Finite Group Databasebeta

← Group #349750

Character table — Group #349750

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444442222444444444444222222444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-111-1-11-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ6111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ7111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-111-1-11111111111-1-1-1-111-1-1-1-111-11
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-111-1-1111111-1-1-1-11111-1-11111-1-11-1
χ91111111111111111-1-1-1-111111-1-1-1-1-1-111111-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ101111111111111111-1-1-1-111111-1-1-1-1-1-111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-111-1-111-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-11
χ121111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-111-1-111-1-1-111-1-11111-1-1-1-1111111-1-1-1-1111-1
χ131111111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ141111111111111111-1-1-1-11-1-1-1-111111111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ151111111111111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-111111-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ161111111111111111-1-1-1-11-1-1-1-11111111-1-1-1-111-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ1722222222222-2-2-22-20000-200002222-2-2-200002200-2-2-2-2-200220000000000000000000000
χ1822222222222-2-2-22-20000-200002222-2-2-20000-2-20022-22200-2-20000000000000000000000
χ1922222222222-2-2-22-20000-20000-2-2-2-222-200002200-2-222200-2-20000000000000000000000
χ2022222222222-2-2-22-20000-20000-2-2-2-222-20000-2-200222-2-200220000000000000000000000
χ2122222222-2-2-2222-222222-2222222-2-222-2000000-2-200-200-2-2000000000000000000000000
χ2222222222-2-2-2222-222222-2-2-2-2-2-2-222-2-2-2000000-2-20020022000000000000000000000000
χ2322222222-2-2-2222-22-2-2-2-2-22222-2-222-2-2-20000002200200-2-2000000000000000000000000
χ2422222222-2-2-2222-22-2-2-2-2-2-2-2-2-222-2-222-20000002200-20022000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-200002000022-2-2-2-2222-2-2000000200000022-2-2000000000000000000
χ2622222222-2-2-2-2-2-2-2-200002000022-2-2-2-22-2-2220000002000000-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-2000020000-2-22222222-2-2000000-2000000-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2000020000-2-222222-2-222000000-200000022-2-2000000000000000000
χ292222-2-2-2-222-222-2-2-222-2-220000000000-22-22-22-22-22-200000000000000000000000000000
χ302222-2-2-2-222-222-2-2-222-2-220000000000-2-22-22-222-2-2200000000000000000000000000000
χ312222-2-2-2-222-222-2-2-2-2-22220000000000-22-22-2-22-22-2200000000000000000000000000000
χ322222-2-2-2-222-222-2-2-2-2-22220000000000-2-22-222-2-222-200000000000000000000000000000
χ332222-2-2-2-222-2-2-22-220000-22i2i−2i−2i000000200002-200-220002i−2i002i−2i2i−2i000000000000000000
χ342222-2-2-2-222-2-2-22-220000-22i2i−2i−2i00000020000-22002-20002i−2i00−2i2i−2i2i000000000000000000
χ352222-2-2-2-222-2-2-22-220000-2−2i−2i2i2i000000200002-200-22000−2i2i00−2i2i−2i2i000000000000000000
χ362222-2-2-2-222-2-2-22-220000-2−2i−2i2i2i00000020000-22002-2000−2i2i002i−2i2i−2i000000000000000000
χ372222-2-2-2-2-2-2222-22-222-2-2-200000000002000000-220002i−2i002i−2i2i−2i−2i2i000000000000000000
χ382222-2-2-2-2-2-2222-22-222-2-2-200000000002000000-22000−2i2i00−2i2i−2i2i2i−2i000000000000000000
χ392222-2-2-2-2-2-2222-22-2-2-222-2000000000020000002-20002i−2i002i−2i−2i2i2i−2i000000000000000000
χ402222-2-2-2-2-2-2222-22-2-2-222-2000000000020000002-2000−2i2i00−2i2i2i−2i−2i2i000000000000000000
χ412222-2-2-2-2-2-22-2-2222000022i2i−2i−2i000000-22-2-220000000−2i2i−2i2i2i−2i0000000000000000000000
χ422222-2-2-2-2-2-22-2-2222000022i2i−2i−2i000000-2-222-200000002i−2i−2i2i−2i2i0000000000000000000000
χ432222-2-2-2-2-2-22-2-222200002−2i−2i2i2i000000-22-2-2200000002i−2i2i−2i−2i2i0000000000000000000000
χ442222-2-2-2-2-2-22-2-222200002−2i−2i2i2i000000-2-222-20000000−2i2i2i−2i2i−2i0000000000000000000000
χ452-22-22-22-20002-220-22-22-202-22-22-2002-20000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ462-22-22-22-20002-220-22-22-202-22-22-2002-20000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ472-22-22-22-20002-220-22-22-20-22-22-2200-220000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ482-22-22-22-20002-220-22-22-20-22-22-2200-220000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ492-22-22-22-20002-220-2-22-2202-22-2-2200-220000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ502-22-22-22-20002-220-2-22-2202-22-2-2200-220000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ512-22-22-22-20002-220-2-22-220-22-222-2002-20000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ522-22-22-22-20002-220-2-22-220-22-222-2002-20000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ5344-4-444-4-400000000000000000004i−4i0000000000000000000000002-22-22i−2i2i−2i0000000000
χ5444-4-444-4-400000000000000000004i−4i000000000000000000000000-22-22−2i2i−2i2i0000000000
χ5544-4-444-4-40000000000000000000−4i4i0000000000000000000000002-22-2−2i2i−2i2i0000000000
χ5644-4-444-4-40000000000000000000−4i4i000000000000000000000000-22-222i−2i2i−2i0000000000
χ574-44-44-44-4000-44-4040000000004-400-440000000000000000000000000000000000000000
χ584-44-44-44-4000-44-404000000000-44004-40000000000000000000000000000000000000000
χ594-44-4-44-440004-4-4044-4-44000000000000000000000000000000000000000000000000000
χ604-44-4-44-440004-4-404-444-4000000000000000000000000000000000000000000000000000
χ614-44-4-44-44000-4440-4000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ624-44-4-44-44000-4440-400000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ634-4-444-4-444-44000-4000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ644-4-444-4-444-44000-400000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ654-4-444-4-44-44-4000400000000000000000000000000000000000000000022−22−22220000000000
χ664-4-444-4-44-44-40004000000000000000000000000000000000000000000−222222−220000000000
χ674-4-44-444-44-4-400040000000000000000000000000000000000000000000000000022−220000
χ684-4-44-444-44-4-4000400000000000000000000000000000000000000000000000000−22220000
χ694-4-44-444-4-444000-400000000000000000000000000000000000000000000000000002i2−2i200
χ704-4-44-444-4-444000-40000000000000000000000000000000000000000000000000000−2i22i200
χ7188-8-8-8-888000000000000000000000000000000000000000000000000000000000000000

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