Finite Group Databasebeta

← Group #349773

Character table — Group #349773

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444444444444444444444222244444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ6111111111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-11
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-11-1
χ91111111111111111-1-1-1-11111111-1-1-1-11-1-111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1
χ101111111111111111-1-1-1-11111111-1-1-1-11-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ111111111111111111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-11-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ131111111111111111-1-1-1-11-1-1-1-1-1-111111-1-11111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-11-1-1-1-1-1-111111-1-11111-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-1-1-11-1-1-1-1-1-111111-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-11-1-1-1-1-1-111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-222-2-20000-22222-2-20000-20022-2-2-2000000-2-2220000000000000000000000
χ182222222222-2-222-2-20000-22222-2-20000-200-2-222-200000022-2-20000000000000000000000
χ192222222222-2-222-2-20000-2-2-2-2-2220000-20022-2-2200000022-2-20000000000000000000000
χ202222222222-2-222-2-20000-2-2-2-2-2220000-200-2-2222000000-2-2220000000000000000000000
χ2122222222-2-222-2-2222222-222-2-2222222-2-2-20000-2-2-2000000000000000000000000000000
χ2222222222-2-222-2-2222222-2-2-222-2-2-2-2-2-2-2-2-20000222000000000000000000000000000000
χ2322222222-2-222-2-222-2-2-2-2-222-2-222-2-2-2-2-2220000-222000000000000000000000000000000
χ2422222222-2-222-2-222-2-2-2-2-2-2-222-2-22222-22200002-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-20000222-2-2-2-20000200000020022-2-2000022-2-2000000000000000000
χ2622222222-2-2-2-2-2-2-2-20000222-2-2-2-200002000000200-2-2220000-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-200002-2-2222200002000000-20022-2-20000-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-200002-2-2222200002000000-200-2-222000022-2-2000000000000000000
χ292222-2-2-2-22222-2-2-2-222-2-220000000000-22-22-22-20002-22-200000000000000000000000000
χ302222-2-2-2-22222-2-2-2-222-2-220000000000-22-2-22-22000-22-2200000000000000000000000000
χ312222-2-2-2-22222-2-2-2-2-2-22220000000000-2-222-22-2000-22-2200000000000000000000000000
χ322222-2-2-2-22222-2-2-2-2-2-22220000000000-2-22-22-220002-22-200000000000000000000000000
χ332222-2-2-2-222-2-2-2-2220000-20000002i2i−2i−2i2002-2-2202i−2i000000002i−2i2i−2i000000000000000000
χ342222-2-2-2-222-2-2-2-2220000-20000002i2i−2i−2i200-222-202i−2i00000000−2i2i−2i2i000000000000000000
χ352222-2-2-2-222-2-2-2-2220000-2000000−2i−2i2i2i2002-2-220−2i2i00000000−2i2i−2i2i000000000000000000
χ362222-2-2-2-222-2-2-2-2220000-2000000−2i−2i2i2i200-222-20−2i2i000000002i−2i2i−2i000000000000000000
χ372222-2-2-2-2-2-22222-2-222-2-2-200000000002-22000000000002i−2i2i−2i2i−2i−2i2i000000000000000000
χ382222-2-2-2-2-2-22222-2-222-2-2-200000000002-2200000000000−2i2i−2i2i−2i2i2i−2i000000000000000000
χ392222-2-2-2-2-2-22222-2-2-2-222-2000000000022-2000000000002i−2i2i−2i−2i2i2i−2i000000000000000000
χ402222-2-2-2-2-2-22222-2-2-2-222-2000000000022-200000000000−2i2i−2i2i2i−2i−2i2i000000000000000000
χ412222-2-2-2-2-2-2-2-22222000020000002i2i−2i−2i-20000000−2i2i2-2-22−2i2i2i−2i0000000000000000000000
χ422222-2-2-2-2-2-2-2-22222000020000002i2i−2i−2i-20000000−2i2i-222-22i−2i−2i2i0000000000000000000000
χ432222-2-2-2-2-2-2-2-2222200002000000−2i−2i2i2i-200000002i−2i2-2-222i−2i−2i2i0000000000000000000000
χ442222-2-2-2-2-2-2-2-2222200002000000−2i−2i2i2i-200000002i−2i-222-2−2i2i2i−2i0000000000000000000000
χ4522-2-22-22-2002-2002-22i−2i2i−2i02i−2i002i−2i2-22-20000000000000000000000i2i2−i2−i222−2−22−2i2−i2000000
χ4622-2-22-22-2002-2002-22i−2i2i−2i02i−2i002i−2i2-22-20000000000000000000000−i2−i2i2i2−2−222−22−i2i2000000
χ4722-2-22-22-2002-2002-22i−2i2i−2i0−2i2i00−2i2i-22-220000000000000000000000i2i2−i2−i2−2−2222−2−i2i2000000
χ4822-2-22-22-2002-2002-22i−2i2i−2i0−2i2i00−2i2i-22-220000000000000000000000−i2−i2i2i222−2−2−22i2−i2000000
χ4922-2-22-22-2002-2002-2−2i2i−2i2i02i−2i002i−2i-22-220000000000000000000000i2i2−i2−i222−2−2−22−i2i2000000
χ5022-2-22-22-2002-2002-2−2i2i−2i2i02i−2i002i−2i-22-220000000000000000000000−i2−i2i2i2−2−2222−2i2−i2000000
χ5122-2-22-22-2002-2002-2−2i2i−2i2i0−2i2i00−2i2i2-22-20000000000000000000000i2i2−i2−i2−2−222−22i2−i2000000
χ5222-2-22-22-2002-2002-2−2i2i−2i2i0−2i2i00−2i2i2-22-20000000000000000000000−i2−i2i2i222−2−22−2−i2i2000000
χ5344-4-44-44-400-4400-44000004i−4i00−4i4i00000000000000000000000000000000000000000000
χ5444-4-44-44-400-4400-4400000−4i4i004i−4i00000000000000000000000000000000000000000000
χ5544-4-4-44-44004-400-444i−4i−4i4i000000000000000000000000000000000000000000000000000
χ5644-4-4-44-44004-400-44−4i4i4i−4i000000000000000000000000000000000000000000000000000
χ5744-4-4-44-4400-44004-4000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ5844-4-4-44-4400-44004-400000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ594-44-44-4-444-4004-400000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ604-44-44-4-444-4004-40000000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ614-44-44-4-44-4400-440000000000000000000000000000000000000002i2−2i22i2−2i200000000000000
χ624-44-44-4-44-4400-44000000000000000000000000000000000000000−2i22i2−2i22i200000000000000
χ634-44-4-444-44-400-44000000000000000000000000000000000000000000000000000002i2−2i200
χ644-44-4-444-44-400-4400000000000000000000000000000000000000000000000000000−2i22i200
χ654-44-4-444-4-44004-40000000000000000000000000000000000000000000000000002i2−2i20000
χ664-44-4-444-4-44004-4000000000000000000000000000000000000000000000000000−2i22i20000
χ674-4-4444-4-40000000000000004i−4i00000000000000000000000000002-2-222i−2i−2i2i0000000000
χ684-4-4444-4-40000000000000004i−4i0000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ694-4-4444-4-4000000000000000−4i4i00000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ704-4-4444-4-4000000000000000−4i4i0000000000000000000000000000-222-22i−2i−2i2i0000000000
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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