Finite Group Databasebeta

← Group #347306

Character table — Group #347306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111222222224444444444444444488888888888888888888888881616161616161616323232
order12222244444422224444444444444222222444444444444444888844888888488
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-11111-1-1111111-1-1-1
χ4111111111111111111111111-1-111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111
χ51111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-11-1-1
χ61111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-111
χ71111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11111-1-11111-1-111-1-1-1-1-11111-1-111-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1-1-1-1-1111-1-11111-1-11111-1-111-1-1-1-1-1-1-1-1-111-1-111111-1-1
χ9111111111111-1-1-1-111-1-111-1-1111111-111-1-11-111-1-111-1-11-1-1-1-1111111-1-111-1-1-11-1
χ10111111111111-1-1-1-111-1-111-1-1111111-111-1-11-111-1-111-1-11-1-1-1-1-1-1-1-1-1-111-1-1111-11
χ11111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1111-1-1-111-1-1-1-1-111111111-1-1-1-111-1-11-11
χ12111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1111-1-1-111-1-1-1-1-11111-1-1-1-11111-1-111-11-1
χ13111111111111-1-1-1-1-1-111-1-11111111-11-1-111-11-1-11111-1-11-1-1-1-1111111-1-1-1-111-1-11
χ14111111111111-1-1-1-1-1-111-1-11111111-11-1-111-11-1-11111-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1
χ15111111111111-1-1-1-1-1-111-1-111-1-1111-1111-1-1-1111-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1
χ16111111111111-1-1-1-1-1-111-1-111-1-1111-1111-1-1-1111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11
χ1722222222-222-222222222222200-2-2-2-2-20000-2-2000000-2-200000000000000000000
χ1822222222-222-22222-2-2-2-2-2-2-2-200-2-2-222000022000000-2-200000000000000000000
χ1922222222-222-2-2-2-2-222-2-222-2-200-2-2-2-220000-220000002200000000000000000000
χ2022222222-222-2-2-2-2-2-2-222-2-22200-2-2-22-200002-20000002200000000000000000000
χ21222222-2-22-2-2222-2-20000000022-2-22000000000000-2-22-2222-2-2000000000000000
χ22222222-2-22-2-2222-2-200000000-2-2-2-22000000000000222-2-2-2-222000000000000000
χ23222222-2-22-2-22-2-2220000000022-2-22000000000000-2-2-222-2-222000000000000000
χ24222222-2-22-2-22-2-22200000000-2-2-2-2200000000000022-22-222-2-2000000000000000
χ25222222-2-2-2-2-2-222-2-2000000000022-2002-22-2002-22-200-2200000000000000000000
χ26222222-2-2-2-2-2-222-2-2000000000022-200-22-2200-22-2200-2200000000000000000000
χ27222222-2-2-2-2-2-2-2-222000000000022-2002-2-22002-2-22002-200000000000000000000
χ28222222-2-2-2-2-2-2-2-222000000000022-200-222-200-222-2002-200000000000000000000
χ292222-2-22-222-220000002200-2-2222-2-20-200-2-20200222-200-20000000000000000000
χ302222-2-22-222-220000002200-2-2-2-22-2-20-200220200-2-2-220020000000000000000000
χ312222-2-22-222-22000000-2-20022222-2-20200220-200-2-22-200-20000000000000000000
χ322222-2-22-222-22000000-2-20022-2-22-2-20200-2-20-20022-220020000000000000000000
χ332222-2-22-2-22-2-20000002200-2-200-222022-2000-2-2200000002-22-2000000000000000
χ342222-2-22-2-22-2-20000002200-2-200-22202-22000-22-20000000-22-22000000000000000
χ352222-2-22-2-22-2-2000000-2-2002200-2220-22-20002-220000000-22-22000000000000000
χ362222-2-22-2-22-2-2000000-2-2002200-2220-2-2200022-200000002-22-2000000000000000
χ372222-2-2-222-22200002200-2-20022-22-2-20-2-200202200-2200-20000000000000000000
χ382222-2-2-222-22200002200-2-200-2-2-22-2-20220020-2-2002-20020000000000000000000
χ392222-2-2-222-2220000-2-200220022-22-2202200-20-2-200-2200-20000000000000000000
χ402222-2-2-222-2220000-2-2002200-2-2-22-220-2-200-2022002-20020000000000000000000
χ412222-2-2-22-2-22-200002200-2-200002-2220002-2-2000-22000002-2-22000000000000000
χ422222-2-2-22-2-22-200002200-2-200002-222000-22-20002-200000-222-2000000000000000
χ432222-2-2-22-2-22-20000-2-2002200002-22-20002-22000-2200000-222-2000000000000000
χ442222-2-2-22-2-22-20000-2-2002200002-22-2000-2220002-2000002-2-22000000000000000
χ4522-2-22-2-2-202202-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000022−2−2002−2i2−i2i2−i2000
χ4622-2-22-2-2-202202-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000−2−22200−22−i2i2−i2i2000
χ4722-2-22-2-2-202202-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000000000000022−2−2002−2−i2i2−i2i2000
χ4822-2-22-2-2-202202-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−2−22200−22i2−i2i2−i2000
χ4922-2-22-2-2-20220-22-222i−2i−2i2i2i−2i−2i2i0000000000000000000000000022−2−200−22i2−i2−i2i2000
χ5022-2-22-2-2-20220-22-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000−2−222002−2−i2i2i2−i2000
χ5122-2-22-2-2-20220-22-22−2i2i2i−2i−2i2i2i−2i0000000000000000000000000022−2−200−22−i2i2i2−i2000
χ5222-2-22-2-2-20220-22-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000−2−222002−2i2−i2−i2i2000
χ5344-4-44-4440-4-404-4-440000000000000000000000000000000000000000000000000
χ5444-4-44-4440-4-40-444-40000000000000000000000000000000000000000000000000
χ5544-4-4-444-40-44000004i−4i00−4i4i0000000000000000000000000000000000000000000
χ5644-4-4-444-40-4400000−4i4i004i−4i0000000000000000000000000000000000000000000
χ5744-4-4-44-4404-400000004i−4i00−4i4i00000000000000000000000000000000000000000
χ5844-4-4-44-4404-40000000−4i4i004i−4i00000000000000000000000000000000000000000
χ594-4-440000400-40000000000004-40000000000000000000000002i−2i2i−2i2i−2i000000000
χ604-4-440000400-40000000000004-4000000000000000000000000−2i2i−2i2i−2i2i000000000
χ614-4-440000400-4000000000000-440000000000000000000000002i−2i2i−2i−2i2i000000000
χ624-4-440000400-4000000000000-44000000000000000000000000−2i2i−2i2i2i−2i000000000
χ638-88-800000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000
χ648-88-80000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000
χ658-8-880000-800800000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).