Finite Group Databasebeta

← Group #506267

Character table — Group #506267

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11222222222444444444444444444488888888888888888888161616161616161632323232
order122224444884444888161616161616161616161616224488888816161616161616161616222244444488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-111-1-1-11-11
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1111-11-1
χ911111111111-1-1-1-111111111111-1-1-1-11-11-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1
χ1011111111111-1-1-1-111111111111-1-1-1-11-11-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ1111111111111-1-1-1-111111111111-1-1-1-1-11-11-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-111
χ1211111111111-1-1-1-111111111111-1-1-1-1-11-11-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-1-1
χ1311111111111-1-1-1-1111-1-1-1-1-1-1-1-111111-11-1-1-111-1-1-1-1-1-11111111111-1-1-1-11-1-11
χ1411111111111-1-1-1-1111-1-1-1-1-1-1-1-111111-11-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-111-1
χ1511111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-11-11-1-1-1-1111111-1-1-1-1111111-1-1-1-1-111-1
χ1611111111111-1-1-1-1111-1-1-1-1-1-1-1-11111-11-11-1-1-1-1111111-1-1-1-111-1-1-1-111111-1-11
χ17222222222-2-22222-2-2-20000000000002-22-2-2-2-2-2220000000000000000000000
χ18222222222-2-22222-2-2-2000000000000-22-22-2-222-2-20000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2-2000000000000222222-2-2-2-20000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2-2000000000000-2-2-2-22222220000000000000000000000
χ21222-2-222-2-2002i2i−2i−2i000i2i2i2i2−i2−i2−i2−i222−2−2020-2002i−2i0022−2−2i2i2−i2−i22−2000000000000
χ22222-2-222-2-2002i2i−2i−2i000i2i2i2i2−i2−i2−i2−i222−2−20-20200−2i2i00−2−222−i2−i2i2i22−2000000000000
χ23222-2-222-2-2002i2i−2i−2i000−i2−i2−i2−i2i2i2i2i2−2−222020-2002i−2i00−2−222−i2−i2i2i2−22000000000000
χ24222-2-222-2-2002i2i−2i−2i000−i2−i2−i2−i2i2i2i2i2−2−2220-20200−2i2i0022−2−2i2i2−i2−i2−22000000000000
χ25222-2-222-2-200−2i−2i2i2i000i2i2i2i2−i2−i2−i2−i2−2−222020-200−2i2i00−2−222i2i2−i2−i2−22000000000000
χ26222-2-222-2-200−2i−2i2i2i000i2i2i2i2−i2−i2−i2−i2−2−2220-202002i−2i0022−2−2−i2−i2i2i2−22000000000000
χ27222-2-222-2-200−2i−2i2i2i000−i2−i2−i2−i2i2i2i2i222−2−2020-200−2i2i0022−2−2−i2−i2i2i22−2000000000000
χ28222-2-222-2-200−2i−2i2i2i000−i2−i2−i2−i2i2i2i2i222−2−20-202002i−2i00−2−222i2i2−i2−i22−2000000000000
χ29222-2-2-2-222-2-200002-222i2i−2i−2i2i2i−2i−2i000000000000000000000000002-22i−2i000000
χ30222-2-2-2-222-2-200002-222i2i−2i−2i2i2i−2i−2i00000000000000000000000000-22−2i2i000000
χ31222-2-2-2-222-2-200002-22−2i−2i2i2i−2i−2i2i2i000000000000000000000000002-2−2i2i000000
χ32222-2-2-2-222-2-200002-22−2i−2i2i2i−2i−2i2i2i00000000000000000000000000-222i−2i000000
χ3322-22-22-22-2002i−2i2i−2i000i2−i2i2−i2i2−i2i2−i222−2−220-2000002i−2ii2−i2i2−i22−22−2−22000000000000
