Finite Group Databasebeta

← Group #486705

Character table — Group #486705

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111222222222222444444444444488888888888888888888881616161616161616161616163232
order122222444444888822224448888884488881616161616161616161616161616161622444444444444
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
χ51111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1
χ61111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ71111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1
χ81111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111
χ9111111-1-1-1-111-1-1-1-111-1-1-1-11-1-111111-111-1-11111-1-1-1-11111-1-1-1-111-1-11-11-11-11-11-1
χ10111111-1-1-1-111-1-1-1-111-1-1-1-11-1-111111-111-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11-11-11-11
χ11111111-1-1-1-111-1-1-1-111-1-1-1-11-1-111111-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-11-11-111-1
χ12111111-1-1-1-111-1-1-1-111-1-1-1-11-1-111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1111-11-11-11-1-11
χ13111111-1-1-1-111-1-1-1-1-1-111-1-11-1-11111-11-1-1111111-1-1-1-1-1-1-1-1111111-1-11-1-111-1-11-11
χ14111111-1-1-1-111-1-1-1-1-1-111-1-11-1-11111-11-1-1111111-1-1-1-1-1-1-1-11111-1-111-111-1-111-11-1
χ15111111-1-1-1-111-1-1-1-1-1-111-1-11-1-11111-11-1-111-1-1-1-111111111-1-1-1-111-1-1-111-1-111-1-11
χ16111111-1-1-1-111-1-1-1-1-1-111-1-11-1-11111-11-1-111-1-1-1-111111111-1-1-1-1-1-1111-1-111-1-111-1
χ17222222222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-22222000000000000000000000000000000
χ192222222222-2-200002222-2-2-2000000-2-2000022−2−222−2−222−2−222−2−200000000000000
χ202222222222-2-200002222-2-2-2000000-2-20000−2−222−2−222−2−222−2−22200000000000000
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
χ23222222-2-2-2-222222222-2-2-2-2222-2-2-2-22-2-2-222000000000000000000000000000000
χ24222222-2-2-2-2222222-2-222-2-2222-2-2-2-2-2222-2-2000000000000000000000000000000
χ25222222-2-2-2-2-2-2000022-2-222-2000000-22000022−2−2−2−22222−2−2−2−22200000000000000
χ26222222-2-2-2-2-2-2000022-2-222-2000000-220000−2−22222−2−2−2−22222−2−200000000000000
χ27222222-2-2-2-2-2-20000-2-22222-20000002-2000022−2−2−2−222−2−22222−2−200000000000000
χ28222222-2-2-2-2-2-20000-2-22222-20000002-20000−2−22222−2−222−2−2−2−22200000000000000
χ292222-2-222-2-222222200002-2-2-2-222-2-2000000000000000000000000002-200-220000
χ302222-2-222-2-222222200002-2-2-2-222-2-200000000000000000000000000-22002-20000
χ312222-2-222-2-222-2-2-2-200002-2-222-2-22200000000000000000000000000002200-2-200
χ322222-2-222-2-222-2-2-2-200002-2-222-2-2220000000000000000000000000000-2-2002200
χ332222-2-2-2-2222222220000-22-2-2-2-2-22200000000000000000000000000002-200-2200
χ342222-2-2-2-2222222220000-22-2-2-2-2-2220000000000000000000000000000-22002-200
χ352222-2-2-2-22222-2-2-2-20000-22-22222-2-2000000000000000000000000002200-2-20000
χ362222-2-2-2-22222-2-2-2-20000-22-22222-2-200000000000000000000000000-2-200220000
χ3722-2-2-222-22-20022−2−22-22-20002−22−22−2002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ3822-2-2-222-22-20022−2−22-22-20002−22−22−2002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ3922-2-2-222-22-20022−2−2-22-220002−22−22−200−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ4022-2-2-222-22-20022−2−2-22-220002−22−22−200−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ4122-2-2-222-22-200−2−2222-22-2000−22−22−2200−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000000000
χ4222-2-2-222-22-200−2−2222-22-2000−22−22−2200−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000000000
χ4322-2-2-222-22-200−2−222-22-22000−22−22−22002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000000000
χ4422-2-2-222-22-200−2−222-22-22000−22−22−22002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000000000
χ4522-2-2-22-22-220022−2−22-2-220002−2−22−2200−222−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000000000
χ4622-2-2-22-22-220022−2−22-2-220002−2−22−2200−222−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000000000
χ4722-2-2-22-22-220022−2−2-222-20002−2−22−22002−2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ700000000000000
χ4822-2-2-22-22-220022−2−2-222-20002−2−22−22002−2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ700000000000000
χ4922-2-2-22-22-2200−2−2222-2-22000−222−22−2002−2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ5022-2-2-22-22-2200−2−2222-2-22000−222−22−2002−2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ5122-2-2-22-22-2200−2−222-222-2000−222−22−200−222−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ500000000000000
χ5222-2-2-22-22-2200−2−222-222-2000−222−22−200−222−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ500000000000000
χ534444-4-444-4-4-4-400000000-444000000000000000000000000000000000000000000
χ544444-4-4-4-444-4-4000000004-44000000000000000000000000000000000000000000
χ5544-4-44-44-4-44002222−22−220000000−222222−22−2222000000000000000000000000000000000000
χ5644-4-44-44-4-4400−22−222222000000022−22−222222−22000000000000000000000000000000000000
χ5744-4-44-4-444-4002222−22−220000000−2222−222222−22000000000000000000000000000000000000
χ5844-4-44-4-444-400−22−222222000000022−2222−22−2222000000000000000000000000000000000000
χ594-4-440000004-44i−4i4i−4i000000000000000000000000000000000002-22i−2i0000000000
χ604-4-440000004-44i−4i4i−4i00000000000000000000000000000000000-22−2i2i0000000000
χ614-4-440000004-4−4i4i−4i4i000000000000000000000000000000000002-2−2i2i0000000000
χ624-4-440000004-4−4i4i−4i4i00000000000000000000000000000000000-222i−2i0000000000
χ638-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000000
χ648-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000000
χ658-8-88000000-8800000000000000000000000000000000000000000000000000000

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