Finite Group Databasebeta

← Group #235035

Character table — Group #235035

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12224444222222224444444422244422224444444444448888888888888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-11-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11-11111
χ91111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-11111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-11-1-1-111-1-1
χ101111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-11-11-1-111
χ111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-11-111111-1-1
χ121111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-111-11-1-1-111
χ131111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-11-1111-1-111
χ141111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-111-11-111-1-1
χ151111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111-11-1-1-1-1-111
χ161111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-11-1111-1-1
χ17222222222222-2-2-2-222-2-2-2-2222-2-2-2-22000000000000000000000000000000000200-2-2020000
χ18222222222222-2-2-2-222-2-2-2-2222-2-2-2-22000000000000000000000000000000000-200220-20000
χ192222222222-2-22222222222-2-2-2-2-2-2-2-20000000022-2-222-2-20000000000000000000000000000
χ202222222222-2-22222222222-2-2-2-2-2-2-2-200000000-2-222-2-2220000000000000000000000000000
χ212222222222-2-2-2-2-2-222-2-2-2-2-2-2-22222-200000000000000000000000000000000000000002i−2i2i−2i
χ222222222222-2-2-2-2-2-222-2-2-2-2-2-2-22222-20000000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-22222-2-2-2-222-2-222-22-22-2-20000000000000000000000000000000020-2-200200000
χ2422222222-2-22222-2-2-2-222-2-222-22-22-2-200000000000000000000000000000000-202200-200000
χ2522222222-2-222-2-222-2-2-2-22222-2-22-22-2000000000000000022-2-222-2-200000000000000000000
χ2622222222-2-222-2-222-2-2-2-22222-2-22-22-20000000000000000-2-222-2-22200000000000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-2-2-22-22-22222-2-222-2-2000000000000000000000000000000000000
χ2822222222-2-2-2-222-2-2-2-222-2-2-2-22-22-222-2-222-2-222000000000000000000000000000000000000
χ2922222222-2-2-2-2-2-222-2-2-2-222-2-222-22-2200000000000000000000000022-2-222-2-2000000000000
χ3022222222-2-2-2-2-2-222-2-2-2-222-2-222-22-22000000000000000000000000-2-222-2-222000000000000
χ312222-2-2-2-222222222-2-2-2-2-2-2-2-2222-2-2-20000000022-2-2-2-2220000000000000000000000000000
χ322222-2-2-2-222222222-2-2-2-2-2-2-2-2222-2-2-200000000-2-22222-2-20000000000000000000000000000
χ332222-2-2-2-22222-2-2-2-2-2-22222-2-22-2-222-200000000000000000000000000000000000000002i−2i−2i2i
χ342222-2-2-2-22222-2-2-2-2-2-22222-2-22-2-222-20000000000000000000000000000000000000000−2i2i2i−2i
χ352222-2-2-2-222-2-2-2-2-2-2-2-2222222-222-2-22000000000000000000000000000000000200-220-20000
χ362222-2-2-2-222-2-2-2-2-2-2-2-2222222-222-2-22000000000000000000000000000000000-2002-2020000
χ372222-2-2-2-2-2-22222-2-222-2-222-2-2-22-2-22222-2-2-2-222000000000000000000000000000000000000
χ382222-2-2-2-2-2-22222-2-222-2-222-2-2-22-2-222-2-22222-2-2000000000000000000000000000000000000
χ392222-2-2-2-2-2-222-2-2222222-2-2-2-2-2-222-2200000000000000000000000022-2-2-2-222000000000000
χ402222-2-2-2-2-2-222-2-2222222-2-2-2-2-2-222-22000000000000000000000000-2-22222-2-2000000000000
χ412222-2-2-2-2-2-2-2-222-2-222-2-222222-222-2-20000000000000000000000000000000020-2200-200000
