Finite Group Databasebeta

← Group #317690

Character table — Group #317690

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888224444444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1
χ91111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-111-1-111
χ111111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ141111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-11111-1-1
χ151111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-111-1-11111-1-1
χ161111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-111-1-1-1-111
χ1722222222222222-2-2-2-222-2-222-2-2-2-20000000000000000002-20000002-2000000000000
χ1822222222222222-2-2-2-222-2-222-2-2-2-2000000000000000000-22000000-22000000000000
χ192222222222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000002-2000000-22000000000000
χ202222222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000-220000002-2000000000000
χ2122222222-2-222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ2222222222-2-222222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-222-2-222-2-200000000000000000000000000002i−2i2i−2i00000000
χ2422222222-2-22222-2-2-2-2-2-222-2-222-2-20000000000000000000000000000−2i2i−2i2i00000000
χ2522222222-2-2-2-2-2-22222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2622222222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000000000002i−2i−2i2i00000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000000000000000−2i2i2i−2i00000000
χ29222-2-22-2-22-20000-2-2222-22-20000002i2i−2i−2i2i2i−2i−2i0000000000002-22i−2i0000000000000000
χ30222-2-22-2-22-20000-2-2222-22-20000002i2i−2i−2i2i2i−2i−2i000000000000-22−2i2i0000000000000000
χ31222-2-22-2-22-20000-2-2222-22-2000000−2i−2i2i2i−2i−2i2i2i0000000000002-2−2i2i0000000000000000
χ32222-2-22-2-22-20000-2-2222-22-2000000−2i−2i2i2i−2i−2i2i2i000000000000-222i−2i0000000000000000
χ33222-2-22-2-2-220000-2-222-22-220000002i2i−2i−2i−2i−2i2i2i000000002-20000002i−2i00000000000000
χ34222-2-22-2-2-220000-2-222-22-220000002i2i−2i−2i−2i−2i2i2i00000000-22000000−2i2i00000000000000
χ35222-2-22-2-2-220000-2-222-22-22000000−2i−2i2i2i2i2i−2i−2i000000002-2000000−2i2i00000000000000
χ36222-2-22-2-2-220000-2-222-22-22000000−2i−2i2i2i2i2i−2i−2i00000000-220000002i−2i00000000000000
χ372-2-2222-2-2002i2i−2i−2i2-22-2000000002i−2i00002i−2i2i−2i000022-2-200000000000000002−2i2−i2i2−i22−2
χ382-2-2222-2-2002i2i−2i−2i2-22-2000000002i−2i00002i−2i2i−2i000022-2-20000000000000000−22−i2i2−i2i2−22
χ392-2-2222-2-2002i2i−2i−2i2-22-2000000002i−2i0000−2i2i−2i2i0000-2-22200000000000000002−2i2−i2−i2i2−22
χ402-2-2222-2-2002i2i−2i−2i2-22-2000000002i−2i0000−2i2i−2i2i0000-2-2220000000000000000−22−i2i2i2−i22−2
χ412-2-2222-2-200−2i−2i2i2i2-22-200000000−2i2i00002i−2i2i−2i0000-2-22200000000000000002−2−i2i2i2−i2−22
χ422-2-2222-2-200−2i−2i2i2i2-22-200000000−2i2i00002i−2i2i−2i0000-2-2220000000000000000−22i2−i2−i2i22−2
χ432-2-2222-2-200−2i−2i2i2i2-22-200000000−2i2i0000−2i2i−2i2i000022-2-200000000000000002−2−i2i2−i2i22−2
χ442-2-2222-2-200−2i−2i2i2i2-22-200000000−2i2i0000−2i2i−2i2i000022-2-20000000000000000−22i2−i2i2−i2−22
χ45444-4-44-4-44-4000044-4-44-4-440000000000000000000000000000000000000000000000
χ46444-4-44-4-4-44000044-4-4-444-40000000000000000000000000000000000000000000000
χ4744-44-4-44-400000000000000004-4002i2−2i22i2−2i2000000002i2−2i22i2−2i2000000000000000000000000
χ4844-44-4-44-400000000000000004-400−2i22i2−2i22i200000000−2i22i2−2i22i2000000000000000000000000
χ4944-44-4-44-40000000000000000-44002i2−2i22i2−2i200000000−2i22i2−2i22i2000000000000000000000000
χ5044-44-4-44-40000000000000000-4400−2i22i2−2i22i2000000002i2−2i22i2−2i2000000000000000000000000
χ5144-4-44-4-44004i−4i4i−4i0000000000000022−22−222200002i22i2−2i2−2i20000000000000000000000000000
χ5244-4-44-4-44004i−4i4i−4i00000000000000−222222−220000−2i2−2i22i22i20000000000000000000000000000
χ5344-4-44-4-4400−4i4i−4i4i0000000000000022−22−22220000−2i2−2i22i22i20000000000000000000000000000
χ5444-4-44-4-4400−4i4i−4i4i00000000000000−222222−2200002i22i2−2i2−2i20000000000000000000000000000
χ554-444-4-4-444-400000000-4400000000000000002i2−2i22i2−2i22i2−2i2−2i22i2000000000000000000000000
χ564-444-4-4-444-400000000-440000000000000000−2i22i2−2i22i2−2i22i22i2−2i2000000000000000000000000
χ574-444-4-4-44-44000000004-400000000000000002i2−2i22i2−2i2−2i22i22i2−2i2000000000000000000000000
χ584-444-4-4-44-44000000004-40000000000000000−2i22i2−2i22i22i2−2i2−2i22i2000000000000000000000000
χ594-44-44-44-4444-4-440000-4-4004-400000000000000000000000000000000000000000000
χ604-44-44-44-444-444-40000-4-400-4400000000000000000000000000000000000000000000
χ614-44-44-44-4-4-44-4-4400004400-4400000000000000000000000000000000000000000000
χ624-44-44-44-4-4-4-444-4000044004-400000000000000000000000000000000000000000000
χ634-4-4444-4-4004i4i−4i−4i-44-4400000000−4i4i0000000000000000000000000000000000000000
χ644-4-4444-4-400−4i−4i4i4i-44-44000000004i−4i0000000000000000000000000000000000000000
χ654-4-4-4-44440000004-4-440000000000000000004-4-440000000000000000000000000000
χ664-4-4-4-44440000004-4-44000000000000000000-444-40000000000000000000000000000
χ674-4-4-4-4444000000-444-4000000000000004-4-4400000000000000000000000000000000
χ684-4-4-4-4444000000-444-400000000000000-444-400000000000000000000000000000000

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