Finite Group Databasebeta

← Group #289003

Character table — Group #289003

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222444444444444444888888888888888888888888888881616161632323232
order12222244444488884448888888888882244444444448888888888888888824882488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1
χ9111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1
χ10111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-1-11
χ11111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-11
χ12111111111111-1-1-1-1111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-111-1
χ13111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-1111111-1-1-11-11
χ14111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111-11-1
χ15111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-1111111-1-11-11-1
χ16111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-111111111-1-111-11-11
χ1722222222-2-2222222-2-2-2-2-2220000000022-2-2-2-2220000-2000000000000000000000000
χ1822222222-2-2222222-2-2-2-2-22200000000-2-22222-2-20000-2000000000000000000000000
χ1922222222-2-222-2-2-2-2-2-2-222-2-20000000022-2-222-2-200002000000000000000000000000
χ2022222222-2-222-2-2-2-2-2-2-222-2-200000000-2-222-2-22200002000000000000000000000000
χ21222222-2-2-2-2-2-200002-2200002i2i2i2i−2i−2i−2i−2i0000000022-2-200000000000000000002i−2i0000
χ22222222-2-2-2-2-2-200002-2200002i2i2i2i−2i−2i−2i−2i00000000-2-2220000000000000000000−2i2i0000
χ23222222-2-2-2-2-2-200002-220000−2i−2i−2i−2i2i2i2i2i0000000022-2-20000000000000000000−2i2i0000
χ24222222-2-2-2-2-2-200002-220000−2i−2i−2i−2i2i2i2i2i00000000-2-22200000000000000000002i−2i0000
χ252222-2-22-222-2200002-2-2000022-2-222-2-200000000000000000000022-2-200002-2000000
χ262222-2-22-222-2200002-2-2000022-2-222-2-2000000000000000000000-2-2220000-22000000
χ272222-2-22-222-2200002-2-20000-2-222-2-22200000000000000000000022-2-20000-22000000
χ282222-2-22-222-2200002-2-20000-2-222-2-222000000000000000000000-2-22200002-2000000
χ292222-2-2-22222-22222-2-2222-2-200000000000000000000-222-2-222-2-20000000000000000
χ302222-2-2-22222-22222-2-2222-2-200000000000000000000-2-2-222-2-2220000000000000000
χ312222-2-2-22222-2-2-2-2-2-2-22-2-22200000000000000000000222-2-2-2-2220000000000000000
χ322222-2-2-22222-2-2-2-2-2-2-22-2-222000000000000000000002-2-22222-2-20000000000000000
χ332222-2-2-22-2-22-2222222-2-2-2-2-22i2i−2i−2i−2i−2i2i2i00000000000020000000000002i2i−2i−2i00000000
χ342222-2-2-22-2-22-2222222-2-2-2-2-2−2i−2i2i2i2i2i−2i−2i0000000000002000000000000−2i−2i2i2i00000000
χ352222-2-2-22-2-22-2-2-2-2-222-222222i2i−2i−2i−2i−2i2i2i000000000000-2000000000000−2i−2i2i2i00000000
χ362222-2-2-22-2-22-2-2-2-2-222-22222−2i−2i2i2i2i2i−2i−2i000000000000-20000000000002i2i−2i−2i00000000
χ372-2-222-22-2002-222-2-2000002-2i2−i2i2−i2i2−i2i2−i2002i−2i2i−2i00000002−22−22−22−20000i2−i2i2−i200000000
χ382-2-222-22-2002-222-2-2000002-2i2−i2i2−i2i2−i2i2−i200−2i2i−2i2i0000000−22−22−22−220000i2−i2i2−i200000000
χ392-2-222-22-2002-222-2-2000002-2−i2i2−i2i2−i2i2−i2i2002i−2i2i−2i0000000−22−22−22−220000−i2i2−i2i200000000
χ402-2-222-22-2002-222-2-2000002-2−i2i2−i2i2−i2i2−i2i200−2i2i−2i2i00000002−22−22−22−20000−i2i2−i2i200000000
χ412-2-222-22-2002-2-2-22200000-22i2−i2i2−i2i2−i2i2−i2002i−2i−2i2i00000002−22−2−22−220000−i2i2−i2i200000000
χ422-2-222-22-2002-2-2-22200000-22i2−i2i2−i2i2−i2i2−i200−2i2i2i−2i0000000−22−222−22−20000−i2i2−i2i200000000
χ432-2-222-22-2002-2-2-22200000-22−i2i2−i2i2−i2i2−i2i2002i−2i−2i2i0000000−22−222−22−20000i2−i2i2−i200000000
χ442-2-222-22-2002-2-2-22200000-22−i2i2−i2i2−i2i2−i2i200−2i2i2i−2i00000002−22−2−22−220000i2−i2i2−i200000000
χ452-2-22-22-2-2002222-2-200000-222−2−22−222−22-200002-2000002−2−222−2−2200002−2−2200000000
χ462-2-22-22-2-2002222-2-200000-222−2−22−222−2-220000-2200000−222−2−222−200002−2−2200000000
χ472-2-22-22-2-2002222-2-200000-22−222−22−2−222-200002-200000−222−2−222−20000−222−200000000
χ482-2-22-22-2-2002222-2-200000-22−222−22−2−22-220000-22000002−2−222−2−220000−222−200000000
χ492-2-22-22-2-20022-2-222000002-22−2−22−222−22-20000-22000002−2−22−222−20000−222−200000000
χ502-2-22-22-2-20022-2-222000002-22−2−22−222−2-2200002-200000−222−22−2−220000−222−200000000
χ512-2-22-22-2-20022-2-222000002-2−222−22−2−222-20000-2200000−222−22−2−2200002−2−2200000000
χ522-2-22-22-2-20022-2-222000002-2−222−22−2−22-2200002-2000002−2−22−222−200002−2−2200000000
χ53444444-4-444-4-40000-44-40000000000000000000000000000000000000000000000000
χ544444-4-44-4-4-4-440000-4440000000000000000000000000000000000000000000000000
χ5544-4-400004-4002i2−2i22i2−2i20002i2−2i20000000000000000002i−2i2i−2i00000000022−2200000000000000
χ5644-4-400004-4002i2−2i22i2−2i20002i2−2i2000000000000000000−2i2i−2i2i000000000−222200000000000000
χ5744-4-400004-400−2i22i2−2i22i2000−2i22i20000000000000000002i−2i2i−2i000000000−222200000000000000
χ5844-4-400004-400−2i22i2−2i22i2000−2i22i2000000000000000000−2i2i−2i2i00000000022−2200000000000000
χ5944-4-40000-44002i2−2i22i2−2i2000−2i22i20000000000000000002i−2i−2i2i0000000000022−22000000000000
χ6044-4-40000-44002i2−2i22i2−2i2000−2i22i2000000000000000000−2i2i2i−2i00000000000−2222000000000000
χ6144-4-40000-4400−2i22i2−2i22i20002i2−2i20000000000000000002i−2i−2i2i00000000000−2222000000000000
χ6244-4-40000-4400−2i22i2−2i22i20002i2−2i2000000000000000000−2i2i2i−2i0000000000022−22000000000000
χ634-4-444-4-4400-440000000000022−2222−22−2222−22220000000000000000000000000000000000000
χ644-4-444-4-4400-4400000000000−2222−222222−2222−220000000000000000000000000000000000000
χ654-4-44-444400-4-4000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000
χ664-4-44-444400-4-400000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000
χ678-88-8000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000000000
χ688-88-800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000000000

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