Finite Group Databasebeta

← Group #342003

Character table — Group #342003

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444244444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-11-1-1-11-1-111-1-1-1-111-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111111-11-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1111-1-1-1-111-1-1-1-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-1111-1-1-1-111-1-1-11
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1111111-1-111-11
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-1-111-1-111111-1
χ9111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111111-11-1-111111-1-1-1-1-1-11-1
χ10111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-1111111-1-1-11
χ11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-111-11
χ12111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-111-1-11111111-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11-1-1-1-11-1-1-1-1-1-1111111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1111111-1-111-1-111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-111-11111-1-111-1-1-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-111-1-1-1-1-11111-1-1-1-111
χ17222222222-2-22-2-222-2-2000000002222-2-2-2-200000000000022-2-2-202000000000000000
χ18222222222-2-22-2-222-2-2000000002222-2-2-2-2000000000000-2-22220-2000000000000000
χ19222222222-2-22-2-222-2-200000000-2-2-2-222220000000000002222-20-2000000000000000
χ20222222222-2-22-2-222-2-200000000-2-2-2-22222000000000000-2-2-2-2202000000000000000
χ2122222222-222-222-2-2-2-22222-2-2-2-20000000000000000222200000-2000-2000000000000
χ2222222222-222-222-2-2-2-22222-2-2-2-20000000000000000-2-2-2-20000020002000000000000
χ2322222222-222-222-2-2-2-2-2-2-2-22222000000000000000022-2-2000002000-2000000000000
χ2422222222-222-222-2-2-2-2-2-2-2-222220000000000000000-2-22200000-20002000000000000
χ252-222-2-2-22200200-2-20022−2−222−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i200002i−2i2-20000000000i2−i22−20000
χ262-222-2-2-22200200-2-20022−2−222−2−200002i2i−2i−2ii2i2i2i2−i2−i2−i2−i20000−2i2i-220000000000−i2i2−220000
χ272-222-2-2-22200200-2-20022−2−222−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i200002i−2i-220000000000i2−i2−220000
χ282-222-2-2-22200200-2-20022−2−222−2−20000−2i−2i2i2i−i2−i2−i2−i2i2i2i2i20000−2i2i2-20000000000−i2i22−20000
χ292-222-2-2-22200200-2-200−2−222−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i200002i−2i2-20000000000−i2i2−220000
χ302-222-2-2-22200200-2-200−2−222−2−22200002i2i−2i−2i−i2−i2−i2−i2i2i2i2i20000−2i2i-220000000000i2−i22−20000
χ312-222-2-2-22200200-2-200−2−222−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i200002i−2i-220000000000−i2i22−20000
χ322-222-2-2-22200200-2-200−2−222−2−2220000−2i−2i2i2ii2i2i2i2−i2−i2−i2−i20000−2i2i2-20000000000i2−i2−220000
χ332-22-22-22-202-202-200002-22-20000i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i22-22-2000000000000i2−i20000i2−i200
χ342-22-22-22-202-202-200002-22-20000i2i2−i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2-22-22000000000000−i2i20000−i2i200
χ352-22-22-22-202-202-200002-22-20000−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i22-22-2000000000000−i2i20000−i2i200
χ362-22-22-22-202-202-200002-22-20000−i2−i2i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2-22-22000000000000i2−i20000i2−i200
χ372-22-22-22-202-202-20000-22-220000i2i2−i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i22-2-22000000000000i2−i20000−i2i200
χ382-22-22-22-202-202-20000-22-220000i2i2−i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2-222-2000000000000−i2i20000i2−i200
χ392-22-22-22-202-202-20000-22-220000−i2−i2i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i22-2-22000000000000−i2i20000i2−i200
χ402-22-22-22-202-202-20000-22-220000−i2−i2i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2-222-2000000000000i2−i20000−i2i200
χ412-2-2-222-22222-2-2-22-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000002i−2i02-20000000000
χ422-2-2-222-22222-2-2-22-22-200000000000000002i−2i2i−2i2i−2i2i−2i00000000000−2i2i0-220000000000
χ432-2-2-222-22222-2-2-22-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000002i−2i0-220000000000
χ442-2-2-222-22222-2-2-22-22-20000000000000000−2i2i−2i2i−2i2i−2i2i00000000000−2i2i02-20000000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-44-4-4000000000022−22−22220000000022−22−222222-2-2-2-22200000000000000000000000000
χ47444-4-44-4-4000000000022−22−222200000000−222222−22-2-22222-2-200000000000000000000000000
χ48444-4-44-4-40000000000−222222−220000000022−22−2222-2-22222-2-200000000000000000000000000
χ49444-4-44-4-40000000000−222222−2200000000−222222−2222-2-2-2-22200000000000000000000000000
χ5044-444-4-4-404-40-440000000000000000000022−22−222222−22−222200000000000000000000000000
χ5144-444-4-4-404-40-4400000000000000000000−222222−22−222222−2200000000000000000000000000
χ5244-444-4-4-40-4404-4000000004-44-4000000000000000000000000000000000000000000
χ5344-444-4-4-40-4404-400000000-44-44000000000000000000000000000000000000000000
χ5444-4-4-4-444400-400-4400000000000000000022−2222−22−2222−222200000000000000000000000000
χ5544-4-4-4-444400-400-44000000000000000000−2222−222222−2222−2200000000000000000000000000
χ5644-4-4-4-444-4004004-400000000004-44-400000000000000000000000000000000000000
χ5744-4-4-4-444-4004004-40000000000-44-4400000000000000000000000000000000000000
χ584-444-4-4-44-400-40044002222−22−22−22−222222000000000000000000000000000000000000000000
χ594-444-4-4-44-400-4004400−22−2222222222−22−22000000000000000000000000000000000000000000
χ604-44-44-44-40-440-440000000000002i22i2−2i2−2i2−2i22i2−2i22i20000000000000000000000000000000000
χ614-44-44-44-40-440-44000000000000−2i2−2i22i22i22i2−2i22i2−2i20000000000000000000000000000000000
χ624-4-44-444-40000000000000022−22−22222i2−2i2−2i22i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ634-4-44-444-40000000000000022−22−2222−2i22i22i2−2i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ644-4-44-444-400000000000000−222222−222i2−2i2−2i22i20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000
χ654-4-44-444-400000000000000−222222−22−2i22i22i2−2i200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000
χ664-4-4-444-444-4-4-4444-4-4400000000000000000000000000000000000000000000000000
χ674-4-4-444-44-4444-4-4-44-4400000000000000000000000000000000000000000000000000
χ684-4-4-444-44-4-4-4444-444-400000000000000000000000000000000000000000000000000

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