Finite Group Databasebeta

← Group #145491

Character table — Group #145491

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size111122222222222244444444488888888888888888888888816161616323232323232
order122222444444888844488888888888888161616161616161616161616161616164444444488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ61111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111
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
χ11222222222-2-220000-2-2-200000022-2-2000022−2−222−2−22222−2−2−2−20000000000
χ12222222222-2-220000-2-2-200000022-2-20000−2−222−2−222−2−2−2−222220000000000
χ13222222222-2-220000-2-2-2000000-2-222000022−2−222−2−2−2−2−2−222220000000000
χ14222222222-2-220000-2-2-2000000-2-2220000−2−222−2−2222222−2−2−2−20000000000
χ15222222-2-2-222-222222-2-222-2-2-2-20000000000000000000000000000002-200
χ16222222-2-2-222-222222-2-222-2-2-2-2000000000000000000000000000000-2200
χ17222222-2-2-222-2-2-2-2-22-2-2-2-22222000000000000000000000000000000002i−2i
χ18222222-2-2-222-2-2-2-2-22-2-2-2-2222200000000000000000000000000000000−2i2i
χ192222-2-22-2-22222222-22-2-2-222-2-200000000000000000000000000002-20000
χ202222-2-22-2-22222222-22-2-2-222-2-20000000000000000000000000000-220000
χ212222-2-22-2-2222-2-2-2-2-22-222-2-2220000000000000000000000002i2i−2i−2i000000
χ222222-2-22-2-2222-2-2-2-2-22-222-2-222000000000000000000000000−2i−2i2i2i000000
χ232222-2-2-22222-22222-2-22-2-2-2-222000000002222-2-2-2-2000000000000000000
χ242222-2-2-22222-22222-2-22-2-2-2-22200000000-2-2-2-22222000000000000000000
χ252222-2-2-22222-2-2-2-2-2-2-222222-2-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000
χ262222-2-2-22222-2-2-2-2-2-2-222222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000
χ272222-2-2-222-2-2-2000022-200000000002i2i−2i−2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000
χ282222-2-2-222-2-2-2000022-200000000002i2i−2i−2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000
χ292222-2-2-222-2-2-2000022-20000000000−2i−2i2i2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000
χ302222-2-2-222-2-2-2000022-20000000000−2i−2i2i2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000
χ3122-2-22-222-200-22−22−20002−22−22−2002-22−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000000000
χ3222-2-22-222-200-22−22−20002−22−22−2002-22−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000000000
χ3322-2-22-222-200-22−22−20002−22−22−200-22−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ70000000000
χ3422-2-22-222-200-22−22−20002−22−22−200-22−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ70000000000
χ3522-2-22-222-200-2−22−22000−22−22−22002-2−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000000000
χ3622-2-22-222-200-2−22−22000−22−22−22002-2−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000000000
χ3722-2-22-222-200-2−22−22000−22−22−2200-222−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ50000000000
χ3822-2-22-222-200-2−22−22000−22−22−2200-222−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ50000000000
χ3922-2-2-22-22-20022−22−2000−22−222−22i−2i00i2−i2−i2i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ70000000000
χ4022-2-2-22-22-20022−22−2000−22−222−22i−2i00i2−i2−i2i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ70000000000
χ4122-2-2-22-22-20022−22−2000−22−222−2−2i2i00−i2i2i2−i2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ70000000000
χ4222-2-2-22-22-20022−22−2000−22−222−2−2i2i00−i2i2i2−i2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ70000000000
χ4322-2-2-22-22-2002−22−220002−22−2−222i−2i00−i2i2i2−i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ50000000000
χ4422-2-2-22-22-2002−22−220002−22−2−222i−2i00−i2i2i2−i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ50000000000
χ4522-2-2-22-22-2002−22−220002−22−2−22−2i2i00i2−i2−i2i2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ3−ζ50000000000
χ4622-2-2-22-22-2002−22−220002−22−2−22−2i2i00i2−i2−i2i2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ3+ζ50000000000
χ47444444-4-4-4-4-4-40000-4440000000000000000000000000000000000000000
χ484444-4-44-4-4-4-4400004-440000000000000000000000000000000000000000
χ4944-4-44-4-4-4400422−2222−2200022−22−2222−22220000000000000000000000000000000000
χ5044-4-44-4-4-44004−2222−2222000−222222−2222−220000000000000000000000000000000000
χ5144-4-4-444-4400-422−2222−22000−222222−22−22220000000000000000000000000000000000
χ5244-4-4-444-4400-4−2222−222200022−22−222222−220000000000000000000000000000000000
χ534-44-4000004-4044-4-40000000000000000000000000000000002-22-2000000
χ544-44-4000004-4044-4-4000000000000000000000000000000000-22-22000000
χ554-44-4000004-40-4-4440000000000000000000000000000000002i−2i−2i2i000000
χ564-44-4000004-40-4-444000000000000000000000000000000000−2i2i2i−2i000000
χ578-88-800000-88000000000000000000000000000000000000000000000000
χ588-8-880000000042−42−42420000000000000000000000000000000000000000000
χ598-8-8800000000−424242−420000000000000000000000000000000000000000000

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