Finite Group Databasebeta

← Group #337846

Character table — Group #337846

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888224444444444888888888888888844448888244
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1111-1-1-1-1-1
χ311111111111111111111111111-1-11111-1-111-1-111111111-1-1-1-111111-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1111
χ51111111111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-111-1-1-1111-1-1
χ71111111111111111111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-111111-111
χ9111111111111111111-1-1-1-111111111-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1
χ10111111111111111111-1-1-1-1111111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11
χ11111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1-111-111-1-1-1-11
χ12111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1111111-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-111-11111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-111-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-11-1-1111-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-1
χ17222222222-22-22-22-2-2-200002222220000-2-200-2-200-2-200000000000000020000000
χ18222222222-22-22-22-2-2-200002222-2-2000022002200-2-2000000000000000-20000000
χ19222222222-22-22-22-2-2-20000-2-2-2-22200002200-2-20022000000000000000-20000000
χ20222222222-22-22-22-2-2-20000-2-2-2-2-2-20000-2-20022002200000000000000020000000
χ2122222222-22-22-22-22-2-2222200000022-2-200-2-200-2-20000000000000020000000000
χ2222222222-22-22-22-22-2-22222000000-2-222002200-2-200000000000000-20000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000000222200-2-2002200000000000000-20000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000-2-2-2-2002200220000000000000020000000000
χ25222-2-2-22-20-202020-2002i2i−2i−2ii2i2−i2−i200002-2002i−2i0000i2−i222−2−2000022−2−2000000i2−i2000
χ26222-2-2-22-20-202020-2002i2i−2i−2ii2i2−i2−i20000-2200−2i2i0000i2−i2−2−222000022−2−2000000−i2i2000
χ27222-2-2-22-20-202020-2002i2i−2i−2i−i2−i2i2i200002-2002i−2i0000−i2i2−2−2220000−2−222000000−i2i2000
χ28222-2-2-22-20-202020-2002i2i−2i−2i−i2−i2i2i20000-2200−2i2i0000−i2i222−2−20000−2−222000000i2−i2000
χ29222-2-2-22-20-202020-200−2i−2i2i2ii2i2−i2−i200002-200−2i2i0000i2−i2−2−2220000−2−222000000i2−i2000
χ30222-2-2-22-20-202020-200−2i−2i2i2ii2i2−i2−i20000-22002i−2i0000i2−i222−2−20000−2−222000000−i2i2000
χ31222-2-2-22-20-202020-200−2i−2i2i2i−i2−i2i2i200002-200−2i2i0000−i2i222−2−2000022−2−2000000−i2i2000
χ32222-2-2-22-20-202020-200−2i−2i2i2i−i2−i2i2i20000-22002i−2i0000−i2i2−2−222000022−2−2000000i2−i2000
χ3322-22-2-2-2220-20-202000i2−i2i2−i22-22-20000002i−2i002i−2ii2−i200000022−2−2i2−i2i2−i200002−200000
χ3422-22-2-2-2220-20-202000i2−i2i2−i22-22-2000000−2i2i00−2i2ii2−i2000000−2−222i2−i2i2−i20000−2200000
χ3522-22-2-2-2220-20-202000i2−i2i2−i2-22-220000002i−2i00−2i2ii2−i2000000−2−222−i2i2−i2i200002−200000
χ3622-22-2-2-2220-20-202000i2−i2i2−i2-22-22000000−2i2i002i−2ii2−i200000022−2−2−i2i2−i2i20000−2200000
χ3722-22-2-2-2220-20-202000−i2i2−i2i22-22-20000002i−2i002i−2i−i2i2000000−2−222−i2i2−i2i20000−2200000
χ3822-22-2-2-2220-20-202000−i2i2−i2i22-22-2000000−2i2i00−2i2i−i2i200000022−2−2−i2i2−i2i200002−200000
χ3922-22-2-2-2220-20-202000−i2i2−i2i2-22-220000002i−2i00−2i2i−i2i200000022−2−2i2−i2i2−i20000−2200000
χ4022-22-2-2-2220-20-202000−i2i2−i2i2-22-22000000−2i2i002i−2i−i2i2000000−2−222i2−i2i2−i200002−200000
χ412-2-2-22-22222-2-222-2-22-20000000000000000000000002-22-22i−2i2i−2i000002i−2i00000000
χ422-2-2-22-22222-2-222-2-22-20000000000000000000000002-22-2−2i2i−2i2i00000−2i2i00000000
χ432-2-2-22-22222-2-222-2-22-2000000000000000000000000-22-222i−2i2i−2i00000−2i2i00000000
χ442-2-2-22-22222-2-222-2-22-2000000000000000000000000-22-22−2i2i−2i2i000002i−2i00000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-4-44-4040-40-4040000002i22i2−2i2−2i200000000000000−2i22i200000000000000000000000
χ47444-4-4-44-4040-40-404000000−2i2−2i22i22i2000000000000002i2−2i200000000000000000000000
χ4844-44-4-4-44-404040-40002i2−2i22i2−2i20000000000000000−2i22i20000000000000000000000000
χ4944-44-4-4-44-404040-4000−2i22i2−2i22i200000000000000002i2−2i20000000000000000000000000
χ5044-4-444-4-4000000000022−22−22222i2−2i2−2i22i2000000000000000000000000−2i2i2i−2i00000000000
χ5144-4-444-4-4000000000022−22−2222−2i22i22i2−2i20000000000000000000000002i−2i−2i2i00000000000
χ5244-4-444-4-40000000000−222222−222i2−2i2−2i22i20000000000000000000000002i−2i−2i2i00000000000
χ5344-4-444-4-40000000000−222222−22−2i22i22i2−2i2000000000000000000000000−2i2i2i−2i00000000000
χ544-44-4-44-444040-40-400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ554-44-4-44-444040-40-40000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ564-44-4-44-44-40-40404000000000004-40000000000000000000000000000000000000
χ574-44-4-44-44-40-4040400000000000-440000000000000000000000000000000000000
χ584-4-44-444-404040-40-40000000000004i−4i00000000000000000000000000000000000
χ594-4-44-444-404040-40-4000000000000−4i4i00000000000000000000000000000000000
χ604-4-44-444-40-40-404040000000000000000000000000022−22−22220000000000000000000
χ614-4-44-444-40-40-4040400000000000000000000000000−222222−220000000000000000000
χ624-4-4-44-4444-4-444-4-44-4400000000000000000000000000000000000000000000000
χ634-4-4-44-444-444-4-444-4-4400000000000000000000000000000000000000000000000
χ644-4-4-44-444-4-444-4-4444-400000000000000000000000000000000000000000000000
χ658-8888-8-8-8000000000000000000000000000000000000000000000000000000000

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