Finite Group Databasebeta

← Group #307998

Character table — Group #307998

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888884444444488888888888888884444444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-111-1111-1-1-1-1-1
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
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111
χ511111111111111111111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1
χ611111111111111111111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1111
χ711111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111
χ811111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-11-11111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-11111-1-111-1-1-1-11111111111-1-1-1-11-1-1-1-1-111-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-11
χ111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1111-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-111-1-1-1-11
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
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1-11111-1
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
χ172222222222-22-2-2-2222220000-2-222220000220000-2-2000000-2-20000000000000-20000000
χ182222222222-22-2-2-2222220000-2-2-2-2-2-20000-2-20000-2-200000022000000000000020000000
χ192222222222-22-2-2-22-2-2-2-20000-2-222220000-2-2000022000000-2-2000000000000020000000
χ202222222222-22-2-2-22-2-2-2-20000-2-2-2-2-2-2000022000022000000220000000000000-20000000
χ2122222222-2-22-2222-200002222-2-2000022220022-2-200-2-2000000000000000000-200000000
χ2222222222-2-22-2222-200002222-2-20000-2-2-2-200-2-2-2-20022000000000000000000200000000
χ2322222222-2-22-2222-20000-2-2-2-2-2-20000222200-2-22200-2-2000000000000000000200000000
χ2422222222-2-22-2222-20000-2-2-2-2-2-20000-2-2-2-20022220022000000000000000000-200000000
χ25222-2-2-2-222-20-2000222-2-20000002i2i−2i−2i22−2−22i−2i0000002−222−2−2000000i2i2−i2−i200000000i2−i2000
χ26222-2-2-2-222-20-2000222-2-20000002i2i−2i−2i−2−2222i−2i000000−22−2−222000000−i2−i2i2i200000000−i2i2000
χ27222-2-2-2-222-20-2000222-2-2000000−2i−2i2i2i22−2−2−2i2i0000002−222−2−2000000−i2−i2i2i200000000−i2i2000
χ28222-2-2-2-222-20-2000222-2-2000000−2i−2i2i2i−2−222−2i2i000000−22−2−222000000i2i2−i2−i200000000i2−i2000
χ29222-2-2-2-222-20-20002-2-2220000002i2i−2i−2i22−2−2−2i2i0000002−2−2−222000000i2i2−i2−i200000000−i2i2000
χ30222-2-2-2-222-20-20002-2-2220000002i2i−2i−2i−2−222−2i2i000000−2222−2−2000000−i2−i2i2i200000000i2−i2000
χ31222-2-2-2-222-20-20002-2-222000000−2i−2i2i2i22−2−22i−2i0000002−2−2−222000000−i2−i2i2i200000000i2−i2000
χ32222-2-2-2-222-20-20002-2-222000000−2i−2i2i2i−2−2222i−2i000000−2222−2−2000000i2i2−i2−i200000000−i2i2000
χ3322-22-22-2-2222-2-22-2-2000022-2-22-20000000000002-200002-22-200000000002-200000000000
χ3422-22-22-2-2222-2-22-2-2000022-2-22-20000000000002-20000-22-220000000000-2200000000000
χ3522-22-22-2-2222-2-22-2-20000-2-2222-2000000000000-2200002-22-20000000000-2200000000000
χ3622-22-22-2-2222-2-22-2-20000-2-2222-2000000000000-220000-22-2200000000002-200000000000
χ3722-22-22-2-2-2-222-22-222i−2i2i−2i22-2-2-22000000000000-222i−2i0000000000000000002i−2i000000000
χ3822-22-22-2-2-2-222-22-222i−2i2i−2i-2-222-220000000000002-22i−2i000000000000000000−2i2i000000000
χ3922-22-22-2-2-2-222-22-22−2i2i−2i2i22-2-2-22000000000000-22−2i2i000000000000000000−2i2i000000000
χ4022-22-22-2-2-2-222-22-22−2i2i−2i2i-2-222-220000000000002-2−2i2i0000000000000000002i−2i000000000
χ4122-22-22-2-2-2-2-222-2222i−2i2i−2i00002-200000000000000−2i2i0000000022-2-200000000002i−2i00000
χ4222-22-22-2-2-2-2-222-2222i−2i2i−2i00002-200000000000000−2i2i00000000-2-2220000000000−2i2i00000
χ4322-22-22-2-2-2-2-222-222−2i2i−2i2i00002-2000000000000002i−2i0000000022-2-20000000000−2i2i00000
χ4422-22-22-2-2-2-2-222-222−2i2i−2i2i00002-2000000000000002i−2i00000000-2-22200000000002i−2i00000
χ452-2-222-2-220020-2-22000002-22-200i2−i2i2−i22-22-2002-20000000000i2−i2i2−i2i2−i2i2−i2i2−i20000000000i2−i20
χ462-2-222-2-220020-2-22000002-22-200i2−i2i2−i2-22-2200-220000000000i2−i2i2−i2i2−i2−i2i2−i2i20000000000−i2i20
χ472-2-222-2-220020-2-22000002-22-200−i2i2−i2i22-22-2002-20000000000−i2i2−i2i2−i2i2−i2i2−i2i20000000000−i2i20
χ482-2-222-2-220020-2-22000002-22-200−i2i2−i2i2-22-2200-220000000000−i2i2−i2i2−i2i2i2−i2i2−i20000000000i2−i20
χ492-2-222-2-220020-2-2200000-22-2200i2−i2i2−i22-22-200-220000000000i2−i2−i2i2−i2i2i2−i2i2−i20000000000−i2i20
χ502-2-222-2-220020-2-2200000-22-2200i2−i2i2−i2-22-22002-20000000000i2−i2−i2i2−i2i2−i2i2−i2i20000000000i2−i20
χ512-2-222-2-220020-2-2200000-22-2200−i2i2−i2i22-22-200-220000000000−i2i2i2−i2i2−i2−i2i2−i2i20000000000i2−i20
χ522-2-222-2-220020-2-2200000-22-2200−i2i2−i2i2-22-22002-20000000000−i2i2i2−i2i2−i2i2−i2i2−i20000000000−i2i20
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4404000-4000000000000002222−22−2200000000−2222000000000000000000000000000
χ55444-4-4-4-44-4404000-400000000000000−22−2222220000000022−22000000000000000000000000000
χ5644-44-44-4-444-4-44-44-400000000-44000000000000000000000000000000000000000000000
χ5744-4-44-44-44-404000-4000000000000000000000000000022−22−222200000000000000000000000
χ5844-4-44-44-44-404000-40000000000000000000000000000−222222−2200000000000000000000000
χ5944-4-44-44-4-440-400044i−4i−4i4i000000000000000000000000000000000000000000000000000
χ6044-4-44-44-4-440-40004−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ614-444-4-44-400404-4-4000004-4-4400000000000000000000000000000000000000000000000
χ624-444-4-44-400404-4-400000-444-400000000000000000000000000000000000000000000000
χ634-444-4-44-400-40-444000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ644-444-4-44-400-40-44400000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ654-4-444-4-4400-4044-4000000000002i2−2i22i2−2i2000000000000000000−2i22i2000000000000000000000
χ664-4-444-4-4400-4044-400000000000−2i22i2−2i22i20000000000000000002i2−2i2000000000000000000000
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
χ718-88-888-8-8000000000000000000000000000000000000000000000000000000000000000

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