χ3422-22-22-22-2002i−2i2i−2i000i2−i2i2−i2i2−i2i2−i222−2−2-20200000−2i2i−i2i2−i2i2−22−22−22000000000000
χ3522-22-22-22-2002i−2i2i−2i000−i2i2−i2i2−i2i2−i2i2−2−22220-2000002i−2i−i2i2−i2i2−22−222−2000000000000
χ3622-22-22-22-2002i−2i2i−2i000−i2i2−i2i2−i2i2−i2i2−2−222-20200000−2i2ii2−i2i2−i22−22−22−2000000000000
χ3722-22-22-22-200−2i2i−2i2i000i2−i2i2−i2i2−i2i2−i2−2−22220-200000−2i2ii2−i2i2−i2−22−222−2000000000000
χ3822-22-22-22-200−2i2i−2i2i000i2−i2i2−i2i2−i2i2−i2−2−222-202000002i−2i−i2i2−i2i22−22−22−2000000000000
χ3922-22-22-22-200−2i2i−2i2i000−i2i2−i2i2−i2i2−i2i222−2−220-200000−2i2i−i2i2−i2i22−22−2−22000000000000
χ4022-22-22-22-200−2i2i−2i2i000−i2i2−i2i2−i2i2−i2i222−2−2-202000002i−2ii2−i2i2−i2−22−22−22000000000000
χ4122-22-2-22-22-2-20000-2222i−2i−2i2i−2i2i2i−2i0000000000000000000000002-200002i−2i0000
χ4222-22-2-22-22-2-20000-2222i−2i−2i2i−2i2i2i−2i000000000000000000000000-220000−2i2i0000
χ4322-22-2-22-22-2-20000-222−2i2i2i−2i2i−2i−2i2i0000000000000000000000002-20000−2i2i0000
χ4422-22-2-22-22-2-20000-222−2i2i2i−2i2i−2i−2i2i000000000000000000000000-2200002i−2i0000
χ4522-2-222-2-22222-2-22-2-222-22-2-22-22222200002-2000000000000-2-2000000000000
χ4622-2-222-2-22222-2-22-2-22-22-222-22-2-2-2-2-200002-200000000000022000000000000
χ4722-2-222-2-2222-222-2-2-222-22-2-22-22-2-2-2-20000-2200000000000022000000000000
χ4822-2-222-2-2222-222-2-2-22-22-222-22-222220000-22000000000000-2-2000000000000
χ4922-2-222-2-22-2-22-2-2222-20000000000000000-2200002i−2i−2i2i−2i2i2i−2i00000000000000
χ5022-2-222-2-22-2-22-2-2222-20000000000000000-220000−2i2i2i−2i2i−2i−2i2i00000000000000
χ5122-2-222-2-22-2-2-222-222-200000000000000002-200002i−2i−2i2i2i−2i−2i2i00000000000000
χ5222-2-222-2-22-2-2-222-222-200000000000000002-20000−2i2i2i−2i−2i2i2i−2i00000000000000
χ5344444-4-4-4-40000000002222−22−22−22−222222000000000000000000000000000000000000
χ5444444-4-4-4-4000000000−22−2222222222−22−22000000000000000000000000000000000000
χ55444-4-4-4-444440000-44-400000000000000000000000000000000000000000000
χ5644-44-4-44-444400004-4-400000000000000000000000000000000000000000000
χ5744-4-44-444-400000000022−22−222222−22−2222000000000000000000000000000000000000
χ5844-4-44-444-4000000000−222222−22−222222−22000000000000000000000000000000000000
χ598-8000000042−420000000000000002ζ+2ζ3−2ζ5−2ζ7−2ζ−2ζ3+2ζ5+2ζ72ζ−2ζ3+2ζ5−2ζ7−2ζ+2ζ3−2ζ5+2ζ700000000000000000000000000000000
χ608-8000000042−42000000000000000−2ζ−2ζ3+2ζ5+2ζ72ζ+2ζ3−2ζ5−2ζ7−2ζ+2ζ3−2ζ5+2ζ72ζ−2ζ3+2ζ5−2ζ700000000000000000000000000000000
χ618-80000000−42420000000000000002ζ−2ζ3+2ζ5−2ζ7−2ζ+2ζ3−2ζ5+2ζ7−2ζ−2ζ3+2ζ5+2ζ72ζ+2ζ3−2ζ5−2ζ700000000000000000000000000000000
χ628-80000000−4242000000000000000−2ζ+2ζ3−2ζ5+2ζ72ζ−2ζ3+2ζ5−2ζ72ζ+2ζ3−2ζ5−2ζ7−2ζ−2ζ3+2ζ5+2ζ700000000000000000000000000000000

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