Finite Group Databasebeta

← Group #344021

Character table — Group #344021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444224444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-11111111-1-1-1-1-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-1-1-1-111-1-11111-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-111-1-1-1-1-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-111-1-11111111-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111111-1-1-1-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1111-1-1-1-1-1-111-11
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111111111-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1-11111-1-1111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-111-1-1-1-1-111-1-11111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-11-1111-1-11111-1-1-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1111-11-11111-1-1-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11-1-11-1-111-1-111-1-111
χ17222222222-2-22-222-2-2-222220000-2-2-2-2000000000000000022-2-20000-22000000000000
χ18222222222-2-22-222-2-2-222220000-2-2-2-20000000000000000-2-22200002-2000000000000
χ19222222222-2-22-222-2-2-2-2-2-2-200002222000000000000000022220000-2-2000000000000
χ20222222222-2-22-222-2-2-2-2-2-2-2000022220000000000000000-2-2-2-2000022000000000000
χ2122222222-222-22-2-22-2-2000022220000-2-2-2-20000000022-2-20000002-200000000000000
χ2222222222-222-22-2-22-2-2000022220000-2-2-2-200000000-2-222000000-2200000000000000
χ2322222222-222-22-2-22-2-20000-2-2-2-200002222000000002222000000-2-200000000000000
χ2422222222-222-22-2-22-2-20000-2-2-2-20000222200000000-2-2-2-20000002200000000000000
χ252-222-2-2-22200-20-220000000i2i2−i2−i222-2-2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i200002-22-2000000000000i2−i2i2−i200
χ262-222-2-2-22200-20-220000000i2i2−i2−i222-2-2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i20000-22-22000000000000−i2i2−i2i200
χ272-222-2-2-22200-20-220000000i2i2−i2−i2-2-222i2i2−i2−i2−i2−i2−i2−i2i2i2i2i200002-2-22000000000000i2−i2−i2i200
χ282-222-2-2-22200-20-220000000i2i2−i2−i2-2-222i2i2−i2−i2−i2−i2−i2−i2i2i2i2i20000-222-2000000000000−i2i2i2−i200
χ292-222-2-2-22200-20-220000000−i2−i2i2i222-2-2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i200002-22-2000000000000−i2i2−i2i200
χ302-222-2-2-22200-20-220000000−i2−i2i2i222-2-2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i20000-22-22000000000000i2−i2i2−i200
χ312-222-2-2-22200-20-220000000−i2−i2i2i2-2-222−i2−i2i2i2i2i2i2i2−i2−i2−i2−i200002-2-22000000000000−i2i2i2−i200
χ322-222-2-2-22200-20-220000000−i2−i2i2i2-2-222−i2−i2i2i2i2i2i2i2−i2−i2−i2−i20000-222-2000000000000i2−i2−i2i200
χ332-22-222-2-22-2-2-222-222-200000000000000002i2i−2i−2i2i2i−2i−2i000000002-200002i−2i0000000000
χ342-22-222-2-22-2-2-222-222-200000000000000002i2i−2i−2i2i2i−2i−2i00000000-220000−2i2i0000000000
χ352-22-222-2-22-2-2-222-222-20000000000000000−2i−2i2i2i−2i−2i2i2i000000002-20000−2i2i0000000000
χ362-22-222-2-22-2-2-222-222-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000-2200002i−2i0000000000
χ372-2-2-2-222202-20-20020022−2−200002−22−22-22-22−22−22−22−22-22-20000000000002−22−2000000
χ382-2-2-2-222202-20-20020022−2−200002−22−22-22-22−22−22−22−2-22-22000000000000−22−22000000
χ392-2-2-2-222202-20-20020022−2−200002−22−2-22-22−22−22−22−222-2-220000000000002−2−22000000
χ402-2-2-2-222202-20-20020022−2−200002−22−2-22-22−22−22−22−22-222-2000000000000−222−2000000
χ412-2-2-2-222202-20-200200−2−2220000−22−222-22-2−22−22−22−222-22-2000000000000−22−22000000
χ422-2-2-2-222202-20-200200−2−2220000−22−222-22-2−22−22−22−22-22-220000000000002−22−2000000
χ432-2-2-2-222202-20-200200−2−2220000−22−22-22-222−22−22−22−22-2-22000000000000−222−2000000
χ442-2-2-2-222202-20-200200−2−2220000−22−22-22-222−22−22−22−2-222-20000000000002−2−22000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-44-440040-4-400000000000000000002222−22−22−22−22222200000000000000000000000000
χ47444-4-4-44-440040-4-40000000000000000000−22−2222222222−22−2200000000000000000000000000
χ48444-4-4-44-4-400-40440004i−4i4i−4i0000000000000000000000000000000000000000000000
χ49444-4-4-44-4-400-4044000−4i4i−4i4i0000000000000000000000000000000000000000000000
χ5044-44-44-4-404-40400-40000004-44-4000000000000000000000000000000000000000000
χ5144-44-44-4-404-40400-4000000-44-44000000000000000000000000000000000000000000
χ5244-44-44-4-40-440-40040000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000
χ5344-44-44-4-40-440-4004000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000
χ5444-4-44-4-4400000000000000000022−22−22222i2−2i2−2i22i22i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ5544-4-44-4-4400000000000000000022−22−2222−2i22i22i2−2i2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5644-4-44-4-44000000000000000000−222222−222i2−2i2−2i22i2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ5744-4-44-4-44000000000000000000−222222−22−2i22i22i2−2i22i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ584-444-4-4-44-400404-400000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ594-444-4-4-44-400404-40000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ604-44-444-4-4444-4-44-4-4-4400000000000000000000000000000000000000000000000000
χ614-44-444-4-4-4444-4-44-44-400000000000000000000000000000000000000000000000000
χ624-44-444-4-4-4-4-444-444-4400000000000000000000000000000000000000000000000000
χ634-4-444-44-400000000002i2−2i2−2i22i22i2−2i2−2i22i2000000002-2-22-222-200000000000000000000000000
χ644-4-444-44-400000000002i2−2i2−2i22i2−2i22i22i2−2i200000000-222-22-2-2200000000000000000000000000
χ654-4-444-44-40000000000−2i22i22i2−2i22i2−2i2−2i22i200000000-222-22-2-2200000000000000000000000000
χ664-4-444-44-40000000000−2i22i22i2−2i2−2i22i22i2−2i2000000002-2-22-222-200000000000000000000000000
χ674-4-4-4-44440-440400-4002222−22−220000−2222−222200000000000000000000000000000000000000
χ684-4-4-4-44440-440400-400−22−222222000022−2222−2200000000000000000000000000000000000000

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