χ422222-2-2-2-2-2-2-2-222-2-222-2-222222-222-2-200000000000000000000000000000000-202-200200000
χ432222-2-2-2-2-2-2-2-2-2-2222222-2-22222-2-22-2000000000000000022-2-2-2-22200000000000000000000
χ442222-2-2-2-2-2-2-2-2-2-2222222-2-22222-2-22-20000000000000000-2-22222-2-200000000000000000000
χ4522-2-22i2i−2i−2i2-2002-22-22i−2i2i−2i2i−2i0000000000000000002-2002i−2i2−22−2i2−i2i2−i22−22−2i2−i2i2−i2000000000000
χ4622-2-22i2i−2i−2i2-2002-22-22i−2i2i−2i2i−2i0000000000000000002-2002i−2i−22−22−i2i2−i2i2−22−22−i2i2−i2i2000000000000
χ4722-2-22i2i−2i−2i2-2002-22-22i−2i2i−2i2i−2i000000000000000000-2200−2i2i2−22−2i2−i2i2−i2−22−22−i2i2−i2i2000000000000
χ4822-2-22i2i−2i−2i2-2002-22-22i−2i2i−2i2i−2i000000000000000000-2200−2i2i−22−22−i2i2−i2i22−22−2i2−i2i2−i2000000000000
χ4922-2-22i2i−2i−2i-2200-222-2−2i2i−2i2i2i−2i00000000000000002-2002i−2i002−2−22i2−i2−i2i22−2−22i2−i2−i2i2000000000000
χ5022-2-22i2i−2i−2i-2200-222-2−2i2i−2i2i2i−2i00000000000000002-2002i−2i00−222−2−i2i2i2−i2−222−2−i2i2i2−i2000000000000
χ5122-2-22i2i−2i−2i-2200-222-2−2i2i−2i2i2i−2i0000000000000000-2200−2i2i002−2−22i2−i2−i2i2−222−2−i2i2i2−i2000000000000
χ5222-2-22i2i−2i−2i-2200-222-2−2i2i−2i2i2i−2i0000000000000000-2200−2i2i00−222−2−i2i2i2−i22−2−22i2−i2−i2i2000000000000
χ5322-2-2−2i−2i2i2i2-2002-22-2−2i2i−2i2i−2i2i0000000000000000002-200−2i2i2−22−2−i2i2−i2i22−22−2−i2i2−i2i2000000000000
χ5422-2-2−2i−2i2i2i2-2002-22-2−2i2i−2i2i−2i2i0000000000000000002-200−2i2i−22−22i2−i2i2−i2−22−22i2−i2i2−i2000000000000
χ5522-2-2−2i−2i2i2i2-2002-22-2−2i2i−2i2i−2i2i000000000000000000-22002i−2i2−22−2−i2i2−i2i2−22−22i2−i2i2−i2000000000000
χ5622-2-2−2i−2i2i2i2-2002-22-2−2i2i−2i2i−2i2i000000000000000000-22002i−2i−22−22i2−i2i2−i22−22−2−i2i2−i2i2000000000000
χ5722-2-2−2i−2i2i2i-2200-222-22i−2i2i−2i−2i2i00000000000000002-200−2i2i002−2−22−i2i2i2−i22−2−22−i2i2i2−i2000000000000
χ5822-2-2−2i−2i2i2i-2200-222-22i−2i2i−2i−2i2i00000000000000002-200−2i2i00−222−2i2−i2−i2i2−222−2i2−i2−i2i2000000000000
χ5922-2-2−2i−2i2i2i-2200-222-22i−2i2i−2i−2i2i0000000000000000-22002i−2i002−2−22−i2i2i2−i2−222−2i2−i2−i2i2000000000000
χ6022-2-2−2i−2i2i2i-2200-222-22i−2i2i−2i−2i2i0000000000000000-22002i−2i00−222−2i2−i2−i2i22−2−22−i2i2i2−i2000000000000
χ6144-4-44i4i−4i−4i4-400-44-444i−4i−4i4i−4i4i0000000000000000000000000000000000000000000000000000
χ6244-4-44i4i−4i−4i-44004-4-44−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ6344-4-4−4i−4i4i4i4-400-44-44−4i4i4i−4i4i−4i0000000000000000000000000000000000000000000000000000
χ6444-4-4−4i−4i4i4i-44004-4-444i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ654-4-444-44-4004-400000000004-40000002-22-22-22-2000000000000000000000000000000000000
χ664-4-444-44-4004-400000000004-4000000-22-22-22-22000000000000000000000000000000000000
χ674-4-444-44-400-440000000000-440000002-2-222-2-22000000000000000000000000000000000000
χ684-4-444-44-400-440000000000-44000000-222-2-222-2000000000000000000000000000000000000
χ694-4-44-44-44004-40000000000-440000002-2-22-222-2000000000000000000000000000000000000
χ704-4-44-44-44004-40000000000-44000000-222-22-2-22000000000000000000000000000000000000
χ714-4-44-44-4400-4400000000004-40000002-22-2-22-22000000000000000000000000000000000000
χ724-4-44-44-4400-4400000000004-4000000-22-222-22-2000000000000000000000000000000000000
χ738-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000

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