Finite Group Databasebeta

← Group #143513

Character table — Group #143513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222222244444444488888888888888888888888816161616323232323232
order122222444444888844488888822448888161616161616161616161616161616168888444488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ9222222222222-2-2-2-2222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000
χ10222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000
χ1122222222-2-2220000-2-2-200000022-2-200002222−2−2−2−22222−2−2−2−20000000000
χ1222222222-2-2220000-2-2-200000022-2-20000−2−2−2−22222−2−2−2−222220000000000
χ1322222222-2-2220000-2-2-2000000-2-22200002222−2−2−2−2−2−2−2−222220000000000
χ1422222222-2-2220000-2-2-2000000-2-2220000−2−2−2−222222222−2−2−2−20000000000
χ15222222-2-222-2-22222-2-2222-2-2-2-2000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ16222222-2-222-2-22222-2-2222-2-2-2-200000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ17222222-2-222-2-2-2-2-2-2-2-22-2-22222000000000000000022-2-222-2-20000000000
χ18222222-2-222-2-2-2-2-2-2-2-22-2-222220000000000000000-2-222-2-2220000000000
χ19222222-2-2-2-2-2-2000022-200000000002i2i−2i−2ii2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000
χ20222222-2-2-2-2-2-2000022-200000000002i2i−2i−2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000
χ21222222-2-2-2-2-2-2000022-20000000000−2i−2i2i2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000
χ22222222-2-2-2-2-2-2000022-20000000000−2i−2i2i2i−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000
χ232222-2-22-2222-222222-2-2-2-222-2-200000000000000000000000022-2-2000000
χ242222-2-22-2222-222222-2-2-2-222-2-2000000000000000000000000-2-222000000
χ252222-2-22-2222-2-2-2-2-22-2-222-2-222000000000000000000000000000002-2000
χ262222-2-22-2222-2-2-2-2-22-2-222-2-22200000000000000000000000000000-22000
χ272222-2-2-2222-222222-22-2-2-2-2-2220000000000000000000000000000200-200
χ282222-2-2-2222-222222-22-2-2-2-2-2220000000000000000000000000000-200200
χ292222-2-2-2222-22-2-2-2-2-22-22222-2-2000000000000000000000000000000002-2
χ302222-2-2-2222-22-2-2-2-2-22-22222-2-200000000000000000000000000000000-22
χ3122-2-22-22200-2-222−2−20002−22−22−22-2002−22−2ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000000000
χ3222-2-22-22200-2-222−2−20002−22−22−22-2002−22−2−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000000000
χ3322-2-22-22200-2-222−2−20002−22−22−2-2200−22−22ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000000000
χ3422-2-22-22200-2-222−2−20002−22−22−2-2200−22−22−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000000000
χ3522-2-22-22200-2-2−2−222000−22−22−222-200−22−22ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000000000
χ3622-2-22-22200-2-2−2−222000−22−22−222-200−22−22−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000000000
χ3722-2-22-22200-2-2−2−222000−22−22−22-22002−22−2ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000000000
χ3822-2-22-22200-2-2−2−222000−22−22−22-22002−22−2−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000000000
χ3922-2-22-2-2-2002222−2−20002−2−22−22002i−2ii2−i2−i2i2ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ70000000000
χ4022-2-22-2-2-2002222−2−20002−2−22−22002i−2ii2−i2−i2i2−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ70000000000
χ4122-2-22-2-2-2002222−2−20002−2−22−2200−2i2i−i2i2i2−i2ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ70000000000
χ4222-2-22-2-2-2002222−2−20002−2−22−2200−2i2i−i2i2i2−i2−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ70000000000
χ4322-2-22-2-2-20022−2−222000−222−22−2002i−2i−i2i2i2−i2ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ50000000000
χ4422-2-22-2-2-20022−2−222000−222−22−2002i−2i−i2i2i2−i2−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ50000000000
χ4522-2-22-2-2-20022−2−222000−222−22−200−2i2ii2−i2−i2i2ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ50000000000
χ4622-2-22-2-2-20022−2−222000−222−22−200−2i2ii2−i2−i2i2−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ50000000000
χ474444-4-44-4-4-44-40000-4440000000000000000000000000000000000000000
χ484444-4-4-44-4-4-4400004-440000000000000000000000000000000000000000
χ4944-4-4-444-400-442222−22−22000−222222−22−22220000000000000000000000000000000000
χ5044-4-4-444-400-44−22−22222200022−22−222222−220000000000000000000000000000000000
χ5144-4-4-44-44004-42222−22−22000−2222−222222−220000000000000000000000000000000000
χ5244-4-4-44-44004-4−22−22222200022−2222−22−22220000000000000000000000000000000000
χ534-4-440000-44004-44-40000000000000000000000000000000000022−22000000
χ544-4-440000-44004-44-400000000000000000000000000000000000−2222000000
χ554-4-440000-4400-44-4400000000000000000000000000000000022−2200000000
χ564-4-440000-4400-44-44000000000000000000000000000000000−222200000000
χ578-88-80000000042−42−42420000000000000000000000000000000000000000000
χ588-88-800000000−424242−420000000000000000000000000000000000000000000
χ598-8-8800008-80000000000000000000000000000000000000000000000000

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