Finite Group Databasebeta

← Group #269727

Character table — Group #269727

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444442222222244888888884444444488888888888888882224444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111-1111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ511111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-111111111-1-1-11-1-1-1-1-1-111-1
χ611111111111111111111-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11
χ711111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-11-11111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-11-1-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111-111-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-11-1-1111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ172222222222-22-2-2-2200002222-2-2000022220000-2-22200-2-200000000000000-20000000000
χ182222222222-22-2-2-2200002222-2-20000-2-2-2-20000-2-2-2-200220000000000000020000000000
χ192222222222-22-2-2-220000-2-2-2-2-2-200002222000022-2-200-2-20000000000000020000000000
χ202222222222-22-2-2-220000-2-2-2-2-2-20000-2-2-2-200002222002200000000000000-20000000000
χ2122222222-2-22-2222-222220000-2-222220000-2-2220000-2-200000000000000000-2000000000
χ2222222222-2-22-2222-222220000-2-2-2-2-2-20000-2-2-2-2000022000000000000000002000000000
χ2322222222-2-22-2222-2-2-2-2-20000-2-22222000022-2-20000-2-2000000000000000002000000000
χ2422222222-2-22-2222-2-2-2-2-20000-2-2-2-2-2-20000222200002200000000000000000-2000000000
χ2522-22-2-2-2200202-2-2022-2-20000002i2i−2i−2i22−2−2002i−2i0000002−2000022−2−2i2i2−i2−i20000000000i2−i20
χ2622-22-2-2-2200202-2-2022-2-20000002i2i−2i−2i−2−222002i−2i000000−220000−2−222−i2−i2i2i20000000000−i2i20
χ2722-22-2-2-2200202-2-2022-2-2000000−2i−2i2i2i22−2−200−2i2i0000002−2000022−2−2−i2−i2i2i20000000000−i2i20
χ2822-22-2-2-2200202-2-2022-2-2000000−2i−2i2i2i−2−22200−2i2i000000−220000−2−222i2i2−i2−i20000000000i2−i20
χ2922-22-2-2-2200202-2-20-2-2220000002i2i−2i−2i22−2−200−2i2i0000002−20000−2−222i2i2−i2−i20000000000−i2i20
χ3022-22-2-2-2200202-2-20-2-2220000002i2i−2i−2i−2−22200−2i2i000000−22000022−2−2−i2−i2i2i20000000000i2−i20
χ3122-22-2-2-2200202-2-20-2-222000000−2i−2i2i2i22−2−2002i−2i0000002−20000−2−222−i2−i2i2i20000000000i2−i20
χ3222-22-2-2-2200202-2-20-2-222000000−2i−2i2i2i−2−222002i−2i000000−22000022−2−2i2i2−i2−i20000000000−i2i20
χ332-2-222-22-22-202000-2000022-2-2002−22−22i−2i2i−2i0000002i−2i2−20022−2−20000i2−i2i2−i200000000i2−i2000
χ342-2-222-22-22-202000-2000022-2-2002−22−2−2i2i−2i2i000000−2i2i2−20022−2−20000−i2i2−i2i200000000−i2i2000
χ352-2-222-22-22-202000-2000022-2-200−22−222i−2i2i−2i0000002i−2i−2200−2−2220000−i2i2−i2i200000000−i2i2000
χ362-2-222-22-22-202000-2000022-2-200−22−22−2i2i−2i2i000000−2i2i−2200−2−2220000i2−i2i2−i200000000i2−i2000
χ372-2-222-22-22-202000-20000-2-222002−22−22i−2i2i−2i000000−2i2i2−200−2−2220000i2−i2i2−i200000000−i2i2000
χ382-2-222-22-22-202000-20000-2-222002−22−2−2i2i−2i2i0000002i−2i2−200−2−2220000−i2i2−i2i200000000i2−i2000
χ392-2-222-22-22-202000-20000-2-22200−22−222i−2i2i−2i000000−2i2i−220022−2−20000−i2i2−i2i200000000i2−i2000
χ402-2-222-22-22-202000-20000-2-22200−22−22−2i2i−2i2i0000002i−2i−220022−2−20000i2−i2i2−i200000000−i2i2000
χ412-2-2-222-22222-2-22-2-22-22-200002-2000000002-200000000002i−2i2i−2i0000000000002i−2i0000000
χ422-2-2-222-22222-2-22-2-22-22-200002-2000000002-20000000000−2i2i−2i2i000000000000−2i2i0000000
χ432-2-2-222-22222-2-22-2-2-22-2200002-200000000-2200000000002i−2i2i−2i000000000000−2i2i0000000
χ442-2-2-222-22222-2-22-2-2-22-2200002-200000000-220000000000−2i2i−2i2i0000000000002i−2i0000000
χ452-2-2-222-22-2-222-22-222-22-22-22-2-2200000000-22002-20000000000000000002-200000000000
χ462-2-2-222-22-2-222-22-222-22-2-22-22-2200000000-2200-22000000000000000000-2200000000000
χ472-2-2-222-22-2-222-22-22-22-222-22-2-22000000002-2002-2000000000000000000-2200000000000
χ482-2-2-222-22-2-222-22-22-22-22-22-22-22000000002-200-220000000000000000002-200000000000
χ492-2-2-222-22-2-2-222-22200002-22-22-2000000000000-2200000000002-22-200000000002-200000
χ502-2-2-222-22-2-2-222-22200002-22-22-2000000000000-220000000000-22-220000000000-2200000
χ512-2-2-222-22-2-2-222-2220000-22-222-20000000000002-200000000002-22-20000000000-2200000
χ522-2-2-222-22-2-2-222-2220000-22-222-20000000000002-20000000000-22-2200000000002-200000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-44-4-4-44-40-400040000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ55444-44-4-4-44-40-40004000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ56444-44-4-4-4-4404000-400004-4-4400000000000000000000000000000000000000000000000
χ57444-44-4-4-4-4404000-40000-444-400000000000000000000000000000000000000000000000
χ5844-44-4-4-4400-40-4440000000000000002222−22−220000000000−22220000000000000000000000000
χ5944-44-4-4-4400-40-444000000000000000−22−222222000000000022−220000000000000000000000000
χ604-444-44-4-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ614-444-44-4-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ624-444-44-4-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ634-444-44-4-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ644-44-4-4-4440040-4-4404-4-44000000000000000000000000000000000000000000000000000
χ654-44-4-4-4440040-4-440-444-4000000000000000000000000000000000000000000000000000
χ664-44-4-4-44400-4044-40000000000000000000000000000000000022−22−222200000000000000000
χ674-44-4-4-44400-4044-400000000000000000000000000000000000−222222−2200000000000000000
χ684-4-444-44-4-440-40004000000000022−2222−22000000000000−2222000000000000000000000000000
χ694-4-444-44-4-440-400040000000000−2222−222200000000000022−22000000000000000000000000000
χ704-4-4-444-4444-4-44-44-400000000-44000000000000000000000000000000000000000000000
χ7188-8-8-888-8000000000000000000000000000000000000000000000000000000000000000

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