Finite Group Databasebeta

← Group #306674

Character table — Group #306674

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-111-1-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-111-1-1111111-1-111-1-1-1-111-1-1-1-1111-111-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-11-1-11-1-11111-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-111-1-11111-1
χ91111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11
χ101111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111111-1-1-11-1-1-1-111-1-111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-11111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-11111111-1-1-11111-1-1-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111111
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111111-1-1111-1-1-1-1-1-1111
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111111-1-11111-1-1-1
χ17222222222-22-22-22-22222-2-20000000000-2-22200220000-2-20000-200000000000000
χ18222222222-22-22-22-22222-2-20000000000-2-2-2-200-2-20000220000200000000000000
χ19222222222-22-22-22-2-2-2-2-2-2-20000000000222200-2-20000220000-200000000000000
χ20222222222-22-22-22-2-2-2-2-2-2-2000000000022-2-200220000-2-20000200000000000000
χ2122222222-22-22-22-220000-2-222222222-2-20000-2-2000000000000000-200000000000
χ2222222222-22-22-22-220000-2-22222-2-2-2-2220000-2-2000000000000000200000000000
χ2322222222-22-22-22-220000-2-2-2-2-2-222-2-2-2-2000022000000000000000200000000000
χ2422222222-22-22-22-220000-2-2-2-2-2-2-2-22222000022000000000000000-200000000000
χ25222-2-2-2-22-20-2020202i2i−2i−2i0022−2−2000000002-22−22i−2ii2i2−i2−i200i2i2−i2−i200000000002−2000
χ26222-2-2-2-22-20-2020202i2i−2i−2i0022−2−200000000-222−2−2i2ii2i2−i2−i200−i2−i2i2i20000000000−22000
χ27222-2-2-2-22-20-2020202i2i−2i−2i00−2−222000000002-2−222i−2i−i2−i2i2i200−i2−i2i2i20000000000−22000
χ28222-2-2-2-22-20-2020202i2i−2i−2i00−2−22200000000-22−22−2i2i−i2−i2i2i200i2i2−i2−i200000000002−2000
χ29222-2-2-2-22-20-202020−2i−2i2i2i0022−2−2000000002-22−2−2i2i−i2−i2i2i200−i2−i2i2i200000000002−2000
χ30222-2-2-2-22-20-202020−2i−2i2i2i0022−2−200000000-222−22i−2i−i2−i2i2i200i2i2−i2−i20000000000−22000
χ31222-2-2-2-22-20-202020−2i−2i2i2i00−2−222000000002-2−22−2i2ii2i2−i2−i200i2i2−i2−i20000000000−22000
χ32222-2-2-2-22-20-202020−2i−2i2i2i00−2−22200000000-22−222i−2ii2i2−i2−i200−i2−i2i2i200000000002−2000
χ332-22-2-222-22-2-222-2-220000-2200002-2002-2000000002i−2i2i−2i0000000000002i−2i0000000
χ342-22-2-222-22-2-222-2-220000-2200002-2002-200000000−2i2i−2i2i000000000000−2i2i0000000
χ352-22-2-222-22-2-222-2-220000-220000-2200-22000000002i−2i2i−2i000000000000−2i2i0000000
χ362-22-2-222-22-2-222-2-220000-220000-2200-2200000000−2i2i−2i2i0000000000002i−2i0000000
χ372-22-2-222-2-222-2-222-22i−2i2i−2i-2200000000002i−2i000000000000000002i−2i0000000002-20
χ382-22-2-222-2-222-2-222-22i−2i2i−2i-2200000000002i−2i00000000000000000−2i2i000000000-220
χ392-22-2-222-2-222-2-222-2−2i2i−2i2i-220000000000−2i2i000000000000000002i−2i000000000-220
χ402-22-2-222-2-222-2-222-2−2i2i−2i2i-220000000000−2i2i00000000000000000−2i2i0000000002-20
χ412-22-2-222-2-2-222-2-2222i−2i2i−2i2-200002-200-22−2i2i000000000000000000002i−2i000000000
χ422-22-2-222-2-2-222-2-2222i−2i2i−2i2-20000-22002-2−2i2i00000000000000000000−2i2i000000000
χ432-22-2-222-2-2-222-2-222−2i2i−2i2i2-200002-200-222i−2i00000000000000000000−2i2i000000000
χ442-22-2-222-2-2-222-2-222−2i2i−2i2i2-20000-22002-22i−2i000000000000000000002i−2i000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-4-444040-40-400000002222−22−220000000000−2222000000000000000000000000000
χ47444-4-4-4-444040-40-40000000−22−222222000000000022−22000000000000000000000000000
χ4844-44-44-4-4040-40-4040000000000004-400000000000000000000000000000000000
χ4944-44-44-4-4040-40-404000000000000-4400000000000000000000000000000000000
χ5044-44-44-4-40-404040-400000000000000000000000000000000000000000022−2200000
χ5144-44-44-4-40-404040-4000000000000000000000000000000000000000000−222200000
χ524-4444-4-4-440-40-40404-4-44000000000000000000000000000000000000000000000
χ534-4444-4-4-440-40-4040-444-4000000000000000000000000000000000000000000000
χ544-4444-4-4-4-404040-4000000000000000000000000022−22−2222000000000000000000000
χ554-4444-4-4-4-404040-40000000000000000000000000−222222−22000000000000000000000
χ564-44-4-444-444-4-444-4-400004-40000000000000000000000000000000000000000000
χ574-4-44-4-4440000000000000022−2222−2200000000000000000022−222-22-2000000000000000
χ584-4-44-4-4440000000000000022−2222−22000000000000000000−2222-22-22000000000000000
χ594-4-44-4-44400000000000000−2222−222200000000000000000022−22-22-22000000000000000
χ604-4-44-4-44400000000000000−2222−2222000000000000000000−22222-22-2000000000000000
χ614-4-4-444-4404040-40-40000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ624-4-4-444-4404040-40-4000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ634-4-4-444-440-40-404040000004-4-44000000000000000000000000000000000000000
χ644-4-4-444-440-40-40404000000-444-4000000000000000000000000000000000000000
χ6588-8-88-88-8000000000000000000000000000000000000000000000000000000000

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