Finite Group Databasebeta

← Group #296273

Character table — Group #296273

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222244444444444444444444444488888888888888882244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-111111-11-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-11-1111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-11-11-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-11-1111-1-111-1-1-1-111
χ172222222222222222-2-2-2-2222222-2-2-2-2-2-2-2-22200000000000000000000000000000000
χ182222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ19222222222222-2-2-2-22222-2-22222-2-2-2-2-2-222-2-200000000000000000000000000000000
χ20222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-22200000000000000000000000000000000
χ2122222222-2-2-2-2222222-2-2-2-2000022-2-2000000000000000000000022-2-2000000000000
χ2222222222-2-2-2-2222222-2-2-2-2000022-2-20000000000000000000000-2-222000000000000
χ2322222222-2-2-2-22222-2-222-2-20000-2-222000000000000000000000000002-22-200000000
χ2422222222-2-2-2-22222-2-222-2-20000-2-22200000000000000000000000000-22-2200000000
χ2522222222-2-2-2-2-2-2-2-222-2-2220000-2-222000000000000000000000000002-2-2200000000
χ2622222222-2-2-2-2-2-2-2-222-2-2220000-2-22200000000000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222000022-2-200000000000000000000002-2-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222000022-2-20000000000000000000000-222-2000000000000
χ29222-22-2-2-22-2-2200000000002i2i−2i−2i2-22-22i−2i000000002i2i−2i−2i000022-2-20000000000000000
χ30222-22-2-2-22-2-2200000000002i2i−2i−2i2-22-22i−2i00000000−2i−2i2i2i0000-2-2220000000000000000
χ31222-22-2-2-22-2-2200000000002i2i−2i−2i-22-22−2i2i00002i2i−2i−2i000022-2-200000000000000000000
χ32222-22-2-2-22-2-2200000000002i2i−2i−2i-22-22−2i2i0000−2i−2i2i2i0000-2-22200000000000000000000
χ33222-22-2-2-22-2-220000000000−2i−2i2i2i2-22-2−2i2i000000002i2i−2i−2i0000-2-2220000000000000000
χ34222-22-2-2-22-2-220000000000−2i−2i2i2i2-22-2−2i2i00000000−2i−2i2i2i000022-2-20000000000000000
χ35222-22-2-2-22-2-220000000000−2i−2i2i2i-22-222i−2i00002i2i−2i−2i0000-2-22200000000000000000000
χ36222-22-2-2-22-2-220000000000−2i−2i2i2i-22-222i−2i0000−2i−2i2i2i000022-2-200000000000000000000
χ372-2-222-2-2222-2-200002-22-2002i−2i2i−2i0000002i−2i002−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ382-2-222-2-2222-2-200002-22-2002i−2i2i−2i0000002i−2i00−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ392-2-222-2-2222-2-200002-22-200−2i2i−2i2i000000−2i2i002−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ402-2-222-2-2222-2-200002-22-200−2i2i−2i2i000000−2i2i00−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ412-2-222-2-2222-2-20000-22-22002i−2i2i−2i000000−2i2i002−22−2−22−22i2−i2i2−i2−i2i2−i2i20000000000000000
χ422-2-222-2-2222-2-20000-22-22002i−2i2i−2i000000−2i2i00−22−222−22−2−i2i2−i2i2i2−i2i2−i20000000000000000
χ432-2-222-2-2222-2-20000-22-2200−2i2i−2i2i0000002i−2i002−22−2−22−22−i2i2−i2i2i2−i2i2−i20000000000000000
χ442-2-222-2-2222-2-20000-22-2200−2i2i−2i2i0000002i−2i00−22−222−22−2i2−i2i2−i2−i2i2−i2i20000000000000000
χ452-2-2-2222-22-22-222-2-200002-22-2-22000000002-2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ462-2-2-2222-22-22-222-2-200002-22-2-22000000002-2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ472-2-2-2222-22-22-222-2-200002-2-222-200000000-22i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ482-2-2-2222-22-22-222-2-200002-2-222-200000000-22−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ492-2-2-2222-22-22-2-2-2220000-222-2-2200000000-22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ502-2-2-2222-22-22-2-2-2220000-222-2-2200000000-22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ512-2-2-2222-22-22-2-2-2220000-22-222-2000000002-2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ522-2-2-2222-22-22-2-2-2220000-22-222-2000000002-2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ53444-44-4-4-4-444-4000000000000004-4-4400000000000000000000000000000000000000
χ54444-44-4-4-4-444-400000000000000-444-400000000000000000000000000000000000000
χ5544-4-4-44-4400004-44-40000000000000000000000000000000000000000000000002i−2i2i−2i
χ5644-4-4-44-4400004-44-4000000000000000000000000000000000000000000000000−2i2i−2i2i
χ5744-4-4-44-440000-44-440000000000000000000000000000000000000000000000002i−2i−2i2i
χ5844-4-4-44-440000-44-44000000000000000000000000000000000000000000000000−2i2i2i−2i
χ594-444-44-4-400004-4-44000000000000000000000000000000000000000000002i−2i2i−2i0000
χ604-444-44-4-400004-4-4400000000000000000000000000000000000000000000−2i2i−2i2i0000
χ614-444-44-4-40000-444-4000000000000000000000000000000000000000000002i−2i−2i2i0000
χ624-444-44-4-40000-444-400000000000000000000000000000000000000000000−2i2i2i−2i0000
χ634-4-444-4-44-4-44400004-4-44000000000000000000000000000000000000000000000000
χ644-4-444-4-44-4-4440000-444-4000000000000000000000000000000000000000000000000
χ654-4-4-4444-4-44-4444-4-40000-440000000000000000000000000000000000000000000000
χ664-4-4-4444-4-44-44-4-44400004-40000000000000000000000000000000000000000000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-8-888000000000000000000000000000000000000000000000000000000000000

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