Finite Group Databasebeta

← Group #288192

Character table — Group #288192

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888222244888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-11-111-1-11-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-1-111-11
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-111-1111-1-11-1
χ91111111111111111-1-1-1-11111111111-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ101111111111111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1111-1-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1111111-1-1-1111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1111-111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-111-1-1-11-1-1111-1
χ172222222222-22-2-2-222222-2-200000000-2-2220000-2-22200000000-2-20000000000000000
χ182222222222-22-2-2-222222-2-200000000-2-2-2-2000022-2-200000000220000000000000000
χ192222222222-22-2-2-22-2-2-2-2-2-20000000022220000-2-2-2-200000000220000000000000000
χ202222222222-22-2-2-22-2-2-2-2-2-20000000022-2-20000222200000000-2-20000000000000000
χ2122222222-2-22-2222-20000-2-22222-2-2-2-2000022-2-20000000000000000000000-22000000
χ2222222222-2-22-2222-20000-2-22222-2-2-2-20000-2-22200000000000000000000002-2000000
χ2322222222-2-22-2222-20000-2-2-2-2-2-22222000022220000000000000000000000-2-2000000
χ2422222222-2-22-2222-20000-2-2-2-2-2-222220000-2-2-2-2000000000000000000000022000000
χ252222-2-2-2-22-20-200022i2i−2i−2i0022−2−222−2−2002-20000002i−2ii2i2−i2−i222−2−200i2i2−i2−i2000000000000
χ262222-2-2-2-22-20-200022i2i−2i−2i0022−2−222−2−200-22000000−2i2ii2i2−i2−i2−2−22200−i2−i2i2i2000000000000
χ272222-2-2-2-22-20-200022i2i−2i−2i00−2−222−2−222002-20000002i−2i−i2−i2i2i2−2−22200−i2−i2i2i2000000000000
χ282222-2-2-2-22-20-200022i2i−2i−2i00−2−222−2−22200-22000000−2i2i−i2−i2i2i222−2−200i2i2−i2−i2000000000000
χ292222-2-2-2-22-20-20002−2i−2i2i2i0022−2−222−2−2002-2000000−2i2i−i2−i2i2i222−2−200−i2−i2i2i2000000000000
χ302222-2-2-2-22-20-20002−2i−2i2i2i0022−2−222−2−200-220000002i−2i−i2−i2i2i2−2−22200i2i2−i2−i2000000000000
χ312222-2-2-2-22-20-20002−2i−2i2i2i00−2−222−2−222002-2000000−2i2ii2i2−i2−i2−2−22200i2i2−i2−i2000000000000
χ322222-2-2-2-22-20-20002−2i−2i2i2i00−2−222−2−22200-220000002i−2ii2i2−i2−i222−2−200−i2−i2i2i2000000000000
χ332-2-222-22-22-202000-22-22-2002−22−22−22−2000000002i−2i002−22−2i2−i2i2−i22i−2ii2−i2i2−i2000000000000
χ342-2-222-22-22-202000-22-22-2002−22−22−22−200000000−2i2i002−22−2−i2i2−i2i2−2i2i−i2i2−i2i2000000000000
χ352-2-222-22-22-202000-22-22-200−22−22−22−22000000002i−2i00−22−22−i2i2−i2i22i−2i−i2i2−i2i2000000000000
χ362-2-222-22-22-202000-22-22-200−22−22−22−2200000000−2i2i00−22−22i2−i2i2−i2−2i2ii2−i2i2−i2000000000000
χ372-2-222-22-22-202000-2-22-22002−22−22−22−2000000002i−2i00−22−22i2−i2i2−i2−2i2i−i2i2−i2i2000000000000
χ382-2-222-22-22-202000-2-22-22002−22−22−22−200000000−2i2i00−22−22−i2i2−i2i22i−2ii2−i2i2−i2000000000000
χ392-2-222-22-22-202000-2-22-2200−22−22−22−22000000002i−2i002−22−2−i2i2−i2i2−2i2ii2−i2i2−i2000000000000
χ402-2-222-22-22-202000-2-22-2200−22−22−22−2200000000−2i2i002−22−2i2−i2i2−i22i−2i−i2i2−i2i2000000000000
χ412-2-22-22-22222-2-22-2-22i−2i−2i2i-22000000002i−2i000000000000002i−2i−2i2i00-222-2000000000000
χ422-2-22-22-22222-2-22-2-22i−2i−2i2i-22000000002i−2i00000000000000−2i2i2i−2i002-2-22000000000000
χ432-2-22-22-22222-2-22-2-2−2i2i2i−2i-2200000000−2i2i000000000000002i−2i−2i2i002-2-22000000000000
χ442-2-22-22-22222-2-22-2-2−2i2i2i−2i-2200000000−2i2i00000000000000−2i2i2i−2i00-222-2000000000000
χ452-2-22-22-2222-2-22-22-22i−2i−2i2i2-22-2-222-2-22−2i2i00000000002i−2i−2i2i0000000000000000000000
χ462-2-22-22-2222-2-22-22-22i−2i−2i2i2-2-222-2-222-2−2i2i0000000000−2i2i2i−2i0000000000000000000000
χ472-2-22-22-2222-2-22-22-2−2i2i2i−2i2-22-2-222-2-222i−2i0000000000−2i2i2i−2i0000000000000000000000
χ482-2-22-22-2222-2-22-22-2−2i2i2i−2i2-2-222-2-222-22i−2i00000000002i−2i−2i2i0000000000000000000000
χ492-2-22-22-22-2-2-222-2220000-222-2-22-222-2000000000000000000000000002-22-200000000
χ502-2-22-22-22-2-2-222-2220000-222-2-22-222-200000000000000000000000000-22-2200000000
χ512-2-22-22-22-2-2-222-2220000-22-222-22-2-22000000000000000000000000002-2-2200000000
χ522-2-22-22-22-2-2-222-2220000-22-222-22-2-2200000000000000000000000000-222-200000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4404000-40000002222−22−22−22−22222200000000000000000000000000000000000000
χ554444-4-4-4-4-4404000-4000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5644-4-444-4-40040-4-4400000000000000000004i−4i00000000000000000000000000000000
χ5744-4-444-4-40040-4-440000000000000000000−4i4i00000000000000000000000000000000
χ5844-4-444-4-400-4044-4000000000000000000000000000000000000000000000002i2−2i20000
χ5944-4-444-4-400-4044-400000000000000000000000000000000000000000000000−2i22i20000
χ604-44-4-444-400404-4-400000000000000000000000000000000000000000000000002i2−2i200
χ614-44-4-444-400404-4-40000000000000000000000000000000000000000000000000−2i22i200
χ624-44-4-444-400-40-4440000000000000000000004-4000000000000000000000000000000
χ634-44-4-444-400-40-444000000000000000000000-44000000000000000000000000000000
χ644-4-444-44-4-440-4000400000022−2222−22−2222−222200000000000000000000000000000000000000
χ654-4-444-44-4-440-40004000000−2222−222222−2222−2200000000000000000000000000000000000000
χ664-4-44-44-44-4-444-44-4400004-40000000000000000000000000000000000000000000000
χ6788-8-8-8-888000000000000000000000000000000000000000000000000000000000000
χ688-88-88-8-88000000000000000000000000000000000000000000000000000000000000

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