Finite Group Databasebeta

← Group #146254

Character table — Group #146254

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222222222444444444444444444444488888888888888883232323232323232
order122222444444448888888844888888888888888888881616161616161616161616161616161624444488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ922222222222222-2-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000
χ11222222-2-2-2-222222222-2-2-2-2-2-222-2-20000000000000000000000002222-2-2-2-200000000
χ12222222-2-2-2-222222222-2-2-2-2-2-222-2-2000000000000000000000000-2-2-2-2222200000000
χ13222222-2-2-2-22222-2-2-2-22222-2-2-2-22200000000000000002222-2-2-2-20000000000000000
χ14222222-2-2-2-22222-2-2-2-22222-2-2-2-2220000000000000000-2-2-2-222220000000000000000
χ152222-2-22222-222-222222222-2-2-2-2-2-2000000000000000000000000000000000000002i−2i
χ162222-2-22222-222-222222222-2-2-2-2-2-200000000000000000000000000000000000000−2i2i
χ172222-2-22222-222-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000002-2000000
χ182222-2-22222-222-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-22000000
χ192222-2-222-2-22-2-22000000002-20000000000002222-2-2-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ202222-2-222-2-22-2-22000000002-20000000000002222-2-2-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ212222-2-222-2-22-2-22000000002-2000000000000-2-2-2-22222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ222222-2-222-2-22-2-22000000002-2000000000000-2-2-2-22222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ232222-2-2-2-2222-2-2200000000-2200002222-2-2-2-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ242222-2-2-2-2222-2-2200000000-2200002222-2-2-2-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ252222-2-2-2-2222-2-2200000000-220000-2-2-2-2222200000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ262222-2-2-2-2222-2-2200000000-220000-2-2-2-2222200000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ272222-2-2-2-2-2-2-222-22222-2-2-2-222-2-22200000000000000000000000000000000002i−2i0000
χ282222-2-2-2-2-2-2-222-22222-2-2-2-222-2-2220000000000000000000000000000000000−2i2i0000
χ292222-2-2-2-2-2-2-222-2-2-2-2-222222222-2-20000000000000000000000000000000000002i−2i00
χ302222-2-2-2-2-2-2-222-2-2-2-2-222222222-2-2000000000000000000000000000000000000−2i2i00
χ312-2-222-2000022-2-2000022-2-200002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002i−2i2i−2i2−22−22−22−200000000
χ322-2-222-2000022-2-2000022-2-200002-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000−2i2i−2i2i−22−22−22−2200000000
χ332-2-222-2000022-2-2000022-2-200002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002i−2i2i−2i−22−22−22−2200000000
χ342-2-222-2000022-2-2000022-2-200002-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000−2i2i−2i2i2−22−22−22−200000000
χ352-2-222-2000022-2-20000-2-2220000-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22i−2i2i−2i00002−22−2−22−2200000000
χ362-2-222-2000022-2-20000-2-2220000-22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2i2i−2i2i0000−22−222−22−200000000
χ372-2-222-2000022-2-20000-2-2220000-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22i−2i2i−2i0000−22−222−22−200000000
χ382-2-222-2000022-2-20000-2-2220000-22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2i2i−2i2i00002−22−2−22−2200000000
χ392-2-22-2200002-22-222-2-20000002-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i22−2−222−2−220000−2i2i2i−2i00000000
χ402-2-22-2200002-22-222-2-20000002-200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2−222−2−222−200002i−2i−2i2i00000000
χ412-2-22-2200002-22-222-2-20000002-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i22−2−222−2−2200002i−2i−2i2i00000000
χ422-2-22-2200002-22-222-2-20000002-200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−222−2−222−20000−2i2i2i−2i00000000
χ432-2-22-2200002-22-2-2-222000000-2200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i22−2−22−222−2−2i2i2i−2i000000000000
χ442-2-22-2200002-22-2-2-222000000-2200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−222−22−2−222i−2i−2i2i000000000000
χ452-2-22-2200002-22-2-2-222000000-2200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i22−2−22−222−22i−2i−2i2i000000000000
χ462-2-22-2200002-22-2-2-222000000-2200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−222−22−2−22−2i2i2i−2i000000000000
χ4744444444-4-4-4-4-4-400000000-4400000000000000000000000000000000000000000000
χ48444444-4-444-4-4-4-4000000004-400000000000000000000000000000000000000000000
χ4944-4-400004-400002i2−2i22i2−2i22i2−2i22i2−2i2000000000022−2222−222i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5044-4-400004-400002i2−2i22i2−2i22i2−2i22i2−2i20000000000−2222−2222−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5144-4-400004-40000−2i22i2−2i22i2−2i22i2−2i22i2000000000022−2222−22−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5244-4-400004-40000−2i22i2−2i22i2−2i22i2−2i22i20000000000−2222−22222i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5344-4-40000-4400002i2−2i22i2−2i2−2i22i2−2i22i200000022−2222−2200002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5444-4-40000-4400002i2−2i22i2−2i2−2i22i2−2i22i2000000−2222−22220000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5544-4-40000-440000−2i22i2−2i22i22i2−2i22i2−2i200000022−2222−220000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5644-4-40000-440000−2i22i2−2i22i22i2−2i22i2−2i2000000−2222−222200002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ574-44-4004-40000002i2−2i2−2i22i22i2−2i2−2i22i20000002i−2i−2i2i2i−2i−2i2i0000−222222−22000000000000000000000000
χ584-44-4004-40000002i2−2i2−2i22i22i2−2i2−2i22i2000000−2i2i2i−2i−2i2i2i−2i000022−22−2222000000000000000000000000
χ594-44-4004-4000000−2i22i22i2−2i2−2i22i22i2−2i20000002i−2i−2i2i2i−2i−2i2i000022−22−2222000000000000000000000000
χ604-44-4004-4000000−2i22i22i2−2i2−2i22i22i2−2i2000000−2i2i2i−2i−2i2i2i−2i0000−222222−22000000000000000000000000
χ614-44-400-440000002i2−2i2−2i22i2−2i22i22i2−2i20000002i−2i−2i2i−2i2i2i−2i−222222−220000000000000000000000000000
χ624-44-400-440000002i2−2i2−2i22i2−2i22i22i2−2i2000000−2i2i2i−2i2i−2i−2i2i22−22−22220000000000000000000000000000
χ634-44-400-44000000−2i22i22i2−2i22i2−2i2−2i22i20000002i−2i−2i2i−2i2i2i−2i22−22−22220000000000000000000000000000
χ644-44-400-44000000−2i22i22i2−2i22i2−2i2−2i22i2000000−2i2i2i−2i2i−2i−2i2i−222222−220000000000000000000000000000
χ654-4-444-40000-4-44444-4-4000000-44000000000000000000000000000000000000000000
χ664-4-444-40000-4-444-4-4440000004-4000000000000000000000000000000000000000000
χ674-4-44-440000-44-44000044-4-40000-440000000000000000000000000000000000000000
χ684-4-44-440000-44-440000-4-44400004-40000000000000000000000000000000000000000

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