Finite Group Databasebeta

← Group #336828

Character table — Group #336828

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-111111111-11-1-1-1-111-1-1-1
χ311111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-111111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ61111111111111111111111-1-1-1-1111111-1-1111111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-1111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-111-1-111-1-11
χ9111111111111111111-1-1-1-1111111-1-111111111-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-11-1-1
χ11111111111111111111-1-1-1-11111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1
χ12111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-111
χ13111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1111-11
χ14111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-111-1-11-11
χ17222222222-2-222-22-2-2-2222200002222-2-2000000-2-2000000000000000-2000000000
χ18222222222-2-222-22-2-2-222220000-2-2-2-222000000-2-20000000000000002000000000
χ19222222222-2-222-22-2-2-2-2-2-2-2000022-2-2-2-2000000220000000000000002000000000
χ20222222222-2-222-22-2-2-2-2-2-2-20000-2-2222200000022000000000000000-2000000000
χ2122222222-222-2-22-22-2-2000022220000002222-2-200-2-2000000000000-20000000000
χ2222222222-222-2-22-22-2-200002222000000-2-2-2-22200-2-200000000000020000000000
χ2322222222-222-2-22-22-2-20000-2-2-2-200000022-2-2220022000000000000-20000000000
χ2422222222-222-2-22-22-2-20000-2-2-2-2000000-2-222-2-2002200000000000020000000000
χ252222-2-2-2-22002-20-200022-2-222−2−22-22-200000000002−2000022−2−222−2−20000002−2000
χ262222-2-2-2-22002-20-200022-2-222−2−2-22-2200000000002−20000−2−22222−2−2000000−22000
χ272222-2-2-2-22002-20-200022-2-2−2−2222-22-20000000000−220000−2−222−2−222000000−22000
χ282222-2-2-2-22002-20-200022-2-2−2−222-22-220000000000−22000022−2−2−2−2220000002−2000
χ292222-2-2-2-22002-20-2000-2-22222−2−22-2-2200000000002−2000022−2−2−2−222000000−22000
χ302222-2-2-2-22002-20-2000-2-22222−2−2-222-200000000002−20000−2−222−2−2220000002−2000
χ312222-2-2-2-22002-20-2000-2-222−2−2222-2-220000000000−220000−2−22222−2−20000002−2000
χ322222-2-2-2-22002-20-2000-2-222−2−222-222-20000000000−22000022−2−222−2−2000000−22000
χ332-22-22-22-2-2-2-2222-222-20000000000000000000000002i2i−2i−2i2-22-20000002i−2i0000000
χ342-22-22-22-2-2-2-2222-222-20000000000000000000000002i2i−2i−2i-22-22000000−2i2i0000000
χ352-22-22-22-2-2-2-2222-222-2000000000000000000000000−2i−2i2i2i2-22-2000000−2i2i0000000
χ362-22-22-22-2-2-2-2222-222-2000000000000000000000000−2i−2i2i2i-22-220000002i−2i0000000
χ372-2-222-2-2202-20020-2002−22−22i−2i2i−2i0000002-22i−2i002−200i2−i2i2−i20000i2−i2i2−i200002−200000
χ382-2-222-2-2202-20020-2002−22−22i−2i2i−2i000000-22−2i2i002−200−i2i2−i2i20000i2−i2i2−i20000−2200000
χ392-2-222-2-2202-20020-2002−22−2−2i2i−2i2i0000002-2−2i2i002−200−i2i2−i2i20000−i2i2−i2i200002−200000
χ402-2-222-2-2202-20020-2002−22−2−2i2i−2i2i000000-222i−2i002−200i2−i2i2−i20000−i2i2−i2i20000−2200000
χ412-2-222-2-2202-20020-200−22−222i−2i2i−2i0000002-22i−2i00−2200−i2i2−i2i20000−i2i2−i2i20000−2200000
χ422-2-222-2-2202-20020-200−22−222i−2i2i−2i000000-22−2i2i00−2200i2−i2i2−i20000−i2i2−i2i200002−200000
χ432-2-222-2-2202-20020-200−22−22−2i2i−2i2i0000002-2−2i2i00−2200i2−i2i2−i20000i2−i2i2−i20000−2200000
χ442-2-222-2-2202-20020-200−22−22−2i2i−2i2i000000-222i−2i00−2200−i2i2−i2i20000i2−i2i2−i200002−200000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ464444-4-4-4-4-400-440400000002222−22−2200000000000000−222200000000000000000000000
χ474444-4-4-4-4-400-44040000000−22−2222220000000000000022−2200000000000000000000000
χ4844-4-444-4-404-400-404000000000000000000004i−4i000000000000000000000000000
χ4944-4-444-4-404-400-40400000000000000000000−4i4i000000000000000000000000000
χ5044-4-444-4-40-440040-40000000000000000000000000022−22−22220000000000000000000
χ5144-4-444-4-40-440040-400000000000000000000000000−222222−220000000000000000000
χ524-44-44-44-4444-4-4-44-44-400000000000000000000000000000000000000000000000
χ534-44-44-44-44-4-4-4-4444-4400000000000000000000000000000000000000000000000
χ544-44-44-44-4-44444-4-4-4-4400000000000000000000000000000000000000000000000
χ554-44-4-44-44400-440-40000000000000004i−4i000000000000000000000000000000000
χ564-44-4-44-44400-440-4000000000000000−4i4i000000000000000000000000000000000
χ574-44-4-44-44-4004-404000000000000000000000000000000022−22−2222000000000000000
χ584-44-4-44-44-4004-4040000000000000000000000000000000−222222−22000000000000000
χ594-4-444-4-440-4400-4040022−2222−220000000000000000−22220000000000000000000000000
χ604-4-444-4-440-4400-40400−2222−2222000000000000000022−220000000000000000000000000
χ614-4-44-444-4000000000022−22−22222i2−2i2−2i22i20000000000000000000000002i−2i−2i2i00000000000
χ624-4-44-444-4000000000022−22−2222−2i22i22i2−2i2000000000000000000000000−2i2i2i−2i00000000000
χ634-4-44-444-40000000000−222222−222i2−2i2−2i22i2000000000000000000000000−2i2i2i−2i00000000000
χ644-4-44-444-40000000000−222222−22−2i22i22i2−2i20000000000000000000000002i−2i−2i2i00000000000
χ6588-8-8-8-888000000000000000000000000000000000000000000000000000000000

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