Finite Group Databasebeta

← Group #309577

Character table — Group #309577

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-111-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-11111-1-1-1-111111111-1-11-1-1-1-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-11111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-11-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-11111-1-111-1
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
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1111-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1111111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11
χ172222222222-2-222-2-200002222-2-200002222002200-2-200-2-2000000000000000-2000000000
χ182222222222-2-222-2-200002222-2-20000-2-2-2-200-2-200-2-200220000000000000002000000000
χ192222222222-2-222-2-20000-2-2-2-2-2-20000222200-2-2002200-2-20000000000000002000000000
χ202222222222-2-222-2-20000-2-2-2-2-2-20000-2-2-2-2002200220022000000000000000-2000000000
χ2122222222-2-222-2-22222220000-2-2222200002200-2-200-2-20000000000000000-20000000000
χ2222222222-2-222-2-22222220000-2-2-2-2-2-20000-2-200-2-20022000000000000000020000000000
χ2322222222-2-222-2-222-2-2-2-20000-2-222220000-2-2002200-2-2000000000000000020000000000
χ2422222222-2-222-2-222-2-2-2-20000-2-2-2-2-2-2000022002200220000000000000000-20000000000
χ2522-22-2-2-22002-2002-22i2i−2i−2i0000002i2i−2i−2ii2i2−i2−i22-200000000i2−i2000022−2−222−2−200000000i2−i2000
χ2622-22-2-2-22002-2002-22i2i−2i−2i0000002i2i−2i−2i−i2−i2i2i22-200000000−i2i20000−2−222−2−22200000000−i2i2000
χ2722-22-2-2-22002-2002-22i2i−2i−2i000000−2i−2i2i2ii2i2−i2−i2-2200000000i2−i2000022−2−2−2−22200000000−i2i2000
χ2822-22-2-2-22002-2002-22i2i−2i−2i000000−2i−2i2i2i−i2−i2i2i2-2200000000−i2i20000−2−22222−2−200000000i2−i2000
χ2922-22-2-2-22002-2002-2−2i−2i2i2i0000002i2i−2i−2ii2i2−i2−i2-2200000000i2−i20000−2−22222−2−200000000−i2i2000
χ3022-22-2-2-22002-2002-2−2i−2i2i2i0000002i2i−2i−2i−i2−i2i2i2-2200000000−i2i2000022−2−2−2−22200000000i2−i2000
χ3122-22-2-2-22002-2002-2−2i−2i2i2i000000−2i−2i2i2ii2i2−i2−i22-200000000i2−i20000−2−222−2−22200000000i2−i2000
χ3222-22-2-2-22002-2002-2−2i−2i2i2i000000−2i−2i2i2i−i2−i2i2i22-200000000−i2i2000022−2−222−2−200000000−i2i2000
χ332-22-22-2-222-2002-20000002i2i−2i−2i00i2−i2i2−i22i−2i2i−2i002-20000i2−i20022−2−200002−22−20000000000i2−i20
χ342-22-22-2-222-2002-20000002i2i−2i−2i00i2−i2i2−i2−2i2i−2i2i00-220000i2−i20022−2−20000−22−220000000000−i2i20
χ352-22-22-2-222-2002-20000002i2i−2i−2i00−i2i2−i2i22i−2i2i−2i002-20000−i2i200−2−2220000−22−220000000000−i2i20
χ362-22-22-2-222-2002-20000002i2i−2i−2i00−i2i2−i2i2−2i2i−2i2i00-220000−i2i200−2−22200002−22−20000000000i2−i20
χ372-22-22-2-222-2002-2000000−2i−2i2i2i00i2−i2i2−i22i−2i2i−2i00-220000i2−i200−2−22200002−22−20000000000−i2i20
χ382-22-22-2-222-2002-2000000−2i−2i2i2i00i2−i2i2−i2−2i2i−2i2i002-20000i2−i200−2−2220000−22−220000000000i2−i20
χ392-22-22-2-222-2002-2000000−2i−2i2i2i00−i2i2−i2i22i−2i2i−2i00-220000−i2i20022−2−20000−22−220000000000i2−i20
