Finite Group Databasebeta

← Group #282788

Character table — Group #282788

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111-1-1-1-11111111111-1-11-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-111-111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111-1111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1111-1-11111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111111111-1-11111-1-1-1-1-1-11
χ172222222222-22-2-2-2222220000-2-2222200002200-2-200000000-2-20000000000000-20000000
χ182222222222-22-2-2-2222220000-2-2-2-2-2-20000-2-200-2-20000000022000000000000020000000
χ192222222222-22-2-2-22-2-2-2-20000-2-222220000-2-2002200000000-2-2000000000000020000000
χ202222222222-22-2-2-22-2-2-2-20000-2-2-2-2-2-2000022002200000000220000000000000-20000000
χ2122222222-2-22-2222-200002222-2-200002222002200-2-2-2-20000000000000000-20000000000
χ2222222222-2-22-2222-200002222-2-20000-2-2-2-200-2-200-2-222000000000000000020000000000
χ2322222222-2-22-2222-20000-2-2-2-2-2-20000222200-2-20022-2-2000000000000000020000000000
χ2422222222-2-22-2222-20000-2-2-2-2-2-20000-2-2-2-200220022220000000000000000-20000000000
χ25222-2-2-22-200-202-220000022-2-20022−2−22i2i−2i−2i002i−2i00000000002−222−2−2i2i2−i2−i20000000000i2−i20
χ26222-2-2-22-200-202-220000022-2-20022−2−2−2i−2i2i2i00−2i2i00000000002−222−2−2−i2−i2i2i20000000000−i2i20
χ27222-2-2-22-200-202-220000022-2-200−2−2222i2i−2i−2i002i−2i0000000000−22−2−222−i2−i2i2i20000000000−i2i20
χ28222-2-2-22-200-202-220000022-2-200−2−222−2i−2i2i2i00−2i2i0000000000−22−2−222i2i2−i2−i20000000000i2−i20
χ29222-2-2-22-200-202-2200000-2-2220022−2−22i2i−2i−2i00−2i2i00000000002−2−2−222i2i2−i2−i20000000000−i2i20
χ30222-2-2-22-200-202-2200000-2-2220022−2−2−2i−2i2i2i002i−2i00000000002−2−2−222−i2−i2i2i20000000000i2−i20
χ31222-2-2-22-200-202-2200000-2-22200−2−2222i2i−2i−2i00−2i2i0000000000−2222−2−2−i2−i2i2i20000000000i2−i20
χ32222-2-2-22-200-202-2200000-2-22200−2−222−2i−2i2i2i002i−2i0000000000−2222−2−2i2i2−i2−i20000000000−i2i20
χ3322-22-22-2-22-20-200022i2i−2i−2i0000002i−2i2i−2i2−22−22-20000002−2i2i2−i2−i2000000i2−i2i2−i2000000002−2000
χ3422-22-22-2-22-20-200022i2i−2i−2i0000002i−2i2i−2i−22−222-2000000−22−i2−i2i2i2000000−i2i2−i2i200000000−22000
χ3522-22-22-2-22-20-200022i2i−2i−2i000000−2i2i−2i2i2−22−2-220000002−2i2i2−i2−i2000000−i2i2−i2i200000000−22000
χ3622-22-22-2-22-20-200022i2i−2i−2i000000−2i2i−2i2i−22−22-22000000−22−i2−i2i2i2000000i2−i2i2−i2000000002−2000
χ3722-22-22-2-22-20-20002−2i−2i2i2i0000002i−2i2i−2i2−22−2-220000002−2−i2−i2i2i2000000i2−i2i2−i200000000−22000
χ3822-22-22-2-22-20-20002−2i−2i2i2i0000002i−2i2i−2i−22−22-22000000−22i2i2−i2−i2000000−i2i2−i2i2000000002−2000
χ3922-22-22-2-22-20-20002−2i−2i2i2i000000−2i2i−2i2i2−22−22-20000002−2−i2−i2i2i2000000−i2i2−i2i2000000002−2000
χ4022-22-22-2-22-20-20002−2i−2i2i2i000000−2i2i−2i2i−22−222-2000000−22i2i2−i2−i2000000i2−i2i2−i200000000−22000
χ412-2-22-2-222222-2-2-22-22i−2i2i−2i2-22-22-20000000000002i−2i2-200000000000000000002i−2i00000000
χ422-2-22-2-222222-2-2-22-22i−2i2i−2i-22-222-20000000000002i−2i-220000000000000000000−2i2i00000000
χ432-2-22-2-222222-2-2-22-2−2i2i−2i2i2-22-22-2000000000000−2i2i2-20000000000000000000−2i2i00000000
χ442-2-22-2-222222-2-2-22-2−2i2i−2i2i-22-222-2000000000000−2i2i-2200000000000000000002i−2i00000000
χ452-2-22-2-22222-2-222-2-22i−2i2i−2i0000-22000000000000−2i2i00000000002i−2i2i−2i00000000002-200000
χ462-2-22-2-22222-2-222-2-22i−2i2i−2i0000-22000000000000−2i2i0000000000−2i2i−2i2i0000000000-2200000
χ472-2-22-2-22222-2-222-2-2−2i2i−2i2i0000-220000000000002i−2i00000000002i−2i2i−2i0000000000-2200000
χ482-2-22-2-22222-2-222-2-2−2i2i−2i2i0000-220000000000002i−2i0000000000−2i2i−2i2i00000000002-200000
χ492-2-22-2-222-2-222-2-22200002-22-2-2200000000000000-22002-22-200000000002-200000000000
χ502-2-22-2-222-2-222-2-22200002-22-2-2200000000000000-2200-22-220000000000-2200000000000
χ512-2-22-2-222-2-222-2-2220000-22-22-22000000000000002-2002-22-20000000000-2200000000000
χ522-2-22-2-222-2-222-2-2220000-22-22-22000000000000002-200-22-2200000000002-200000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-44-40040-44-4000000000002222−22−22000000000000000000−2222000000000000000000000
χ55444-4-4-44-40040-44-400000000000−22−22222200000000000000000022−22000000000000000000000
χ5644-44-44-4-4-4404000-40000000000000022−2222−2200000000−2222000000000000000000000000000
χ5744-44-44-4-4-4404000-400000000000000−2222−22220000000022−22000000000000000000000000000
χ5844-4-44-4-440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ5944-4-44-4-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ6044-4-44-4-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ6144-4-44-4-44000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ624-4444-4-4-44-404000-44-4-44000000000000000000000000000000000000000000000000000
χ634-4444-4-4-44-404000-4-444-4000000000000000000000000000000000000000000000000000
χ644-4444-4-4-4-440-4000400000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ654-4444-4-4-4-440-400040000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ664-4-44-4-444-4-4-4444-44000000004-4000000000000000000000000000000000000000000000
χ674-4-4-4444-400404-4-4000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ684-4-4-4444-400404-4-400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ694-4-4-4444-400-40-444000004-4-4400000000000000000000000000000000000000000000000
χ704-4-4-4444-400-40-44400000-444-400000000000000000000000000000000000000000000000
χ718-88-8-88-88000000000000000000000000000000000000000000000000000000000000000

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