Finite Group Databasebeta

← Group #310552

Character table — Group #310552

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111111111-11-1-1-1-1-1-1-1-1-1-111-1
χ311111111111111111111111111-1-111111111-1-1-1-1111111-1-1-1-11-11111-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ51111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-111-1-11111-1-111-1
χ91111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1111
χ101111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1111111-1
χ111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111111-1-1-1-1-1-1-11111-1-1-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11111-1111-1-111-1-111-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-111-1-111-1-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11-1-1-11111-1-11111-1
χ172222222222-2-22-2-220000-2-22222000022-2-2-2-200000000-2-20000200000000000000
χ182222222222-2-22-2-220000-2-222220000-2-2222200000000-2-20000-200000000000000
χ192222222222-2-22-2-220000-2-2-2-2-2-2000022-2-22200000000220000-200000000000000
χ202222222222-2-22-2-220000-2-2-2-2-2-20000-2-222-2-200000000220000200000000000000
χ2122222222-2-222-222-22222-2-2000022-2-200000022-2-200000000000-20000000000000
χ2222222222-2-222-222-22222-2-20000-2-2-2-2000000-2-2220000000000020000000000000
χ2322222222-2-222-222-2-2-2-2-2-2-200002222000000-2-22200000000000-20000000000000
χ2422222222-2-222-222-2-2-2-2-2-2-20000-2-22200000022-2-20000000000020000000000000
χ252-2-22-22-222-2222-2-2-22i2i−2i−2i-220000002i−2i2i−2i2i−2i000000000000000000002-2000000000
χ262-2-22-22-222-2222-2-2-22i2i−2i−2i-220000002i−2i−2i2i−2i2i00000000000000000000-22000000000
χ272-2-22-22-222-2222-2-2-2−2i−2i2i2i-22000000−2i2i2i−2i2i−2i00000000000000000000-22000000000
χ282-2-22-22-222-2222-2-2-2−2i−2i2i2i-22000000−2i2i−2i2i−2i2i000000000000000000002-2000000000
χ292-2-22-22-222-2-2-2222-200002-2000000002i−2i−2i2i00000022-2-2000000002i−2i00000000000
χ302-2-22-22-222-2-2-2222-200002-2000000002i−2i−2i2i000000-2-22200000000−2i2i00000000000
χ312-2-22-22-222-2-2-2222-200002-200000000−2i2i2i−2i00000022-2-200000000−2i2i00000000000
χ322-2-22-22-222-2-2-2222-200002-200000000−2i2i2i−2i000000-2-222000000002i−2i00000000000
χ332-2-22-22-22-2222-2-2-222i2i−2i−2i2-2000000−2i2i000000000000000000000000002-22i−2i00000
χ342-2-22-22-22-2222-2-2-222i2i−2i−2i2-2000000−2i2i00000000000000000000000000-22−2i2i00000
χ352-2-22-22-22-2222-2-2-22−2i−2i2i2i2-20000002i−2i000000000000000000000000002-2−2i2i00000
χ362-2-22-22-22-2222-2-2-22−2i−2i2i2i2-20000002i−2i00000000000000000000000000-222i−2i00000
χ372-2-2-2222-2002-202-202i−2i2i−2i00i2i2−i2−i22i−2i000000002-2002−22−2i2−i2i2i2−i2−i20000000000002−20
χ382-2-2-2222-2002-202-202i−2i2i−2i00i2i2−i2−i2−2i2i00000000-22002−22−2i2−i2−i2−i2i2i2000000000000−220
χ392-2-2-2222-2002-202-202i−2i2i−2i00−i2−i2i2i22i−2i000000002-200−22−22−i2i2−i2−i2i2i2000000000000−220
χ402-2-2-2222-2002-202-202i−2i2i−2i00−i2−i2i2i2−2i2i00000000-2200−22−22−i2i2i2i2−i2−i20000000000002−20
χ412-2-2-2222-2002-202-20−2i2i−2i2i00i2i2−i2−i22i−2i00000000-2200−22−22i2−i2−i2−i2i2i20000000000002−20
χ422-2-2-2222-2002-202-20−2i2i−2i2i00i2i2−i2−i2−2i2i000000002-200−22−22i2−i2i2i2−i2−i2000000000000−220
χ432-2-2-2222-2002-202-20−2i2i−2i2i00−i2−i2i2i22i−2i00000000-22002−22−2−i2i2i2i2−i2−i2000000000000−220
χ442-2-2-2222-2002-202-20−2i2i−2i2i00−i2−i2i2i2−2i2i000000002-2002−22−2−i2i2−i2−i2i2i20000000000002−20
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-44-4-4004-40-4404-4-44000000000000000000000000000000000000000000000
χ47444-4-44-4-4004-40-440-444-4000000000000000000000000000000000000000000000
χ48444-4-44-4-400-4404-4000000000000000000000000022−22−2222000000000000000000000
χ49444-4-44-4-400-4404-40000000000000000000000000−222222−22000000000000000000000
χ5044-444-4-4-44-400-400400000000000000000000000000000022−2222−22000000000000000
χ5144-444-4-4-44-400-4004000000000000000000000000000000−2222−2222000000000000000
χ5244-444-4-4-4-4400400-40000004-44-4000000000000000000000000000000000000000
χ5344-444-4-4-4-4400400-4000000-44-44000000000000000000000000000000000000000
χ544-444-4-44-44400-400-40000000000000000000000000000000000000000000022−22000
χ554-444-4-44-44400-400-400000000000000000000000000000000000000000000−2222000
χ564-444-4-44-4-4-40040040000000000000000004i−4i00000000000000000000000000000
χ574-444-4-44-4-4-4004004000000000000000000−4i4i00000000000000000000000000000
χ584-44-44-4-44000000000000002i2−2i2−2i22i200000000000022−220000002i−2i−2i2i000000000000000
χ594-44-44-4-44000000000000002i2−2i2−2i22i2000000000000−2222000000−2i2i2i−2i000000000000000
χ604-44-44-4-4400000000000000−2i22i22i2−2i200000000000022−22000000−2i2i2i−2i000000000000000
χ614-44-44-4-4400000000000000−2i22i22i2−2i2000000000000−22220000002i−2i−2i2i000000000000000
χ624-4-44-44-44-44-4-4-44440000-440000000000000000000000000000000000000000000
χ634-4-4-4444-400-440-4400000002i22i2−2i2−2i2000000000000000000−2i22i20000000000000000000
χ644-4-4-4444-400-440-440000000−2i2−2i22i22i20000000000000000002i2−2i20000000000000000000
χ6588-8-8-8-888000000000000000000000000000000000000000000000000000000000

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