χ402-22-22-2-222-2002-2000000−2i−2i2i2i00−i2i2−i2i2−2i2i−2i2i002-20000−i2i20022−2−200002−22−20000000000−i2i20
χ412-2-222-22-222-2-2-2-2222i−2i2i−2i0000-220000000000002i−2i0000002-22-20000000000002i−2i0000000
χ422-2-222-22-222-2-2-2-2222i−2i2i−2i0000-220000000000002i−2i000000-22-22000000000000−2i2i0000000
χ432-2-222-22-222-2-2-2-222−2i2i−2i2i0000-22000000000000−2i2i0000002-22-2000000000000−2i2i0000000
χ442-2-222-22-222-2-2-2-222−2i2i−2i2i0000-22000000000000−2i2i000000-22-220000000000002i−2i0000000
χ452-2-222-22-2-2-22222-2-200002i−2i2i−2i-22000000000000002i−2i000000002-22-200000000002i−2i00000
χ462-2-222-22-2-2-22222-2-200002i−2i2i−2i-22000000000000002i−2i00000000-22-220000000000−2i2i00000
χ472-2-222-22-2-2-22222-2-20000−2i2i−2i2i-2200000000000000−2i2i000000002-22-20000000000−2i2i00000
χ482-2-222-22-2-2-22222-2-20000−2i2i−2i2i-2200000000000000−2i2i00000000-22-2200000000002i−2i00000
χ492-2-222-22-2-2-2-2-222222i−2i2i−2i2i−2i2i−2i2-2000000000000−2i2i−2i2i00000000000000002-200000000000
χ502-2-222-22-2-2-2-2-222222i−2i2i−2i−2i2i−2i2i2-2000000000000−2i2i2i−2i0000000000000000-2200000000000
χ512-2-222-22-2-2-2-2-22222−2i2i−2i2i2i−2i2i−2i2-20000000000002i−2i−2i2i0000000000000000-2200000000000
χ522-2-222-22-2-2-2-2-22222−2i2i−2i2i−2i2i−2i2i2-20000000000002i−2i2i−2i00000000000000002-200000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ5444-44-4-4-4400-4400-44000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ5544-44-4-4-4400-4400-4400000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ5644-4-444-4-44-400-440000000000000000000000000000000022−22−2222000000000000000000000
χ5744-4-444-4-44-400-4400000000000000000000000000000000−222222−22000000000000000000000
χ5844-4-444-4-4-44004-40000004-4-4400000000000000000000000000000000000000000000000
χ5944-4-444-4-4-44004-4000000-444-400000000000000000000000000000000000000000000000
χ604-444-44-4-4004-400-44000000000000000000000000000000000022−22−222200000000000000000
χ614-444-44-4-4004-400-440000000000000000000000000000000000−222222−2200000000000000000
χ624-444-44-4-400-44004-44-4-44000000000000000000000000000000000000000000000000000
χ634-444-44-4-400-44004-4-444-4000000000000000000000000000000000000000000000000000
χ644-44-44-4-44-4400-440000000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ654-44-44-4-44-4400-44000000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ664-4-444-44-44444-4-4-4-4000000004-4000000000000000000000000000000000000000000000
χ674-4-4-4-444400000000000000000022−22−222222−22−2222000000000000000000002-2-220000000000000
χ684-4-4-4-444400000000000000000022−22−2222−222222−2200000000000000000000-222-20000000000000
χ694-4-4-4-4444000000000000000000−222222−2222−22−222200000000000000000000-222-20000000000000
χ704-4-4-4-4444000000000000000000−222222−22−222222−22000000000000000000002-2-220000000000000
χ71888-8-8-88-8000000000000000000000000000000000000000000000000000000000000000

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