Finite Group Databasebeta

← Group #255468

Character table — Group #255468

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444422444444444888888888888888824444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111-1-1111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ71111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ81111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ91111111111111-1-1-1-1111-1-11111-1-1111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-1-1-111-1-1
χ101111111111111-1-1-1-1111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1-111-1-111-1-111
χ111111111111111-1-1-1-1111-1-11111-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-111-1-111-1-1-1-111
χ121111111111111-1-1-1-1111-1-11111-1-11111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1111111-1-1
χ131111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-111-1-1111111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1-111
χ141111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-111-1-111-1-1-1-11111-1-1-1-11111-1111-1-111-1-111-1-1
χ151111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1-111-1-11111-1-1
χ161111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-11-11111-1-1-1-1-1-111
χ172222222222-2-2-2222222-2-2-2000022-2-20022-20022000000000000000000-2-2000000000000
χ182222222222-2-2-2222222-2-2-2000022-2-200-2-2-200-2-200000000000000000022000000000000
χ192222222222-2-2-2-2-2-2-222-2220000-2-2-2-20022200-2-20000000000000000002-2000000000000
χ202222222222-2-2-2-2-2-2-222-2220000-2-2-2-200-2-220022000000000000000000-22000000000000
χ2122222222-2-22222222-2-22222222-2-2-2-2-2-200-2-2-20022000000000000000000000000000000
χ2222222222-2-22222222-2-2222-2-2-2-2-2-2-2-22200-22200-2-2000000000000000000000000000000
χ2322222222-2-2222-2-2-2-2-2-22-2-2222222-2-2-2-20022200-2-2000000000000000000000000000000
χ2422222222-2-2222-2-2-2-2-2-22-2-2-2-2-2-222-2-222002-2-20022000000000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-20000-2-22200002000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-22222-2-2-2-2-20000-2-2220000200000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222000022220000-2000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222000022220000-200000000000000000000000000-222-2000000
χ29222-2-22-2-2002-2-222-2-20022-22i2i−2i−2i00000000000002i−2i0000000022−2−222−2−20000000000i2−i2i2−i2
χ30222-2-22-2-2002-2-222-2-20022-22i2i−2i−2i00000000000002i−2i00000000−2−222−2−2220000000000−i2i2−i2i2
χ31222-2-22-2-2002-2-222-2-20022-2−2i−2i2i2i0000000000000−2i2i0000000022−2−222−2−20000000000−i2i2−i2i2
χ32222-2-22-2-2002-2-222-2-20022-2−2i−2i2i2i0000000000000−2i2i00000000−2−222−2−2220000000000i2−i2i2−i2
χ33222-2-22-2-2002-2-2-2-222002-222i2i−2i−2i0000000000000−2i2i0000000022−2−2−2−2220000000000i2−i2−i2i2
χ34222-2-22-2-2002-2-2-2-222002-222i2i−2i−2i0000000000000−2i2i00000000−2−22222−2−20000000000−i2i2i2−i2
χ35222-2-22-2-2002-2-2-2-222002-22−2i−2i2i2i00000000000002i−2i0000000022−2−2−2−2220000000000−i2i2i2−i2
χ36222-2-22-2-2002-2-2-2-222002-22−2i−2i2i2i00000000000002i−2i00000000−2−22222−2−20000000000i2−i2−i2i2
χ3722-22-2-22-22-20002i−2i2i−2i2-200000002i−2i00002-20002i−2i00i2i2−i2−i222−2−2i2−i2i2−i22−22−200000000000000
