Finite Group Databasebeta

← Group #305372

Character table — Group #305372

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882222444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-11111111111-1-1-1-1-11-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111
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
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111111-1-1-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-11111111111-1-1-1-111111-1-1-1-1-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-111-1-1-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-111-1-1111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11111-111-1-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-1-111-1111111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-11111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1111111111-1-1111-1-1-1-1-1-11
χ172222222222-2-222-2-200002222-2-20000222200-2-20022000000-2-200000000-2000000000000
χ182222222222-2-222-2-200002222-2-20000-2-2-2-200-2-200-2-200000022000000002000000000000
χ192222222222-2-222-2-20000-2-2-2-2-2-200002222002200-2-2000000-2-2000000002000000000000
χ202222222222-2-222-2-20000-2-2-2-2-2-20000-2-2-2-2002200220000002200000000-2000000000000
χ2122222222-2-222-2-22222220000-2-222220000-2-2002200-2-20000000000000000000-20000000
χ2222222222-2-222-2-22222220000-2-2-2-2-2-20000-2-200-2-20022000000000000000000020000000
χ2322222222-2-222-2-222-2-2-2-20000-2-2222200002200-2-200-2-2000000000000000000020000000
χ2422222222-2-222-2-222-2-2-2-20000-2-2-2-2-2-2000022002200220000000000000000000-20000000
χ25222-2-22-2-22222-2-2-2-222-2-222-2-22-2000000002-22-2000000000000000000000002-200000000
χ26222-2-22-2-22222-2-2-2-222-2-2-2-2222-2000000002-2-2200000000000000000000000-2200000000
χ27222-2-22-2-22222-2-2-2-2-2-22222-2-22-200000000-222-200000000000000000000000-2200000000
χ28222-2-22-2-22222-2-2-2-2-2-222-2-2222-200000000-22-22000000000000000000000002-200000000
χ29222-2-22-2-222-2-2-2-222000022-2-2-220000000000-220000000000002i2i−2i−2i000002i−2i0000000000
χ30222-2-22-2-222-2-2-2-222000022-2-2-220000000000-22000000000000−2i−2i2i2i00000−2i2i0000000000
χ31222-2-22-2-222-2-2-2-2220000-2-222-2200000000002-20000000000002i2i−2i−2i00000−2i2i0000000000
χ32222-2-22-2-222-2-2-2-2220000-2-222-2200000000002-2000000000000−2i−2i2i2i000002i−2i0000000000
χ33222-2-22-2-2-2-22222-2-222-2-20000-2200000000-22000000002i2i−2i−2i00000000000000002i−2i00000
χ34222-2-22-2-2-2-22222-2-222-2-20000-2200000000-2200000000−2i−2i2i2i0000000000000000−2i2i00000
χ35222-2-22-2-2-2-22222-2-2-2-2220000-22000000002-2000000002i2i−2i−2i0000000000000000−2i2i00000
χ36222-2-22-2-2-2-22222-2-2-2-2220000-22000000002-200000000−2i−2i2i2i00000000000000002i−2i00000
χ3722-22-2-22-2002-2002-22i−2i2i−2i00000022-2-2i2i2−i2−i200002i−2i00000000i2−i22−22−2i2i2−i2−i2000000002−2000
χ3822-22-2-22-2002-2002-22i−2i2i−2i00000022-2-2−i2−i2i2i200002i−2i00000000−i2i2−22−22−i2−i2i2i200000000−22000
χ3922-22-2-22-2002-2002-22i−2i2i−2i000000-2-222i2i2−i2−i20000−2i2i00000000i2−i22−22−2−i2−i2i2i200000000−22000
