Finite Group Databasebeta

← Group #486297

Character table — Group #486297

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111222222222222444444444444488888888888888888888881616161616161616161616163232
order122222222244888844444448888882488881616161616161616161616161616161622222244444444
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111-1-1111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111-1-1111-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ71111111111111111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ81111111111111111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ911111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111-11-1-1111111-1-1-1-11111-1-1-1-111-1-11-11-11-11-11-1
χ1011111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111-11-1-1111111-1-1-1-11111-1-1-1-1-1-111-11-11-11-11-11
χ1111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111-11-1-111-1-1-1-11111-1-1-1-1111111-1-1-11-11-11-111-1
χ1211111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-11111-11-1-111-1-1-1-11111-1-1-1-11111-1-1111-11-11-11-1-11
χ1311111-1-1-1-1111-1-1-1-1-1-11-1-111-1-111111-111-1-11111-1-1-1-1-1-1-1-1111111-1-11-11-1-11-11-11
χ1411111-1-1-1-1111-1-1-1-1-1-11-1-111-1-111111-111-1-11111-1-1-1-1-1-1-1-11111-1-111-11-111-11-11-1
χ1511111-1-1-1-1111-1-1-1-1-1-11-1-111-1-111111-111-1-1-1-1-1-111111111-1-1-1-111-1-1-11-111-11-1-11
χ1611111-1-1-1-1111-1-1-1-1-1-11-1-111-1-111111-111-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1-11-111-1
χ17222222222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ192222222222-2-2000022-2-2-222000000-2-2000022−2−222−2−222−2−222−2−200000000000000
χ202222222222-2-2000022-2-2-222000000-2-20000−2−222−2−222−2−222−2−22200000000000000
χ212222222222-2-20000-2-2-2-2-2-2-200000022000022−2−222−2−2−2−222−2−22200000000000000
χ222222222222-2-20000-2-2-2-2-2-2-2000000220000−2−222−2−22222−2−222−2−200000000000000
χ2322222-2-2-2-22222222222-2-2-2-222-2-2-2-2-2222-2-2000000000000000000000000000000
χ2422222-2-2-2-22222222-2-22-2-22222-2-2-2-22-2-2-222000000000000000000000000000000
χ2522222-2-2-2-22-2-2000022-222-2-20000002-2000022−2−2−2−22222−2−2−2−22200000000000000
χ2622222-2-2-2-22-2-2000022-222-2-20000002-20000−2−22222−2−2−2−22222−2−200000000000000
χ2722222-2-2-2-22-2-20000-2-2-22222000000-22000022−2−2−2−222−2−22222−2−200000000000000
χ2822222-2-2-2-22-2-20000-2-2-22222000000-220000−2−22222−2−222−2−2−2−22200000000000000
χ292222-222-2-2-222222200-22-200-2-222-2-20000000000000000000000000022-2-2000000
χ302222-222-2-2-222222200-22-200-2-222-2-200000000000000000000000000-2-222000000
χ312222-222-2-2-222-2-2-2-200-22-20022-2-2220000000000000000000000000000002-2-2200
χ322222-222-2-2-222-2-2-2-200-22-20022-2-222000000000000000000000000000000-222-200
χ332222-2-2-222-222222200-2-2200-2-2-2-22200000000000000000000000000000022-2-200
χ342222-2-2-222-222222200-2-2200-2-2-2-222000000000000000000000000000000-2-22200
χ352222-2-2-222-222-2-2-2-200-2-22002222-2-2000000000000000000000000002-2-22000000
χ362222-2-2-222-222-2-2-2-200-2-22002222-2-200000000000000000000000000-222-2000000
χ3722-2-222-22-2-20022−2−22i−2i0002i−2i2−22−22−200i2−i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000
χ3822-2-222-22-2-20022−2−22i−2i0002i−2i2−22−22−200i2−i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000
χ3922-2-222-22-2-20022−2−2−2i2i000−2i2i2−22−22−200−i2i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000
χ4022-2-222-22-2-20022−2−2−2i2i000−2i2i2−22−22−200−i2i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000
χ4122-2-222-22-2-200−2−2222i−2i0002i−2i−22−22−2200−i2i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ4222-2-222-22-2-200−2−2222i−2i0002i−2i−22−22−2200−i2i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ4322-2-222-22-2-200−2−222−2i2i000−2i2i−22−22−2200i2−i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ4422-2-222-22-2-200−2−222−2i2i000−2i2i−22−22−2200i2−i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ4522-2-22-22-22-20022−2−22i−2i000−2i2i2−2−22−2200i2−i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ4622-2-22-22-22-20022−2−22i−2i000−2i2i2−2−22−2200i2−i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ4722-2-22-22-22-20022−2−2−2i2i0002i−2i2−2−22−2200−i2i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ4822-2-22-22-22-20022−2−2−2i2i0002i−2i2−2−22−2200−i2i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ4922-2-22-22-22-200−2−2222i−2i000−2i2i−222−22−200−i2i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000
χ5022-2-22-22-22-200−2−2222i−2i000−2i2i−222−22−200−i2i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000
χ5122-2-22-22-22-200−2−222−2i2i0002i−2i−222−22−200i2−i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ700000000000000
χ5222-2-22-22-22-200−2−222−2i2i0002i−2i−222−22−200i2−i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ700000000000000
χ534444-444-4-4-4-4-40000004-4400000000000000000000000000000000000000000000
χ544444-4-4-444-4-4-400000044-400000000000000000000000000000000000000000000
χ5544-4-4-44-4-444002222−22−220000000−222222−22−2222000000000000000000000000000000000000
χ5644-4-4-44-4-44400−22−222222000000022−22−222222−22000000000000000000000000000000000000
χ5744-4-4-4-444-44002222−22−220000000−2222−222222−22000000000000000000000000000000000000
χ5844-4-4-4-444-4400−22−222222000000022−2222−22−2222000000000000000000000000000000000000
χ594-4-44000000-444-44-4000000000000000000000000000000000002-22-20000000000
χ604-4-44000000-444-44-400000000000000000000000000000000000-22-220000000000
χ614-4-44000000-44-44-44000000000000000000000000000000000002-2-220000000000
χ624-4-44000000-44-44-4400000000000000000000000000000000000-222-20000000000
χ638-88-80000000042−42−42420000000000000000000000000000000000000000000000000
χ648-88-800000000−424242−420000000000000000000000000000000000000000000000000
χ658-8-880000008-800000000000000000000000000000000000000000000000000000

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