Finite Group Databasebeta

← Group #318090

Character table — Group #318090

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888888888888888888882222444488888888444488884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-11-11
χ111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-11-11
χ121111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1111-11-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111111-11-1-1-1111-1-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111-11-1111-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-11-11-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1-11-1111-1-11-1-11
χ172222222222-2-22-22-200000000-2-200002222-2-2-2-20000000022-2-2-2-22200000000000000000000
χ182222222222-2-22-22-200000000-2-200002222-2-2-2-200000000-2-22222-2-200000000000000000000
χ192222222222-2-22-22-200000000-2-20000-2-2-2-22222000000002222-2-2-2-200000000000000000000
χ202222222222-2-22-22-200000000-2-20000-2-2-2-2222200000000-2-2-2-2222200000000000000000000
χ2122222222-2-222-22-2222222222-2-2-2-2-2-2000000000000000000000000000000002-2-2200000000
χ2222222222-2-222-22-2222222222-2-2-2-2-2-200000000000000000000000000000000-222-200000000
χ2322222222-2-222-22-22-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000022-2-200000000
χ2422222222-2-222-22-22-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2-22200000000
χ252222-2-2-2-22-200-20202222−2−2−2−20022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i2002-22i−2i00i2i2−i2−i222−2−2000000000000
χ262222-2-2-2-22-200-20202222−2−2−2−20022−2−22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i200-22−2i2i00−i2−i2i2i2−2−222000000000000
χ272222-2-2-2-22-200-20202222−2−2−2−20022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i2002-2−2i2i00−i2−i2i2i222−2−2000000000000
χ282222-2-2-2-22-200-20202222−2−2−2−20022−2−2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i200-222i−2i00i2i2−i2−i2−2−222000000000000
χ292222-2-2-2-22-200-2020−2−2−2−2222200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2002-22i−2i00−i2−i2i2i2−2−222000000000000
χ302222-2-2-2-22-200-2020−2−2−2−2222200−2−2222i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i200-22−2i2i00i2i2−i2−i222−2−2000000000000
χ312222-2-2-2-22-200-2020−2−2−2−2222200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2002-2−2i2i00i2i2−i2−i2−2−222000000000000
χ322222-2-2-2-22-200-2020−2−2−2−2222200−2−222−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i200-222i−2i00−i2−i2i2i222−2−2000000000000
χ3322-2-222-2-2-2200-202022−2−222−2−2002−22−22i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i22-200002i−2i2−22−2i2−i2i2−i2000000000000
χ3422-2-222-2-2-2200-202022−2−222−2−2002−22−22i−2i2i−2i0000i2i2−i2−i2i2i2−i2−i2-220000−2i2i−22−22−i2i2−i2i2000000000000
χ3522-2-222-2-2-2200-202022−2−222−2−2002−22−2−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i22-20000−2i2i2−22−2−i2i2−i2i2000000000000
χ3622-2-222-2-2-2200-202022−2−222−2−2002−22−2−2i2i−2i2i0000−i2−i2i2i2−i2−i2i2i2-2200002i−2i−22−22i2−i2i2−i2000000000000
χ3722-2-222-2-2-2200-2020−2−222−2−22200−22−222i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i22-200002i−2i−22−22−i2i2−i2i2000000000000
χ3822-2-222-2-2-2200-2020−2−222−2−22200−22−222i−2i2i−2i0000−i2−i2i2i2−i2−i2i2i2-220000−2i2i2−22−2i2−i2i2−i2000000000000
χ3922-2-222-2-2-2200-2020−2−222−2−22200−22−22−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i22-20000−2i2i−22−22i2−i2i2−i2000000000000
χ4022-2-222-2-2-2200-2020−2−222−2−22200−22−22−2i2i−2i2i0000i2i2−i2−i2i2i2−i2−i2-2200002i−2i2−22−2−i2i2−i2i2000000000000
χ4122-2-2-2-22222-2-2-22-2222-2-2-2-2222-2-222-20000000000000000000000000000000000002i−2i2i−2i0000
χ4222-2-2-2-22222-2-2-22-2222-2-2-2-2222-2-222-2000000000000000000000000000000000000−2i2i−2i2i0000
χ4322-2-2-2-22222-2-2-22-22-2-22222-2-22-22-2-220000000000000000000000000000000000002i−2i−2i2i0000
χ4422-2-2-2-22222-2-2-22-22-2-22222-2-22-22-2-22000000000000000000000000000000000000−2i2i2i−2i0000
χ4522-2-2-2-222-2-2222-22-2000000002-200002-2-2222-2-200000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ4622-2-2-2-222-2-2222-22-2000000002-200002-2-2222-2-20000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ4722-2-2-2-222-2-2222-22-2000000002-20000-222-2-2-22200000000000000002i−2i−2i2i2i−2i−2i2i000000000000
χ4822-2-2-2-222-2-2222-22-2000000002-20000-222-2-2-2220000000000000000−2i2i2i−2i−2i2i2i−2i000000000000
χ4922-2-2-2-222-2-2-2-2222222-2-2-2-222-222-2-222-2-22-2-22222-2-2-2-2220000000000000000000000000000
χ5022-2-2-2-222-2-2-2-2222222-2-2-2-222-222-2-22-222-222-2-2-2-22222-2-20000000000000000000000000000
χ5122-2-2-2-222-2-2-2-22222-2-22222-2-2-22-222-22-2-22-2-222-2-22222-2-20000000000000000000000000000
χ5222-2-2-2-222-2-2-2-22222-2-22222-2-2-22-222-2-222-222-2-222-2-2-2-2220000000000000000000000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-440040-4022222222−22−22−22−2200−22−22222200000000000000000000000000000000000000000000
χ554444-4-4-4-4-440040-40−22−22−22−2222222222002222−22−2200000000000000000000000000000000000000000000
χ5644-4-444-4-44-40040-402222−22−222222−22−2200−2222−222200000000000000000000000000000000000000000000
χ5744-4-444-4-44-40040-40−22−222222−22−2222220022−2222−2200000000000000000000000000000000000000000000
χ5844-4-4-4-4444444-4-4-4-400000000-44000000000000000000000000000000000000000000000000
χ594-44-44-44-4000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000022−2222−222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ604-44-44-44-4000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000−2222−2222−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ614-44-44-44-400000000−2i22i2−2i22i2−2i22i2−2i22i2000000000022−2222−22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ624-44-44-44-400000000−2i22i2−2i22i2−2i22i2−2i22i20000000000−2222−22222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ634-44-4-44-44004-4040-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ644-44-4-44-44004-4040-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ654-44-4-44-4400-440-404000000000000000000000022−2222−22−2222−22220000000000000000000000000000
χ664-44-4-44-4400-440-4040000000000000000000000−2222−222222−2222−220000000000000000000000000000
χ674-4-444-4-44004-40-404000000000000000000000022−22−222222−22−22220000000000000000000000000000
χ684-4-444-4-44004-40-4040000000000000000000000−222222−22−222222−220000000000000000000000000000
χ694-4-444-4-4400-44040-44i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ704-4-444-4-4400-44040-4−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ714-4-44-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000022−22−2222−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ724-4-44-444-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000−222222−222i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ734-4-44-444-400000000−2i22i22i2−2i22i2−2i2−2i22i2000000000022−22−22222i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ744-4-44-444-400000000−2i22i22i2−2i22i2−2i2−2i22i20000000000−222222−22−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000

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