Finite Group Databasebeta

← Group #317792

Character table — Group #317792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444444444448888444444888888888844444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1111111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1
χ9111111111111111111-1-1-1-11111-1-1111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1
χ10111111111111111111-1-1-1-11111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111
χ14111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-111-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-111
χ17222222222-2-222-2-22-2-222-2-200002-222-2-200000000002-2000000000000000000
χ18222222222-2-222-2-22-2-222-2-200002-2-2-2220000000000-22000000000000000000
χ19222222222-2-222-2-22-2-2-2-2220000-2222-2-20000000000-22000000000000000000
χ20222222222-2-222-2-22-2-2-2-2220000-22-2-22200000000002-2000000000000000000
χ2122222222-222-2-222-2-2-222222222-2-20000-2-222-2-2000000000000000000000000
χ2222222222-222-2-222-2-2-22222-2-2-2-2-2-2000022-2-222000000000000000000000000
χ2322222222-222-2-222-2-2-2-2-2-2-22222220000-2-2-2-222000000000000000000000000
χ2422222222-222-2-222-2-2-2-2-2-2-2-2-2-2-22200002222-2-2000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000-2200000000002i2i−2i−2i000000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000-220000000000−2i−2i2i2i00000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-222-2-22200002-200000000002i2i−2i−2i00000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-222-2-22200002-20000000000−2i−2i2i2i000000000000002i−2i0000
χ29222-2-2-2-222-2-2-2-22222-200002i2i−2i−2i0000002i−2i0000000000002i−2i2-2000000000000
χ30222-2-2-2-222-2-2-2-22222-200002i2i−2i−2i0000002i−2i000000000000−2i2i-22000000000000
χ31222-2-2-2-222-2-2-2-22222-20000−2i−2i2i2i000000−2i2i0000000000002i−2i-22000000000000
χ32222-2-2-2-222-2-2-2-22222-20000−2i−2i2i2i000000−2i2i000000000000−2i2i2-2000000000000
χ33222-2-2-2-22-2-2-22222-2-2200002i2i−2i−2i000000−2i2i00000000002i−2i00002-20000000000
χ34222-2-2-2-22-2-2-22222-2-2200002i2i−2i−2i000000−2i2i0000000000−2i2i0000-220000000000
χ35222-2-2-2-22-2-2-22222-2-220000−2i−2i2i2i0000002i−2i00000000002i−2i0000-220000000000
χ36222-2-2-2-22-2-2-22222-2-220000−2i−2i2i2i0000002i−2i0000000000−2i2i00002-20000000000
χ372-2-222-2-2202-2002-20002i−2i2i−2i2i−2i2i−2i000000002-200000000000000002−2i2−i200i2−i22−2
χ382-2-222-2-2202-2002-20002i−2i2i−2i2i−2i2i−2i000000002-20000000000000000−22−i2i200−i2i2−22
χ392-2-222-2-2202-2002-20002i−2i2i−2i−2i2i−2i2i00000000-2200000000000000002−2i2−i200−i2i2−22
χ402-2-222-2-2202-2002-20002i−2i2i−2i−2i2i−2i2i00000000-220000000000000000−22−i2i200i2−i22−2
χ412-2-222-2-2202-2002-2000−2i2i−2i2i2i−2i2i−2i00000000-2200000000000000002−2−i2i200i2−i2−22
χ422-2-222-2-2202-2002-2000−2i2i−2i2i2i−2i2i−2i00000000-220000000000000000−22i2−i200−i2i22−2
χ432-2-222-2-2202-2002-2000−2i2i−2i2i−2i2i−2i2i000000002-200000000000000002−2−i2i200−i2i22−2
χ442-2-222-2-2202-2002-2000−2i2i−2i2i−2i2i−2i2i000000002-20000000000000000−22i2−i200i2−i2−22
χ45444-4-4-4-44444-4-4-4-44-4400000000000000000000000000000000000000000000
χ46444-4-4-4-44-44444-4-4-44-400000000000000000000000000000000000000000000
χ4744-44-44-4-44004-400-4000000000000000000000022−2222−2200000000000000000000
χ4844-44-44-4-44004-400-40000000000000000000000−2222−222200000000000000000000
χ4944-44-44-4-4-400-4400400000000000000000000002i2−2i2−2i22i200000000000000000000
χ5044-44-44-4-4-400-440040000000000000000000000−2i22i22i2−2i200000000000000000000
χ5144-4-44-44-4400-4400-4000000000000004-4000000000000000000000000000000
χ5244-4-44-44-4400-4400-400000000000000-44000000000000000000000000000000
χ5344-4-44-44-4-4004-40040000000000004i−4i00000000000000000000000000000000
χ5444-4-44-44-4-4004-4004000000000000−4i4i00000000000000000000000000000000
χ554-4-444-4-440-4400-440004i−4i−4i4i0000000000000000000000000000000000000000
χ564-4-444-4-440-4400-44000−4i4i4i−4i0000000000000000000000000000000000000000
χ574-4-4-4-444404-400-440000000000000000000004-4000000000000000000000000
χ584-4-4-4-444404-400-44000000000000000000000-44000000000000000000000000
χ594-4-4-4-44440-44004-400000004-4-44000000000000000000000000000000000000
χ604-4-4-4-44440-44004-40000000-444-4000000000000000000000000000000000000
χ618-888-8-88-8000000000000000000000000000000000000000000000000000000
χ628-88-888-8-8000000000000000000000000000000000000000000000000000000

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