002i−2i002−22−20000−i2i2−i2i200000000−22i2−i20000
χ442-222-22-2-200-22-2002000000−2i2i−2i2i-22002i−2i00−22−220000i2−i2i2−i2000000002−2−i2i20000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ46444-44-4-4-44-40004-40000000000000000000000022−2222−2200000000000000000000
χ47444-44-4-4-44-40004-400000000000000000000000−2222−222200000000000000000000
χ48444-44-4-4-4-44000-4404-44-4000000000000000000000000000000000000000000
χ49444-44-4-4-4-44000-440-44-44000000000000000000000000000000000000000000
χ5044-44-4-4-444-4000-4404i−4i−4i4i000000000000000000000000000000000000000000
χ5144-44-4-4-444-4000-440−4i4i4i−4i000000000000000000000000000000000000000000
χ5244-44-4-4-44-440004-4000000000000000000000002i2−2i2−2i22i200000000000000000000
χ5344-44-4-4-44-440004-400000000000000000000000−2i22i22i2−2i200000000000000000000
χ5444-4-4-444-4444-4-4-4-440000-440000000000000000000000000000000000000000
χ554-444-44-4-4004-4400-400000000000000000022−22−2222000000000000000000000000
χ564-444-44-4-4004-4400-4000000000000000000−222222−22000000000000000000000000
χ574-4-4-444-440044-400-40000004i−4i−4i4i000000000000000000000000000000000000
χ584-4-4-444-440044-400-4000000−4i4i4i−4i000000000000000000000000000000000000
χ594-4-4-444-4400-4-440040000000000000000000000000022−22−22220000000000000000
χ604-4-4-444-4400-4-4400400000000000000000000000000−222222−220000000000000000
χ618-88-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-888-88-8000000000000000000000000000000000000000000000000000000

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