Finite Group Databasebeta

← Group #140421

Character table — Group #140421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order1222224444444488888888888844888888888888888888888888888888888816161616161616164444
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
χ511111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-11111-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1i−ii−i
χ101111-1-11111-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−ii−ii
χ111111-1-11111-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−ii−ii
χ121111-1-11111-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111i−ii−i
χ131111-1-11111-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111i−i−ii
χ141111-1-11111-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−iii−i
χ151111-1-11111-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−iii−i
χ161111-1-11111-1-1-1-1-1-1-1-111111111-1111-1-1-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1i−i−ii
χ172222222222222222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ1922222222-2-222-2-2000000002222-2-2-2-222-2-20000000000000000000022-2-222-2-2000000000000
χ2022222222-2-222-2-2000000002222-2-2-2-222-2-200000000000000000000-2-222-2-222000000000000
χ2122222222-2-222-2-200000000-2-2-2-2-2-222-2-2220000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2222222222-2-222-2-200000000-2-2-2-2-2-222-2-222000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ23222222-2-222-2-2-2-22222-2-2-2-200002-2000000-2-222000000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ24222222-2-222-2-2-2-22222-2-2-2-200002-2000000-2-222000000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ25222222-2-222-2-2-2-2-2-2-2-2222200002-200000022-2-2000000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ26222222-2-222-2-2-2-2-2-2-2-2222200002-200000022-2-2000000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ272222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2-22-2-2222222-2-2-2-2-2-222220000000000000000000000000000
χ282222-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-22-2-22222-2-2222222-2-2-2-20000000000000000000000000000
χ292222-2-222-2-2-2-2220000000022222-2-2-2-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ302222-2-222-2-2-2-2220000000022222-2-2-2-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ312222-2-222-2-2-2-22200000000-2-2-2-22-22222-2-200000000000022-2-2-2-22200000000000000000000
χ322222-2-222-2-2-2-22200000000-2-2-2-22-22222-2-2000000000000-2-22222-2-200000000000000000000
χ332222-2-2-2-2222222222222220000-2-2000000-2-2-2-2000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ342222-2-2-2-2222222222222220000-2-2000000-2-2-2-2000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ352222-2-2-2-2222222-2-2-2-2-2-2-2-20000-2-20000002222000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ362222-2-2-2-2222222-2-2-2-2-2-2-2-20000-2-20000002222000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ3722-2-22-22-2002-200i2i2−i2−i2i2i2−i2−i222-2-200002-200i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2i2−i2i2−i2002-2002-2000000000000
χ3822-2-22-22-2002-200i2i2−i2−i2i2i2−i2−i222-2-200002-200i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2−i2i2−i2i200-2200-22000000000000
χ3922-2-22-22-2002-200i2i2−i2−i2i2i2−i2−i2-2-2220000-2200i2−i2i2−i2−i2−i2i2i2−i2−i2i2i22−2−222−2−222i−2i002i−2i00000000000000
χ4022-2-22-22-2002-200i2i2−i2−i2i2i2−i2−i2-2-2220000-2200i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2−222−2−222−2−2i2i00−2i2i00000000000000
χ4122-2-22-22-2002-200−i2−i2i2i2−i2−i2i2i222-2-200002-200−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2i2−i2i2−i200-2200-22000000000000
χ4222-2-22-22-2002-200−i2−i2i2i2−i2−i2i2i222-2-200002-200−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2−i2i2−i2i2002-2002-2000000000000
χ4322-2-22-22-2002-200−i2−i2i2i2−i2−i2i2i2-2-2220000-2200−i2i2−i2i2i2i2−i2−i2i2i2−i2−i22−2−222−2−22−2i2i00−2i2i00000000000000
