Finite Group Databasebeta

← Group #511966

Character table — Group #511966

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1122222222222224444444444444444444444444444444444444444444444444444444443232323232323232
order122224444881616161622222244444488888888888888816161616161616161616161616161616161616161616161616161616161622444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-111-1-1-1-111-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111-1-111-1-1-1-111-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ911111111111-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1
χ1011111111111-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11
χ1111111111111-1-1-1-111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-1-11-11
χ1211111111111-1-1-1-111-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-111-11-1
χ1311111111111-1-1-1-1-1-111-1-1-1-111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-111-1-11
χ1411111111111-1-1-1-1-1-111-1-1-1-111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-111-1-111-1
χ1511111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-11-111-1
χ1611111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-111-11-1-11
χ17222222222-2-20000222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000
χ18222222222-2-2000022-2-2-2-222-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000
χ19222222222-2-20000-2-222-2-2-2-222-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000
χ20222222222-2-20000-2-2-2-222-2-2-2-222-2-2-222222222-2-2-2-200000000000000000000000000000000000000
χ2122222-2-2-2-20022−2−22-22-22-22-22-22-2000000000000000222−2−2−22222−2−2−2−22222−2−2−2−22222−2−2−2−200000000
χ2222222-2-2-2-20022−2−22-2-22-222-2-22-22000000000000000222−2−2−22222−2−2−2−2−2−2−2−22222−2−2−2−2222200000000
χ2322222-2-2-2-20022−2−2-222-2-22-222-2-22000000000000000222−2−2−2−2−2−2−222222222−2−2−2−2−2−2−2−2222200000000
χ2422222-2-2-2-20022−2−2-22-222-2-22-222-2000000000000000222−2−2−2−2−2−2−22222−2−2−2−222222222−2−2−2−200000000
χ2522222-2-2-2-200−2−2222-22-22-22-22-22-2000000000000000−2−2−2222−2−2−2−22222−2−2−2−22222−2−2−2−2222200000000
χ2622222-2-2-2-200−2−2222-2-22-222-2-22-22000000000000000−2−2−2222−2−2−2−222222222−2−2−2−22222−2−2−2−200000000
χ2722222-2-2-2-200−2−222-222-2-22-222-2-22000000000000000−2−2−22222222−2−2−2−2−2−2−2−222222222−2−2−2−200000000
χ2822222-2-2-2-200−2−222-22-222-2-22-222-2000000000000000−2−2−22222222−2−2−2−22222−2−2−2−2−2−2−2−2222200000000
χ29222-2-222-2-20022−2−20000220000-2-20002i2i−2i−2i2i2i−2i−2i00002−2−222−2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000
χ30222-2-222-2-20022−2−20000220000-2-2000−2i−2i2i2i−2i−2i2i2i00002−2−222−2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000
χ31222-2-222-2-20022−2−20000-2-20000220002i2i−2i−2i−2i−2i2i2i00002−2−222−2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000
χ32222-2-222-2-20022−2−20000-2-2000022000−2i−2i2i2i2i2i−2i−2i00002−2−222−2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000
χ33222-2-222-2-200−2−2220000220000-2-20002i2i−2i−2i2i2i−2i−2i0000−222−2−22−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000
χ34222-2-222-2-200−2−2220000220000-2-2000−2i−2i2i2i−2i−2i2i2i0000−222−2−22i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000
χ35222-2-222-2-200−2−2220000-2-20000220002i2i−2i−2i−2i−2i2i2i0000−222−2−22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i222−2−222−2−200000000
χ36222-2-222-2-200−2−2220000-2-2000022000−2i−2i2i2i2i2i−2i−2i0000−222−2−22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000
χ37222-2-2-2-22222222200002-20000-222-2-20000000022-2-22-2-2-2-22000000000000000022-2-2-2-22200000000
χ38222-2-2-2-2222222220000-2200002-22-2-200000000-2-2222-2-2-2-220000000000000000-2-22222-2-200000000
χ39222-2-2-2-22222-2-2-2-200002-20000-222-2-20000000022-2-2-22222-20000000000000000-2-22222-2-200000000
χ40222-2-2-2-22222-2-2-2-20000-2200002-22-2-200000000-2-222-22222-2000000000000000022-2-2-2-22200000000
χ41222-2-2-2-222-2-2000000002-20000-22-22200000000-2-2220000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ42222-2-2-2-222-2-2000000002-20000-22-22200000000-2-222000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ43222-2-2-2-222-2-200000000-2200002-2-2220000000022-2-20000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ44222-2-2-2-222-2-200000000-2200002-2-2220000000022-2-2000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ4522-22-22-22-20022−2−200220000-2-2000002i−2i2i−2i00002i−2i2i−2i−22−22−22i2−i2i2−i2i2−i2i2−i22−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ4622-22-22-22-20022−2−200220000-2-200000−2i2i−2i2i0000−2i2i−2i2i−22−22−22−i2i2−i2i2−i2i2−i2i22−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ4722-22-22-22-20022−2−200-2-2000022000002i−2i2i−2i0000−2i2i−2i2i−22−22−22i2−i2i2−i2i2−i2i2−i2−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000