χ4022-22-2-22-2002-2002-22i−2i2i−2i000000-2-222−i2−i2i2i20000−2i2i00000000−i2i2−22−22i2i2−i2−i2000000002−2000
χ4122-22-2-22-2002-2002-2−2i2i−2i2i00000022-2-2i2i2−i2−i20000−2i2i00000000i2−i2−22−22i2i2−i2−i200000000−22000
χ4222-22-2-22-2002-2002-2−2i2i−2i2i00000022-2-2−i2−i2i2i20000−2i2i00000000−i2i22−22−2−i2−i2i2i2000000002−2000
χ4322-22-2-22-2002-2002-2−2i2i−2i2i000000-2-222i2i2−i2−i200002i−2i00000000i2−i2−22−22−i2−i2i2i2000000002−2000
χ4422-22-2-22-2002-2002-2−2i2i−2i2i000000-2-222−i2−i2i2i200002i−2i00000000−i2i22−22−2i2i2−i2−i200000000−22000
χ452-222-2-2-222-2002-20000002i−2i2i−2i00i2−i2i2−i22i−2i2i−2i0000002-2i2−i22−22−20000002−22−20000000000i2−i20
χ462-222-2-2-222-2002-20000002i−2i2i−2i00i2−i2i2−i2−2i2i−2i2i000000-22i2−i22−22−2000000−22−220000000000−i2i20
χ472-222-2-2-222-2002-20000002i−2i2i−2i00−i2i2−i2i22i−2i2i−2i0000002-2−i2i2−22−22000000−22−220000000000−i2i20
χ482-222-2-2-222-2002-20000002i−2i2i−2i00−i2i2−i2i2−2i2i−2i2i000000-22−i2i2−22−220000002−22−20000000000i2−i20
χ492-222-2-2-222-2002-2000000−2i2i−2i2i00i2−i2i2−i22i−2i2i−2i000000-22i2−i2−22−220000002−22−20000000000−i2i20
χ502-222-2-2-222-2002-2000000−2i2i−2i2i00i2−i2i2−i2−2i2i−2i2i0000002-2i2−i2−22−22000000−22−220000000000i2−i20
χ512-222-2-2-222-2002-2000000−2i2i−2i2i00−i2i2−i2i22i−2i2i−2i000000-22−i2i22−22−2000000−22−220000000000i2−i20
χ522-222-2-2-222-2002-2000000−2i2i−2i2i00−i2i2−i2i2−2i2i−2i2i0000002-2−i2i22−22−20000002−22−20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-44-4-4-4-4-4-44444000000004-4000000000000000000000000000000000000000000000
χ5544-44-4-44-400-4400-44000000000000002i22i2−2i2−2i200000000000000−2i22i2000000000000000000000
χ5644-44-4-44-400-4400-4400000000000000−2i2−2i22i22i2000000000000002i2−2i2000000000000000000000
χ5744-4-44-4-44004-400-444i−4i−4i4i000000000000000000000000000000000000000000000000000
χ5844-4-44-4-44004-400-44−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ5944-4-44-4-4400-44004-400000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ6044-4-44-4-4400-44004-40000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ614-444-4-4-44-4400-440000000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ624-444-4-4-44-4400-44000000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ634-44-44-44-44-400-440000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ644-44-44-44-44-400-44000000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ654-44-44-44-4-44004-40000000000000000000000000000002i2−2i2−2i22i200000000000000000000000
χ664-44-44-44-4-44004-4000000000000000000000000000000−2i22i22i2−2i200000000000000000000000
χ674-4-4444-4-40000000000000000002i2−2i2−2i22i222−22−222200000000000000000000−2i2i2i−2i0000000000000
χ684-4-4444-4-40000000000000000002i2−2i2−2i22i2−222222−22000000000000000000002i−2i−2i2i0000000000000
χ694-4-4444-4-4000000000000000000−2i22i22i2−2i222−22−2222000000000000000000002i−2i−2i2i0000000000000
χ704-4-4444-4-4000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000−2i2i2i−2i0000000000000
χ718-8-8-8-8888000000000000000000000000000000000000000000000000000000000000000

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