Finite Group Databasebeta

← Group #290703

Character table — Group #290703

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222222222222244444444444444444488888888888888882224444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-11111
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1
χ5111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-1-1111-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1111111-1-1-1-1-1
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-1-1-111111
χ91111111111-1-1-1-111-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-11-11-1-1-1-111-1-1
χ101111111111-1-1-1-111-1-111-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-11-11111-1-111
χ111111111111-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-11-11-1-1111-1-1
χ121111111111-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-11-11-111-1-1-111
χ131111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111111111-1-11-11-1-1-1-1-111
χ141111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-11-111111-1-1
χ151111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-111-11-1-1-11-1-111
χ161111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-111-1-11-1111-111-1-1
χ17222222222222222222-2-2-2-2-2-22222-2-222-2-2-2-200000000000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ192222222222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-22200000000000000000000000000000000
χ202222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-22222-2-200000000000000000000000000000000
χ2122222222-2-22222-2-2-2-22-222-2-200002-20000000000000000000000002-2-200000020000
χ2222222222-2-22222-2-2-2-22-222-2-200002-2000000000000000000000000-222000000-20000
χ2322222222-2-22222-2-2-2-2-22-2-2220000-220000000000000000000000000002-2-220000000
χ2422222222-2-22222-2-2-2-2-22-2-2220000-22000000000000000000000000000-222-20000000
χ2522222222-2-2-2-2-2-2-2-2222-2-2-22200002-20000000000000000000000002-22000000-20000
χ2622222222-2-2-2-2-2-2-2-2222-2-2-22200002-2000000000000000000000000-22-200000020000
χ2722222222-2-2-2-2-2-2-2-222-2222-2-20000-2200000000000000000000000000022-2-20000000
χ2822222222-2-2-2-2-2-2-2-222-2222-2-20000-22000000000000000000000000000-2-2220000000
χ29222-2-22-2-22-200002-200002i−2i2i−2i22-2-20000002i−2i22−2−2i2i2−i2−i222−2−2i2i2−i2−i20000000000000000
χ30222-2-22-2-22-200002-200002i−2i2i−2i22-2-20000002i−2i−2−222−i2−i2i2i2−2−222−i2−i2i2i20000000000000000
χ31222-2-22-2-22-200002-200002i−2i2i−2i-2-222000000−2i2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i20000000000000000
χ32222-2-22-2-22-200002-200002i−2i2i−2i-2-222000000−2i2i−2−222−i2−i2i2i222−2−2i2i2−i2−i20000000000000000
χ33222-2-22-2-22-200002-20000−2i2i−2i2i22-2-2000000−2i2i22−2−2−i2−i2i2i222−2−2−i2−i2i2i20000000000000000
χ34222-2-22-2-22-200002-20000−2i2i−2i2i22-2-2000000−2i2i−2−222i2i2−i2−i2−2−222i2i2−i2−i20000000000000000
χ35222-2-22-2-22-200002-20000−2i2i−2i2i-2-2220000002i−2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i20000000000000000
χ36222-2-22-2-22-200002-20000−2i2i−2i2i-2-2220000002i−2i−2−222i2i2−i2−i222−2−2−i2−i2i2i20000000000000000
χ3722-22-2-22-22-20000-22002-200002i−2i2i−2i-22002i−2i0000002i−2i2i−2i00002-22-20000000000000000
χ3822-22-2-22-22-20000-22002-200002i−2i2i−2i-22002i−2i000000−2i2i−2i2i0000-22-220000000000000000
χ3922-22-2-22-22-20000-22002-20000−2i2i−2i2i-2200−2i2i0000002i−2i2i−2i0000-22-220000000000000000
χ4022-22-2-22-22-20000-22002-20000−2i2i−2i2i-2200−2i2i000000−2i2i−2i2i00002-22-20000000000000000
χ4122-22-2-22-22-20000-2200-2200002i−2i2i−2i2-200−2i2i002-22-200002i−2i2i−2i00000000000000000000
χ4222-22-2-22-22-20000-2200-2200002i−2i2i−2i2-200−2i2i00-22-220000−2i2i−2i2i00000000000000000000
χ4322-22-2-22-22-20000-2200-220000−2i2i−2i2i2-2002i−2i002-22-20000−2i2i−2i2i00000000000000000000
χ4422-22-2-22-22-20000-2200-220000−2i2i−2i2i2-2002i−2i00-22-2200002i−2i2i−2i00000000000000000000
χ4522-2-22-2-222222-2-2-2-22-20000002i−2i−2i2i002i−2i00002−2−222−2−22i2−i2−i2i2−i2i2i2−i20000000000000000
χ4622-2-22-2-222222-2-2-2-22-20000002i−2i−2i2i002i−2i0000−222−2−222−2−i2i2i2−i2i2−i2−i2i20000000000000000
χ4722-2-22-2-222222-2-2-2-22-2000000−2i2i2i−2i00−2i2i00002−2−222−2−22−i2i2i2−i2i2−i2−i2i20000000000000000
χ4822-2-22-2-222222-2-2-2-22-2000000−2i2i2i−2i00−2i2i0000−222−2−222−2i2−i2−i2i2−i2i2i2−i20000000000000000
χ4922-2-22-2-2222-2-222-2-2-220000002i−2i−2i2i00−2i2i00002−2−22−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ5022-2-22-2-2222-2-222-2-2-220000002i−2i−2i2i00−2i2i0000−222−22−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ5122-2-22-2-2222-2-222-2-2-22000000−2i2i2i−2i002i−2i00002−2−22−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ5222-2-22-2-2222-2-222-2-2-22000000−2i2i2i−2i002i−2i0000−222−22−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ53444-4-44-4-4-440000-4400004i−4i−4i4i00000000000000000000000000000000000000000000
χ54444-4-44-4-4-440000-440000−4i4i4i−4i00000000000000000000000000000000000000000000
χ5544-44-4-44-4-4400004-4004400000000-4-400000000000000000000000000000000000000
χ5644-44-4-44-4-4400004-400-4-4000000004400000000000000000000000000000000000000
χ5744-4-44-4-44-4-444-4-444-4400000000000000000000000000000000000000000000000000
χ5844-4-44-4-44-4-4-4-444444-400000000000000000000000000000000000000000000000000
χ594-44-4-4-444004-44-4000000000000000000000000000000000000002-200000002-200000
χ604-44-4-4-444004-44-400000000000000000000000000000000000000-220000000-2200000
χ614-44-4-4-44400-44-44000000000000000000000000000000000000002-20000000-2200000
χ624-44-4-4-44400-44-4400000000000000000000000000000000000000-2200000002-200000
χ634-4-44-44-44004-4-44000000000000000000000000000000000000000000000000002-22-2
χ644-4-44-44-44004-4-4400000000000000000000000000000000000000000000000000-22-22
χ654-4-44-44-4400-444-4000000000000000000000000000000000000000000000000002-2-22
χ664-4-44-44-4400-444-400000000000000000000000000000000000000000000000000-222-2
χ678-8888-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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