χ4822-22-22-22-20022−2−200-2-200002200000−2i2i−2i2i00002i−2i2i−2i−22−22−22−i2i2−i2i2−i2i2−i2i2−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000
χ4922-22-22-22-200−2−22200220000-2-2000002i−2i2i−2i00002i−2i2i−2i2−22−22−2−i2i2−i2i2−i2i2−i2i2−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000
χ5022-22-22-22-200−2−22200220000-2-200000−2i2i−2i2i0000−2i2i−2i2i2−22−22−2i2−i2i2−i2i2−i2i2−i2−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000
χ5122-22-22-22-200−2−22200-2-2000022000002i−2i2i−2i0000−2i2i−2i2i2−22−22−2−i2i2−i2i2−i2i2−i2i22−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ5222-22-22-22-200−2−22200-2-200002200000−2i2i−2i2i00002i−2i2i−2i2−22−22−2i2−i2i2−i2i2−i2i2−i22−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ5322-22-2-22-22222222002-20000-2200-22-200002-22-20000-22-2-22-2000000002-22-2-22-220000000000000000
χ5422-22-2-22-2222222200-2200002-200-22-20000-22-220000-22-2-22-200000000-22-222-22-20000000000000000
χ5522-22-2-22-2222-2-2-2-2002-20000-2200-22-200002-22-200002-222-2200000000-22-222-22-20000000000000000
χ5622-22-2-22-2222-2-2-2-200-2200002-200-22-20000-22-2200002-222-22000000002-22-2-22-220000000000000000
χ5722-22-2-22-22-2-20000002-20000-22002-220000-22-2200000000002i−2i2i−2i−2i2i−2i2i000000002i−2i2i−2i−2i2i−2i2i00000000
χ5822-22-2-22-22-2-20000002-20000-22002-220000-22-220000000000−2i2i−2i2i2i−2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i00000000
χ5922-22-2-22-22-2-2000000-2200002-2002-2200002-22-200000000002i−2i2i−2i−2i2i−2i2i00000000−2i2i−2i2i2i−2i2i−2i00000000
χ6022-22-2-22-22-2-2000000-2200002-2002-2200002-22-20000000000−2i2i−2i2i2i−2i2i−2i000000002i−2i2i−2i−2i2i−2i2i00000000
χ6122-2-222-2-222222222-20000-220000-2-222-2-2200000000-2-222-2-22-2-222-2-22000000000000000000000000
χ6222-2-222-2-22222222-2200002-20000-2-22-222-200000000-2-222-2-2-222-2-222-2000000000000000000000000
χ6322-2-222-2-2222-2-2-2-22-20000-220000-2-222-2-220000000022-2-222-222-2-222-2000000000000000000000000
χ6422-2-222-2-2222-2-2-2-2-2200002-20000-2-22-222-20000000022-2-2222-2-222-2-22000000000000000000000000
χ6522-2-222-2-22-2-200002-20000-22000022-2-222-200000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000
χ6622-2-222-2-22-2-200002-20000-22000022-2-222-20000000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000
χ6722-2-222-2-22-2-20000-2200002-2000022-22-2-2200000000000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i00000000
χ6822-2-222-2-22-2-20000-2200002-2000022-22-2-220000000000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i00000000
χ6922-2-22-222-20022−2−2220000-2-2000000000002i−2i−2i2i2i−2i−2i2i−2−22−2222−2−22−222−2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ7022-2-22-222-20022−2−2220000-2-200000000000−2i2i2i−2i−2i2i2i−2i−2−22−2222−2−22−222−2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ7122-2-22-222-20022−2−2-2-2000022000000000002i−2i−2i2i−2i2i2i−2i−2−22−222−222−22−2−22i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ7222-2-22-222-20022−2−2-2-200002200000000000−2i2i2i−2i2i−2i−2i2i−2−22−222−222−22−2−22−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ7322-2-22-222-200−2−222220000-2-2000000000002i−2i−2i2i2i−2i−2i2i22−22−2−2−222−22−2−22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ7422-2-22-222-200−2−222220000-2-200000000000−2i2i2i−2i−2i2i2i−2i22−22−2−2−222−22−2−22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ7522-2-22-222-200−2−222-2-2000022000000000002i−2i−2i2i−2i2i2i−2i22−22−2−22−2−22−222−2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ7622-2-22-222-200−2−222-2-200002200000000000−2i2i2i−2i2i−2i−2i2i22−22−2−22−2−22−222−2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ778-8000000042−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ500000000000000000000000000000000000000000000000000000000000000000
χ788-8000000042−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ500000000000000000000000000000000000000000000000000000000000000000
χ798-80000000−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ700000000000000000000000000000000000000000000000000000000000000000
χ808-80000000−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ700000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.