χ3822-22-2-22-22-20002i−2i2i−2i2-200000002i−2i00002-20002i−2i00−i2−i2i2i2−2−222−i2i2−i2i2−22−2200000000000000
χ3922-22-2-22-22-20002i−2i2i−2i2-200000002i−2i0000-22000−2i2i00i2i2−i2−i222−2−2−i2i2−i2i2−22−2200000000000000
χ4022-22-2-22-22-20002i−2i2i−2i2-200000002i−2i0000-22000−2i2i00−i2−i2i2i2−2−222i2−i2i2−i22−22−200000000000000
χ4122-22-2-22-22-2000−2i2i−2i2i2-20000000−2i2i00002-2000−2i2i00i2i2−i2−i2−2−222i2−i2i2−i2−22−2200000000000000
χ4222-22-2-22-22-2000−2i2i−2i2i2-20000000−2i2i00002-2000−2i2i00−i2−i2i2i222−2−2−i2i2−i2i22−22−200000000000000
χ4322-22-2-22-22-2000−2i2i−2i2i2-20000000−2i2i0000-220002i−2i00i2i2−i2−i2−2−222−i2i2−i2i22−22−200000000000000
χ4422-22-2-22-22-2000−2i2i−2i2i2-20000000−2i2i0000-220002i−2i00−i2−i2i2i222−2−2i2−i2i2−i2−22−2200000000000000
χ452-2-22-22-222-222-20000-22-2002-22-2002-22-20000000002i−2i2i−2i000000000000002i−2i0000000000
χ462-2-22-22-222-222-20000-22-2002-22-2002-22-2000000000−2i2i−2i2i00000000000000−2i2i0000000000
χ472-2-22-22-222-222-20000-22-200-22-22002-2-220000000002i−2i2i−2i00000000000000−2i2i0000000000
χ482-2-22-22-222-222-20000-22-200-22-22002-2-22000000000−2i2i−2i2i000000000000002i−2i0000000000
χ492-2-22-22-22-2222-200002-2-2002-22-200-22-2200000000000002i−2i2i−2i00000000000000002i−2i0000
χ502-2-22-22-22-2222-200002-2-2002-22-200-22-220000000000000−2i2i−2i2i0000000000000000−2i2i0000
χ512-2-22-22-22-2222-200002-2-200-22-2200-222-200000000000002i−2i2i−2i0000000000000000−2i2i0000
χ522-2-22-22-22-2222-200002-2-200-22-2200-222-20000000000000−2i2i−2i2i00000000000000002i−2i0000
χ53444-4-44-4-400-44444-4-400-4-440000000000000000000000000000000000000000000000000
χ54444-4-44-4-400-444-4-44400-44-40000000000000000000000000000000000000000000000000
χ5544-44-4-44-4-440004i−4i4i−4i-440000000−4i4i0000000000000000000000000000000000000000000
χ5644-44-4-44-4-44000−4i4i−4i4i-4400000004i−4i0000000000000000000000000000000000000000000
χ5744-4-44-4-44000004i−4i−4i4i000000000000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ5844-4-44-4-44000004i−4i−4i4i00000000000000000000000000000000−2i2i2i−2i-222-200000000000000
χ5944-4-44-4-4400000−4i4i4i−4i000000000000000000000000000000002i−2i−2i2i-222-200000000000000
χ6044-4-44-4-4400000−4i4i4i−4i00000000000000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ614-4444-4-4-4440000000-4-4000000000000000000000022−22−222200000000000000000000000000
χ624-4444-4-4-4440000000-4-40000000000000000000000−222222−2200000000000000000000000000
χ634-4444-4-4-4-4-4000000044000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ644-4444-4-4-4-4-400000004400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ654-4-44-44-444-4-4-440000-44400000000-4400000000000000000000000000000000000000000
χ664-4-44-44-44-44-4-4400004-44000000004-400000000000000000000000000000000000000000
χ674-4-4-4444-4004-44000000-4004i−4i−4i4i000000000000000000000000000000000000000000000
χ684-4-4-4444-4004-44000000-400−4i4i4i−4i000000000000000000000000000000000000000000000
χ694-4-4-4444-400-44-400000040000000000000004-40000000000000000000000000000000000
χ704-4-4-4444-400-44-40000004000000000000000-440000000000000000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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