Finite Group Databasebeta

← Group #309527

Character table — Group #309527

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888882444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-1111-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-11111-1-1-1-111111111-1-1-11-1-1-1-1-1-111-1
χ611111111111111111111-1-1-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-11
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-111-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-111111-1-1-1-1-1-1-111-1-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ111111111111111111-1-1-1-1111111-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-1111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-11111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111-111-1-11111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111-1-1111111-1
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
χ1722222222222-2-2-2-2200002222-2-200002222002200-2-200-2-2000000000000-2000000000000
χ1822222222222-2-2-2-2200002222-2-20000-2-2-2-200-2-200-2-200220000000000002000000000000
χ1922222222222-2-2-2-220000-2-2-2-2-2-20000222200-2-2002200-2-20000000000002000000000000
χ2022222222222-2-2-2-220000-2-2-2-2-2-20000-2-2-2-2002200220022000000000000-2000000000000
χ2122222222-2-2-22222-222220000-2-2222200002200-2-200-2-200000000000000000-2000000000
χ2222222222-2-2-22222-222220000-2-2-2-2-2-20000-2-200-2-20022000000000000000002000000000
χ2322222222-2-2-22222-2-2-2-2-20000-2-222220000-2-2002200-2-2000000000000000002000000000
χ2422222222-2-2-22222-2-2-2-2-20000-2-2-2-2-2-20000220022002200000000000000000-2000000000
χ25222-2-2-22-2-22-200002000022-2-20022−2−22i2i−2i−2i002i−2i00002−20022−2−20000i2i2−i2−i200000000i2−i2000
χ26222-2-2-22-2-22-200002000022-2-20022−2−2−2i−2i2i2i00−2i2i00002−20022−2−20000−i2−i2i2i200000000−i2i2000
χ27222-2-2-22-2-22-200002000022-2-200−2−2222i2i−2i−2i002i−2i0000−2200−2−2220000−i2−i2i2i200000000−i2i2000
χ28222-2-2-22-2-22-200002000022-2-200−2−222−2i−2i2i2i00−2i2i0000−2200−2−2220000i2i2−i2−i200000000i2−i2000
χ29222-2-2-22-2-22-2000020000-2-2220022−2−22i2i−2i−2i00−2i2i00002−200−2−2220000i2i2−i2−i200000000−i2i2000
χ30222-2-2-22-2-22-2000020000-2-2220022−2−2−2i−2i2i2i002i−2i00002−200−2−2220000−i2−i2i2i200000000i2−i2000
χ31222-2-2-22-2-22-2000020000-2-22200−2−2222i2i−2i−2i00−2i2i0000−220022−2−20000−i2−i2i2i200000000i2−i2000
χ32222-2-2-22-2-22-2000020000-2-22200−2−222−2i−2i2i2i002i−2i0000−220022−2−20000i2i2−i2−i200000000−i2i2000
χ3322-2-222-2-22-2-222-2-2200002i−2i2i−2i-22000000000000002i−2i0000000022-2-200000000002i−2i00000
χ3422-2-222-2-22-2-222-2-2200002i−2i2i−2i-22000000000000002i−2i00000000-2-2220000000000−2i2i00000
χ3522-2-222-2-22-2-222-2-220000−2i2i−2i2i-2200000000000000−2i2i0000000022-2-20000000000−2i2i00000
χ3622-2-222-2-22-2-222-2-220000−2i2i−2i2i-2200000000000000−2i2i00000000-2-22200000000002i−2i00000
χ3722-2-222-2-22-2-2-2-22222i2i−2i−2i2i−2i2i−2i2-20000000000002i−2i−2i2i000000000000000002-20000000000
χ3822-2-222-2-22-2-2-2-22222i2i−2i−2i−2i2i−2i2i2-20000000000002i−2i2i−2i00000000000000000-220000000000
χ3922-2-222-2-22-2-2-2-2222−2i−2i2i2i2i−2i2i−2i2-2000000000000−2i2i−2i2i00000000000000000-220000000000
χ4022-2-222-2-22-2-2-2-2222−2i−2i2i2i−2i2i−2i2i2-2000000000000−2i2i2i−2i000000000000000002-20000000000
χ4122-2-222-2-2-222-2-222-22i2i−2i−2i0000-22000000000000−2i2i0000002-22-20000000000002i−2i0000000
χ4222-2-222-2-2-222-2-222-22i2i−2i−2i0000-22000000000000−2i2i000000-22-22000000000000−2i2i0000000
χ4322-2-222-2-2-222-2-222-2−2i−2i2i2i0000-220000000000002i−2i0000002-22-2000000000000−2i2i0000000
χ4422-2-222-2-2-222-2-222-2−2i−2i2i2i0000-220000000000002i−2i000000-22-220000000000002i−2i0000000
χ452-2-222-22-20002-22-202-22-20000002-22-2i2−i2i2−i22-200000000i2−i20000i2−i2i2−i2i2−i2i2−i20000000000i2−i20
χ462-2-222-22-20002-22-202-22-20000002-22-2−i2i2−i2i22-200000000−i2i20000−i2i2−i2i2−i2i2−i2i20000000000−i2i20
χ472-2-222-22-20002-22-202-22-2000000-22-22i2−i2i2−i2-2200000000i2−i20000i2−i2i2−i2−i2i2−i2i20000000000−i2i20
χ482-2-222-22-20002-22-202-22-2000000-22-22−i2i2−i2i2-2200000000−i2i20000−i2i2−i2i2i2−i2i2−i20000000000i2−i20
χ492-2-222-22-20002-22-20-22-220000002-22-2i2−i2i2−i2-2200000000i2−i20000−i2i2−i2i2i2−i2i2−i20000000000−i2i20
χ502-2-222-22-20002-22-20-22-220000002-22-2−i2i2−i2i2-2200000000−i2i20000i2−i2i2−i2−i2i2−i2i20000000000i2−i20
χ512-2-222-22-20002-22-20-22-22000000-22-22i2−i2i2−i22-200000000i2−i20000−i2i2−i2i2−i2i2−i2i20000000000i2−i20
χ522-2-222-22-20002-22-20-22-22000000-22-22−i2i2−i2i22-200000000−i2i20000i2−i2i2−i2i2−i2i2−i20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-44-44-440000-400000000002222−22−22000000000000−2222000000000000000000000000000
χ55444-4-4-44-44-440000-40000000000−22−22222200000000000022−22000000000000000000000000000
χ5644-44-4-4-4444-40000-400000000000000000000000000000022−22−2222000000000000000000000
χ5744-44-4-4-4444-40000-4000000000000000000000000000000−222222−22000000000000000000000
χ5844-44-4-4-44-4-440000400004i−4i−4i4i00000000000000000000000000000000000000000000000
χ5944-44-4-4-44-4-44000040000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ6044-4-444-4-4-44444-4-4-4000000004-4000000000000000000000000000000000000000000000
χ614-44-44-4-440004-4-44000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ624-44-44-4-440004-4-4400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ634-44-44-4-44000-444-404i−4i−4i4i000000000000000000000000000000000000000000000000000
χ644-44-44-4-44000-444-40−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ654-4-444-44-4000-44-440000000000000002i2−2i22i2−2i20000000000−2i22i20000000000000000000000000
χ664-4-444-44-4000-44-44000000000000000−2i22i2−2i22i200000000002i2−2i20000000000000000000000000
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
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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