Finite Group Databasebeta

← Group #317639

Character table — Group #317639

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888844444444448888888888884444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-11111111111-111-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-11111111111-111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ111111111111111111-1-1-1-11111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111
χ121111111111111111-1-1-1-11111111111-1-1-111-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ141111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ172222222222-2-2-2-22222-2-2-2-22222-2-2-2-220000-2000022-2-2000000000000000000000000
χ182222222222-2-2-2-22222-2-2-2-2-2-2-2-2222220000-20000-2-222000000000000000000000000
χ192222222222-2-2-2-222-2-222-2-22222-2-2-2-2-2000020000-2-222000000000000000000000000
χ202222222222-2-2-2-222-2-222-2-2-2-2-2-22222-200002000022-2-2000000000000000000000000
χ2122222222-2-22222-2-22222-2-200000000-222-2-2-2-2-2220000000000000000000000000000
χ2222222222-2-22222-2-22222-2-200000000-2-2-222-222-2-20000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-200000000222222-2-2-2-20000000000000000000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2000000002-2-2-2-2222220000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-22200000000-200002000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-22200000000-20000200000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000000020000-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000000020000-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-2-2-22-2-2-222-2-22200002-22i2i−2i−2i2i2i−2i−2i0000000000000000000000002-2002i−2i00000000
χ30222-2-2-22-2-2-222-2-22200002-22i2i−2i−2i2i2i−2i−2i000000000000000000000000-2200−2i2i00000000
χ31222-2-2-22-2-2-222-2-22200002-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000002-200−2i2i00000000
χ32222-2-2-22-2-2-222-2-22200002-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000-22002i−2i00000000
χ33222-2-2-22-2-2-2-2-222220000-222i2i−2i−2i−2i−2i2i2i00000000000000000000002i−2i002-20000000000
χ34222-2-2-22-2-2-2-2-222220000-222i2i−2i−2i−2i−2i2i2i0000000000000000000000−2i2i00-220000000000
χ35222-2-2-22-2-2-2-2-222220000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000002i−2i00-220000000000
χ36222-2-2-22-2-2-2-2-222220000-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000−2i2i002-20000000000
χ3722-2-22-2-22002-22-2002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i20002i−2i02-2002−22−2i2−i2i2−i22−22−20000000000000000
χ3822-2-22-2-22002-22-2002i−2i2i−2i00i2−i2i2−i2i2−i2i2−i2000−2i2i0-22002−22−2−i2i2−i2i2−22−220000000000000000
χ3922-2-22-2-22002-22-2002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i20002i−2i02-200−22−22−i2i2−i2i2−22−220000000000000000
χ4022-2-22-2-22002-22-2002i−2i2i−2i00−i2i2−i2i2−i2i2−i2i2000−2i2i0-2200−22−22i2−i2i2−i22−22−20000000000000000
χ4122-2-22-2-22002-22-200−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i20002i−2i0-2200−22−22−i2i2−i2i22−22−20000000000000000
χ4222-2-22-2-22002-22-200−2i2i−2i2i00i2−i2i2−i2i2−i2i2−i2000−2i2i02-200−22−22i2−i2i2−i2−22−220000000000000000
χ4322-2-22-2-22002-22-200−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i20002i−2i0-22002−22−2i2−i2i2−i2−22−220000000000000000
χ4422-2-22-2-22002-22-200−2i2i−2i2i00−i2i2−i2i2−i2i2−i2i2000−2i2i02-2002−22−2−i2i2−i2i22−22−20000000000000000
χ4522-2-22-2-2200-22-22002i−2i−2i2i00i2−i2i2−i2−i2i2−i2i202i−2i000002-22−2−222−2−22−i2i2i2−i20000000000000000
χ4622-2-22-2-2200-22-22002i−2i−2i2i00i2−i2i2−i2−i2i2−i2i20−2i2i00000-222−2−22−222−2i2−i2−i2i20000000000000000
χ4722-2-22-2-2200-22-22002i−2i−2i2i00−i2i2−i2i2i2−i2i2−i202i−2i000002-2−222−2−222−2i2−i2−i2i20000000000000000
χ4822-2-22-2-2200-22-22002i−2i−2i2i00−i2i2−i2i2i2−i2i2−i20−2i2i00000-22−222−22−2−22−i2i2i2−i20000000000000000
χ4922-2-22-2-2200-22-2200−2i2i2i−2i00i2−i2i2−i2−i2i2−i2i202i−2i00000-22−222−22−2−22i2−i2−i2i20000000000000000
χ5022-2-22-2-2200-22-2200−2i2i2i−2i00i2−i2i2−i2−i2i2−i2i20−2i2i000002-2−222−2−222−2−i2i2i2−i20000000000000000
χ5122-2-22-2-2200-22-2200−2i2i2i−2i00−i2i2−i2i2i2−i2i2−i202i−2i00000-222−2−22−222−2−i2i2i2−i20000000000000000
χ5222-2-22-2-2200-22-2200−2i2i2i−2i00−i2i2−i2i2i2−i2i2−i20−2i2i000002-22−2−222−2−22i2−i2−i2i20000000000000000
χ53444-4-4-44-44444-4-4-4-40000-440000000000000000000000000000000000000000000000
χ54444-4-4-44-444-4-444-4-400004-40000000000000000000000000000000000000000000000
χ5544-44-44-4-4004-4-440000000022−22−222222−22−222200000000000000000000000000000000000000
χ5644-44-44-4-4004-4-4400000000−222222−22−222222−2200000000000000000000000000000000000000
χ5744-44-44-4-400-444-40000000022−22−2222−222222−2200000000000000000000000000000000000000
χ5844-44-44-4-400-444-400000000−222222−2222−22−222200000000000000000000000000000000000000
χ594-4444-4-4-44-400004-400000000000000000000000000000000000000000000000022−2200
χ604-4444-4-4-44-400004-4000000000000000000000000000000000000000000000000−222200
χ614-4444-4-4-4-440000-440000000000000000000000000000000000000000000000000022−22
χ624-4444-4-4-4-440000-4400000000000000000000000000000000000000000000000000−2222
χ634-44-4-44-444-40000-4400000000000000000000000000000000000000000000002i2−2i20000
χ644-44-4-44-444-40000-440000000000000000000000000000000000000000000000−2i22i20000
χ654-44-4-44-44-4400004-4000000000000000000000000000000000000000000002i2−2i2000000
χ664-44-4-44-44-4400004-400000000000000000000000000000000000000000000−2i22i2000000
χ678-8-88-8-888000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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