Finite Group Databasebeta

← Group #247185

Character table — Group #247185

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444422444444444888888888888888822224444448888
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
χ5111111111111111111111111-1-1-1-111-1-1111-1-111-1-11111111111111111-1-1-1-11-1-11-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111
χ7111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-111-111-1-1-1-1
χ91111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111-1-1-111-1-1
χ101111111111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111-111-1-111
χ111111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-11-1-1-1-111
χ121111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-111111-1-1
χ131111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-111-1-1111111-1-1-1-11111-1-1-1-111-1-11-1-1-111-1-111
χ141111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-111-1-111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-111-1-1
χ151111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-1
χ161111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111-1111-1-1-1-111
χ172222222222-2-2-2222222-2-2-2220000-2-20022-200220000000000000000000000-200-2000000
χ182222222222-2-2-2222222-2-2-2220000-2-200-2-2-200-2-200000000000000000000002002000000
χ192222222222-2-2-2-2-2-2-222-222-2-20000-2-20022200-2-20000000000000000000000-2002000000
χ202222222222-2-2-2-2-2-2-222-222-2-20000-2-200-2-2200220000000000000000000000200-2000000
χ2122222222-2-22222222-2-2222-2-22222-2-2-2-200-22200-2-2000000000000000000000000000000
χ2222222222-2-22222222-2-2222-2-2-2-2-2-2-2-22200-2-2-20022000000000000000000000000000000
χ2322222222-2-2222-2-2-2-2-2-22-2-2222222-2-2-2-2002-2-20022000000000000000000000000000000
χ2422222222-2-2222-2-2-2-2-2-22-2-222-2-2-2-2-2-2220022200-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-20000220000200000000000000000000002-20002-20000000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-2000022000020000000000000000000000-22000-220000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-200000000000000000000002-2000-220000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-20000000000000000000000-220002-20000000
χ29222-2-22-2-22-20002i2i−2i−2i2-20002i−2i000000002i−2i0002-20022−2−2i2i2−i2−i2i2i2−i2−i222−2−200000000000000
χ30222-2-22-2-22-20002i2i−2i−2i2-20002i−2i000000002i−2i0002-200−2−222−i2−i2i2i2−i2−i2i2i2−2−22200000000000000
χ31222-2-22-2-22-20002i2i−2i−2i2-20002i−2i00000000−2i2i000-220022−2−2i2i2−i2−i2−i2−i2i2i2−2−22200000000000000
χ32222-2-22-2-22-20002i2i−2i−2i2-20002i−2i00000000−2i2i000-2200−2−222−i2−i2i2i2i2i2−i2−i222−2−200000000000000
χ33222-2-22-2-22-2000−2i−2i2i2i2-2000−2i2i000000002i−2i000-220022−2−2−i2−i2i2i2i2i2−i2−i2−2−22200000000000000
χ34222-2-22-2-22-2000−2i−2i2i2i2-2000−2i2i000000002i−2i000-2200−2−222i2i2−i2−i2−i2−i2i2i222−2−200000000000000
χ35222-2-22-2-22-2000−2i−2i2i2i2-2000−2i2i00000000−2i2i0002-20022−2−2−i2−i2i2i2−i2−i2i2i222−2−200000000000000
χ36222-2-22-2-22-2000−2i−2i2i2i2-2000−2i2i00000000−2i2i0002-200−2−222i2i2−i2−i2i2i2−i2−i2−2−22200000000000000
χ3722-2-22-2-220022-22-22-200-22-2002i2i−2i−2i00000002i−2i0000000000002−22−22−22−20000000000i2−i2i2−i2
χ3822-2-22-2-220022-22-22-200-22-2002i2i−2i−2i00000002i−2i000000000000−22−22−22−220000000000−i2i2−i2i2
χ3922-2-22-2-220022-22-22-200-22-200−2i−2i2i2i0000000−2i2i0000000000002−22−22−22−20000000000−i2i2−i2i2
χ4022-2-22-2-220022-22-22-200-22-200−2i−2i2i2i0000000−2i2i000000000000−22−22−22−220000000000i2−i2i2−i2
χ4122-2-22-2-220022-2-22-2200-2-22002i2i−2i−2i0000000−2i2i0000000000002−22−2−22−220000000000i2−i2−i2i2
χ4222-2-22-2-220022-2-22-2200-2-22002i2i−2i−2i0000000−2i2i000000000000−22−222−22−20000000000−i2i2i2−i2
χ4322-2-22-2-220022-2-22-2200-2-2200−2i−2i2i2i00000002i−2i0000000000002−22−2−22−220000000000−i2i2i2−i2
χ4422-2-22-2-220022-2-22-2200-2-2200−2i−2i2i2i00000002i−2i000000000000−22−222−22−20000000000i2−i2−i2i2
χ452-2-2-2-22222-22-2-20000-22200002-22-22-22-200000000000002-22-200000000000000002-20000
χ462-2-2-2-22222-22-2-20000-22200002-22-22-22-20000000000000-22-220000000000000000-220000
χ472-2-2-2-22222-22-2-20000-2220000-22-222-2-2200000000000002-22-20000000000000000-220000
χ482-2-2-2-22222-22-2-20000-2220000-22-222-2-220000000000000-22-2200000000000000002-20000
χ492-2-2-2-2222-222-2-200002-2200002-22-2-22-220000000002-22-2000000000000002-20000000000
χ502-2-2-2-2222-222-2-200002-2200002-22-2-22-22000000000-22-2200000000000000-220000000000
χ512-2-2-2-2222-222-2-200002-220000-22-22-222-20000000002-22-200000000000000-220000000000
χ522-2-2-2-2222-222-2-200002-220000-22-22-222-2000000000-22-22000000000000002-20000000000
χ53444-4-44-4-4-440004i4i−4i−4i-44000−4i4i00000000000000000000000000000000000000000000000
χ54444-4-44-4-4-44000−4i−4i4i4i-440004i−4i00000000000000000000000000000000000000000000000
χ5544-44-4-44-4000004i−4i−4i4i000000000000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ5644-44-4-44-4000004i−4i−4i4i00000000000000000000000000000000−2i2i2i−2i-222-200000000000000
χ5744-44-4-44-400000−4i4i4i−4i000000000000000000000000000000002i−2i−2i2i-222-200000000000000
χ5844-44-4-44-400000−4i4i4i−4i00000000000000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ5944-4-44-4-4400-4-444-44-4004-440000000000000000000000000000000000000000000000000
χ6044-4-44-4-4400-4-44-44-440044-40000000000000000000000000000000000000000000000000
χ614-444-4-4-44004-44000000-400004i−4i−4i4i0000000000000000000000000000000000000000000
χ624-444-4-4-44004-44000000-40000−4i4i4i−4i0000000000000000000000000000000000000000000
χ634-444-4-4-4400-44-4000000400000000000000000004-4000000000000000000000000000000
χ644-444-4-4-4400-44-400000040000000000000000000-44000000000000000000000000000000
χ654-4-4444-4-4440000000-4-4000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ664-4-4444-4-4440000000-4-400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ674-4-4444-4-4-4-4000000044000000000000000000000022−22−222200000000000000000000000000
χ684-4-4444-4-4-4-40000000440000000000000000000000−222222−2200000000000000000000000000
χ694-4-4-4-44444-4-4440000-44-400000000-4400000000000000000000000000000000000000000
χ704-4-4-4-4444-44-44400004-4-4000000004-400000000000000000000000000000000000000000
χ718-88-88-88-8000000000000000000000000000000000000000000000000000000000000000

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