Finite Group Databasebeta

← Group #311305

Character table — Group #311305

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888844444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-11
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1111-1-1111-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-11111111-1-1-111-1-1-11
χ91111111111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ101111111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1
χ111111111111111111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-1111111-11-1-1-1-111-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-11-1-111-1-11-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-11-11111-1-11-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-11-111-1-111-11
χ17222222222-2-22-2-2222222-2-200000000000022-2-2-2-2-2-200000000220000000000000000
χ18222222222-2-22-2-2222222-2-2000000000000-2-2-2-2222200000000-2-20000000000000000
χ19222222222-2-22-2-222-2-2-2-2-2-20000000000002222-2-22200000000-2-20000000000000000
χ20222222222-2-22-2-222-2-2-2-2-2-2000000000000-2-22222-2-200000000220000000000000000
χ2122222222-222-222-2-20000-2-22222-2-2-2-22222000000000000000000000000-2-200000000
χ2222222222-222-222-2-20000-2-22222-2-2-2-2-2-2-2-20000000000000000000000002200000000
χ2322222222-222-222-2-20000-2-2-2-2-2-2222222-2-20000000000000000000000002-200000000
χ2422222222-222-222-2-20000-2-2-2-2-2-22222-2-222000000000000000000000000-2200000000
χ2522-22-2-2-22-200-200222i2i−2i−2i0022−2−222−2−2000000002-22i−2ii2i2−i2−i222−2−200i2i2−i2−i2000000000000
χ2622-22-2-2-22-200-200222i2i−2i−2i0022−2−222−2−200000000-22−2i2ii2i2−i2−i2−2−22200−i2−i2i2i2000000000000
χ2722-22-2-2-22-200-200222i2i−2i−2i00−2−222−2−222000000002-22i−2i−i2−i2i2i2−2−22200−i2−i2i2i2000000000000
χ2822-22-2-2-22-200-200222i2i−2i−2i00−2−222−2−22200000000-22−2i2i−i2−i2i2i222−2−200i2i2−i2−i2000000000000
χ2922-22-2-2-22-200-20022−2i−2i2i2i0022−2−222−2−2000000002-2−2i2i−i2−i2i2i222−2−200−i2−i2i2i2000000000000
χ3022-22-2-2-22-200-20022−2i−2i2i2i0022−2−222−2−200000000-222i−2i−i2−i2i2i2−2−22200i2i2−i2−i2000000000000
χ3122-22-2-2-22-200-20022−2i−2i2i2i00−2−222−2−222000000002-2−2i2ii2i2−i2−i2−2−22200i2i2−i2−i2000000000000
χ3222-22-2-2-22-200-20022−2i−2i2i2i00−2−222−2−22200000000-222i−2ii2i2−i2−i222−2−200−i2−i2i2i2000000000000
χ332-222-2-22-22-2-2-2222-20000-222i−2i2i−2i2i−2i2i−2i000000000000000000000000002-2002i−2i000000
χ342-222-2-22-22-2-2-2222-20000-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000-2200−2i2i000000
χ352-222-2-22-22-2-2-2222-20000-22−2i2i−2i2i−2i2i−2i2i000000000000000000000000002-200−2i2i000000
χ362-222-2-22-22-2-2-2222-20000-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000-22002i−2i000000
χ372-222-2-22-2-2222-2-2-222i−2i2i−2i-22000000000000002i−2i000000002i−2i2i−2i002-22-2000000000000
χ382-222-2-22-2-2222-2-2-222i−2i2i−2i-22000000000000002i−2i00000000−2i2i−2i2i00-22-22000000000000
χ392-222-2-22-2-2222-2-2-22−2i2i−2i2i-2200000000000000−2i2i000000002i−2i2i−2i00-22-22000000000000
χ402-222-2-22-2-2222-2-2-22−2i2i−2i2i-2200000000000000−2i2i00000000−2i2i−2i2i002-22-2000000000000
χ412-222-2-22-2-2-2-2222-222i−2i2i−2i2-22i−2i2i−2i−2i2i−2i2i000000−2i2i00002-22-20000000000000000000000
χ422-222-2-22-2-2-2-2222-222i−2i2i−2i2-2−2i2i−2i2i2i−2i2i−2i000000−2i2i0000-22-220000000000000000000000
χ432-222-2-22-2-2-2-2222-22−2i2i−2i2i2-22i−2i2i−2i−2i2i−2i2i0000002i−2i0000-22-220000000000000000000000
χ442-222-2-22-2-2-2-2222-22−2i2i−2i2i2-2−2i2i−2i2i2i−2i2i−2i0000002i−2i00002-22-20000000000000000000000
χ452-2-2222-2-2200-200-222-2-2200i2−i2−i2i2−i2i2i2−i200002-2000000−i2i2i2−i2i2−i2−i2i22-2−i2i2i2−i2000000000000
χ462-2-2222-2-2200-200-222-2-2200i2−i2−i2i2−i2i2i2−i20000-22000000−i2i2i2−i2−i2i2i2−i2-22i2−i2−i2i2000000000000
χ472-2-2222-2-2200-200-222-2-2200−i2i2i2−i2i2−i2−i2i200002-2000000i2−i2−i2i2−i2i2i2−i22-2i2−i2−i2i2000000000000
χ482-2-2222-2-2200-200-222-2-2200−i2i2i2−i2i2−i2−i2i20000-22000000i2−i2−i2i2i2−i2−i2i2-22−i2i2i2−i2000000000000
χ492-2-2222-2-2200-200-22-222-200i2−i2−i2i2−i2i2i2−i200002-2000000i2−i2−i2i2i2−i2−i2i2-22i2−i2−i2i2000000000000
χ502-2-2222-2-2200-200-22-222-200i2−i2−i2i2−i2i2i2−i20000-22000000i2−i2−i2i2−i2i2i2−i22-2−i2i2i2−i2000000000000
χ512-2-2222-2-2200-200-22-222-200−i2i2i2−i2i2−i2−i2i200002-2000000−i2i2i2−i2−i2i2i2−i2-22−i2i2i2−i2000000000000
χ522-2-2222-2-2200-200-22-222-200−i2i2i2−i2i2−i2−i2i20000-22000000−i2i2i2−i2i2−i2−i2i22-2i2−i2−i2i2000000000000
χ5344444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000000
χ54444-44-4-4-404-404-400000000000000004-4000000000000000000000000000000000000
χ55444-44-4-4-404-404-40000000000000000-44000000000000000000000000000000000000
χ56444-44-4-4-40-440-4400000000000000000000000000000000000000000000000022−220000
χ57444-44-4-4-40-440-44000000000000000000000000000000000000000000000000−22220000
χ5844-44-4-4-44400400-4-40000002222−22−22−22−22222200000000000000000000000000000000000000
χ5944-44-4-4-44400400-4-4000000−22−2222222222−22−2200000000000000000000000000000000000000
χ604-444-4-44-4444-4-4-44-400004-40000000000000000000000000000000000000000000000
χ614-44-4-44-4404-40-44000000000000000000000000000000000000000000000000002i2−2i200
χ624-44-4-44-4404-40-4400000000000000000000000000000000000000000000000000−2i22i200
χ634-44-4-44-440-4404-40000000000000000004i−4i0000000000000000000000000000000000
χ644-44-4-44-440-4404-4000000000000000000−4i4i0000000000000000000000000000000000
χ654-4-4444-4-4-4004004-40000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ664-4-4444-4-4-4004004-4000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ6788-8-8-888-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-88-888000000000000000000000000000000000000000000000000000000000000

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