Finite Group Databasebeta

← Group #309574

Character table — Group #309574

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11-1-111-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ511111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1-111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-111-1-1-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111111-1-1-111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11111-111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-11111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111-1-1111-1-1-1-1-1-11
χ17222222222-222-2-22-222220000-2-222220000-2-2220000-2-200000000000000-2000000000000
χ18222222222-222-2-22-222220000-2-2-2-2-2-20000-2-2-2-2000022000000000000002000000000000
χ19222222222-222-2-22-2-2-2-2-20000-2-22222000022-2-20000-2-2000000000000002000000000000
χ20222222222-222-2-22-2-2-2-2-20000-2-2-2-2-2-20000222200002200000000000000-2000000000000
χ2122222222-22-2-222-2200002222-2-200002222000022-2-200-2-200000000000000000-20000000
χ2222222222-22-2-222-2200002222-2-20000-2-2-2-20000-2-2-2-200220000000000000000020000000
χ2322222222-22-2-222-220000-2-2-2-2-2-2000022220000-2-22200-2-20000000000000000020000000
χ2422222222-22-2-222-220000-2-2-2-2-2-20000-2-2-2-200002222002200000000000000000-20000000
χ25222-2-2-2-22-202-2002022-2-20000002i2i−2i−2i22−2−2002i−2i0000002−2000022−2−2i2i2−i2−i200000000i2−i2000
χ26222-2-2-2-22-202-2002022-2-20000002i2i−2i−2i−2−222002i−2i000000−220000−2−222−i2−i2i2i200000000−i2i2000
χ27222-2-2-2-22-202-2002022-2-2000000−2i−2i2i2i22−2−200−2i2i0000002−2000022−2−2−i2−i2i2i200000000−i2i2000
χ28222-2-2-2-22-202-2002022-2-2000000−2i−2i2i2i−2−22200−2i2i000000−220000−2−222i2i2−i2−i200000000i2−i2000
χ29222-2-2-2-22-202-20020-2-2220000002i2i−2i−2i22−2−200−2i2i0000002−20000−2−222i2i2−i2−i200000000−i2i2000
χ30222-2-2-2-22-202-20020-2-2220000002i2i−2i−2i−2−22200−2i2i000000−22000022−2−2−i2−i2i2i200000000i2−i2000
χ31222-2-2-2-22-202-20020-2-222000000−2i−2i2i2i22−2−2002i−2i0000002−20000−2−222−i2−i2i2i200000000i2−i2000
χ32222-2-2-2-22-202-20020-2-222000000−2i−2i2i2i−2−222002i−2i000000−22000022−2−2i2i2−i2−i200000000−i2i2000
χ332-22-22-22-222-2-2-2-2222i−2i2i−2i2i2i−2i−2i2-2000000002i−2i00002i−2i00000000000000000002-200000000
χ342-22-22-22-222-2-2-2-2222i−2i2i−2i−2i−2i2i2i2-2000000002i−2i0000−2i2i0000000000000000000-2200000000
χ352-22-22-22-222-2-2-2-222−2i2i−2i2i2i2i−2i−2i2-200000000−2i2i00002i−2i0000000000000000000-2200000000
χ362-22-22-22-222-2-2-2-222−2i2i−2i2i−2i−2i2i2i2-200000000−2i2i0000−2i2i00000000000000000002-200000000
χ372-22-22-22-22-2-2-2222-22i−2i2i−2i0000-2200000000−2i2i000000000022-2-2000000000000002i−2i00000
χ382-22-22-22-22-2-2-2222-22i−2i2i−2i0000-2200000000−2i2i0000000000-2-22200000000000000−2i2i00000
χ392-22-22-22-22-2-2-2222-2−2i2i−2i2i0000-22000000002i−2i000000000022-2-200000000000000−2i2i00000
χ402-22-22-22-22-2-2-2222-2−2i2i−2i2i0000-22000000002i−2i0000000000-2-222000000000000002i−2i00000
χ412-22-22-22-2-2222-2-2-2200002i2i−2i−2i-2200000000000000−2i2i000000002-22-2000002i−2i0000000000
χ422-22-22-22-2-2222-2-2-2200002i2i−2i−2i-2200000000000000−2i2i00000000-22-2200000−2i2i0000000000
χ432-22-22-22-2-2222-2-2-220000−2i−2i2i2i-22000000000000002i−2i000000002-22-200000−2i2i0000000000
χ442-22-22-22-2-2222-2-2-220000−2i−2i2i2i-22000000000000002i−2i00000000-22-22000002i−2i0000000000
χ452-2-2-2-222202002-20-200002i−2i2i−2i002−22−22-22-200002i−2i002−200i2−i2i2−i200002−22−20000000000i2−i20
χ462-2-2-2-222202002-20-200002i−2i2i−2i002−22−2-22-220000−2i2i002−200i2−i2i2−i20000−22−220000000000−i2i20
χ472-2-2-2-222202002-20-200002i−2i2i−2i00−22−222-22-200002i−2i00−2200−i2i2−i2i20000−22−220000000000−i2i20
χ482-2-2-2-222202002-20-200002i−2i2i−2i00−22−22-22-220000−2i2i00−2200−i2i2−i2i200002−22−20000000000i2−i20
χ492-2-2-2-222202002-20-20000−2i2i−2i2i002−22−22-22-20000−2i2i002−200−i2i2−i2i200002−22−20000000000−i2i20
χ502-2-2-2-222202002-20-20000−2i2i−2i2i002−22−2-22-2200002i−2i002−200−i2i2−i2i20000−22−220000000000i2−i20
χ512-2-2-2-222202002-20-20000−2i2i−2i2i00−22−222-22-20000−2i2i00−2200i2−i2i2−i20000−22−220000000000i2−i20
χ522-2-2-2-222202002-20-20000−2i2i−2i2i00−22−22-22-2200002i−2i00−2200i2−i2i2−i200002−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-4-4440-4400-40000000000000002222−22−220000000000−22220000000000000000000000000
χ55444-4-4-4-4440-4400-4000000000000000−22−222222000000000022−220000000000000000000000000
χ5644-44-4-44-40400-440-400004-4-4400000000000000000000000000000000000000000000000
χ5744-44-4-44-40400-440-40000-444-400000000000000000000000000000000000000000000000
χ5844-44-4-44-40-4004-4040000000000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ5944-44-4-44-40-4004-404000000000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ604-444-44-4-4404-400-40000000000000000000000000000000000022−22−222200000000000000000
χ614-444-44-4-4404-400-400000000000000000000000000000000000−222222−2200000000000000000
χ624-444-44-4-4-40-4400404i−4i−4i4i000000000000000000000000000000000000000000000000000
χ634-444-44-4-4-40-440040−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ644-44-44-44-4-4-44444-4-4000000004-4000000000000000000000000000000000000000000000
χ654-4-444-4-440000000000000000002i2−2i2−2i22i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ664-4-444-4-440000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ674-4-444-4-44000000000000000000−2i22i22i2−2i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ684-4-444-4-44000000000000000000−2i22i22i2−2i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ694-4-4-4-44440-400-4404000000000022−2222−22000000000000−2222000000000000000000000000000
χ704-4-4-4-44440-400-44040000000000−2222−222200000000000022−22000000000000000000000000000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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