χ4422-2-22-22-2002-200−i2−i2i2i2−i2−i2i2i2-2-2220000-2200−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2−222−2−222−22i−2i002i−2i00000000000000
χ4522-2-2-222-200-2200i2i2−i2−i2−i2−i2i2i222-2-20000-2200i2−i2−i2i2i2i2−i2−i2−i2−i2i2i22−22−2−22−2200−2i2i002i−2i000000000000
χ4622-2-2-222-200-2200i2i2−i2−i2−i2−i2i2i222-2-20000-2200i2−i2−i2i2i2i2−i2−i2−i2−i2i2i2−22−222−22−2002i−2i00−2i2i000000000000
χ4722-2-2-222-200-2200i2i2−i2−i2−i2−i2i2i2-2-22200002-200i2−i2−i2i2−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2−i2i2i2−i2-22002-200000000000000
χ4822-2-2-222-200-2200i2i2−i2−i2−i2−i2i2i2-2-22200002-200i2−i2−i2i2−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2i2−i2−i2i22-200-2200000000000000
χ4922-2-2-222-200-2200−i2−i2i2i2i2i2−i2−i222-2-20000-2200−i2i2i2−i2−i2−i2i2i2i2i2−i2−i22−22−2−22−22002i−2i00−2i2i000000000000
χ5022-2-2-222-200-2200−i2−i2i2i2i2i2−i2−i222-2-20000-2200−i2i2i2−i2−i2−i2i2i2i2i2−i2−i2−22−222−22−200−2i2i002i−2i000000000000
χ5122-2-2-222-200-2200−i2−i2i2i2i2i2−i2−i2-2-22200002-200−i2i2i2−i2i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2−i2i2i2−i22-200-2200000000000000
χ5222-2-2-222-200-2200−i2−i2i2i2i2i2−i2−i2-2-22200002-200−i2i2i2−i2i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2i2−i2−i2i2-22002-200000000000000
χ53444444-4-4-4-4-4-444000000000000-440000000000000000000000000000000000000000000000
χ544444-4-4-4-4-4-444-4-4000000000000440000000000000000000000000000000000000000000000
χ5544-4-44-4-4400-44002i22i2−2i2−2i2−2i2−2i22i22i2000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ5644-4-44-4-4400-4400−2i2−2i22i22i22i22i2−2i2−2i20000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ5744-4-4-44-44004-4002i22i2−2i2−2i22i22i2−2i2−2i2000000000000−2i22i2−2i22i2000000000000000000000000000000000000
χ5844-4-4-44-44004-400−2i2−2i22i22i2−2i2−2i22i22i20000000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ594-44-4000000004-42i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i20000002i2−2i200002-22-22-22-20000000000000000000000000000
χ604-44-4000000004-42i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i2000000−2i22i20000-22-22-22-220000000000000000000000000000
χ614-44-4000000004-4−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i20000002i2−2i20000-22-22-22-220000000000000000000000000000
χ624-44-4000000004-4−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2−2i22i2000000−2i22i200002-22-22-22-20000000000000000000000000000
χ634-44-400000000-442i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2000000−2i22i200002-22-2-22-220000000000000000000000000000
χ644-44-400000000-442i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i20000002i2−2i20000-22-222-22-20000000000000000000000000000
χ654-44-400000000-44−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2000000−2i22i20000-22-222-22-20000000000000000000000000000
χ664-44-400000000-44−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i20000002i2−2i200002-22-2-22-220000000000000000000000000000
χ674-4-4400004-4000000004-4-442i2−2i2−2i22i2002i2−2i2000000000000−2i22i22i2−2i20000000000000000000000000000
χ684-4-4400004-4000000004-4-44−2i22i22i2−2i200−2i22i20000000000002i2−2i2−2i22i20000000000000000000000000000
χ694-4-4400004-400000000-444-42i2−2i2−2i22i2002i2−2i20000000000002i2−2i2−2i22i20000000000000000000000000000
χ704-4-4400004-400000000-444-4−2i22i22i2−2i200−2i22i2000000000000−2i22i22i2−2i20000000000000000000000000000
χ714-4-440000-4400004-4-4400002i2−2i2−2i22i200−2i22i200000000−2i22i22i2−2i200000000000000000000000000000000
χ724-4-440000-4400004-4-440000−2i22i22i2−2i2002i2−2i2000000002i2−2i2−2i22i200000000000000000000000000000000
χ734-4-440000-440000-444-400002i2−2i2−2i22i200−2i22i2000000002i2−2i2−2i22i200000000000000000000000000000000
χ744-4-440000-440000-444-40000−2i22i22i2−2i2002i2−2i200000000−2i22i22i2−2i200000000000000000000000000000000

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