Finite Group Databasebeta

← Group #326170

Character table — Group #326170

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888888888888888888882244444488888888244488884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ91111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-111-111-1
χ101111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1111-1-11-1-11
χ111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-1111-1-11
χ121111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-111-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-11-11-111-1-11-11-1
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-11-11-1-111-11-11
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111-11-111-1-1-11-11
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-11-11-1-1111-11-1
χ17222222222-22-22-22-200000000-2-200002222-2-2-2-20000000022-2-222-2-200000000000000000000
χ18222222222-22-22-22-200000000-2-200002222-2-2-2-200000000-2-222-2-22200000000000000000000
χ19222222222-22-22-22-200000000-2-20000-2-2-2-22222000000002222-2-2-2-200000000000000000000
χ20222222222-22-22-22-200000000-2-20000-2-2-2-2222200000000-2-2-2-2222200000000000000000000
χ2122222222-22-22-22-2222222222-2-2-2-2-2-2000000000000000000000000000000002-2-2200000000
χ2222222222-22-22-22-2222222222-2-2-2-2-2-200000000000000000000000000000000-222-200000000
χ2322222222-22-22-22-22-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000022-2-200000000
χ2422222222-22-22-22-22-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000-2-22200000000
χ252222-2-2-2-2-20-2020202222−2−2−2−20022−2−2000022-2-22222−2−2−2−200002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2000000000000
χ262222-2-2-2-2-20-2020202222−2−2−2−20022−2−2000022-2-22222−2−2−2−20000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2000000000000
χ272222-2-2-2-2-20-2020202222−2−2−2−20022−2−20000-2-222−2−2−2−2222200002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2000000000000
χ282222-2-2-2-2-20-2020202222−2−2−2−20022−2−20000-2-222−2−2−2−222220000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2000000000000
χ292222-2-2-2-2-20-202020−2−2−2−2222200−2−222000022-2-2−2−2−2−2222200002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2000000000000
χ302222-2-2-2-2-20-202020−2−2−2−2222200−2−222000022-2-2−2−2−2−222220000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2000000000000
χ312222-2-2-2-2-20-202020−2−2−2−2222200−2−2220000-2-2222222−2−2−2−200002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2000000000000
χ322222-2-2-2-2-20-202020−2−2−2−2222200−2−2220000-2-2222222−2−2−2−20000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2000000000000
χ332-22-22-22-2-202020-20i2i2−i2−i2i2i2−i2−i200i2−i2i2−i200002i−2i2i−2i22−2−222−2−22-22i−2i00002−22−2i2−i2i2−i2000000000000
χ342-22-22-22-2-202020-20i2i2−i2−i2i2i2−i2−i200i2−i2i2−i200002i−2i2i−2i22−2−222−2−2-22−2i2i0000−22−22−i2i2−i2i2000000000000
χ352-22-22-22-2-202020-20i2i2−i2−i2i2i2−i2−i200i2−i2i2−i20000−2i2i−2i2i−2−222−2−2222-2−2i2i0000−22−22i2−i2i2−i2000000000000
χ362-22-22-22-2-202020-20i2i2−i2−i2i2i2−i2−i200i2−i2i2−i20000−2i2i−2i2i−2−222−2−222-222i−2i00002−22−2−i2i2−i2i2000000000000
χ372-22-22-22-2-202020-20−i2−i2i2i2−i2−i2i2i200−i2i2−i2i200002i−2i2i−2i−2−222−2−2222-22i−2i0000−22−22−i2i2−i2i2000000000000
χ382-22-22-22-2-202020-20−i2−i2i2i2−i2−i2i2i200−i2i2−i2i200002i−2i2i−2i−2−222−2−222-22−2i2i00002−22−2i2−i2i2−i2000000000000
χ392-22-22-22-2-202020-20−i2−i2i2i2−i2−i2i2i200−i2i2−i2i20000−2i2i−2i2i22−2−222−2−22-2−2i2i00002−22−2−i2i2−i2i2000000000000
χ402-22-22-22-2-202020-20−i2−i2i2i2−i2−i2i2i200−i2i2−i2i20000−2i2i−2i2i22−2−222−2−2-222i−2i0000−22−22i2−i2i2−i2000000000000
χ412-22-2-22-2222-2-222-2-22i2i−2i−2i−2i−2i2i2i-222i−2i−2i2i2i2i−2i−2i2i−2i−2i2i22-2-2-2-2220000000000000000000000000000
χ422-22-2-22-2222-2-222-2-22i2i−2i−2i−2i−2i2i2i-222i−2i−2i2i−2i−2i2i2i−2i2i2i−2i-2-22222-2-20000000000000000000000000000
χ432-22-2-22-2222-2-222-2-2−2i−2i2i2i2i2i−2i−2i-22−2i2i2i−2i2i2i−2i−2i2i−2i−2i2i-2-22222-2-20000000000000000000000000000
χ442-22-2-22-2222-2-222-2-2−2i−2i2i2i2i2i−2i−2i-22−2i2i2i−2i−2i−2i2i2i−2i2i2i−2i22-2-2-2-2220000000000000000000000000000
χ452-22-2-22-222-2-222-2-22000000002-200002i2i−2i−2i−2i2i2i−2i00000000000000002i−2i−2i2i2-2-22000000000000
χ462-22-2-22-222-2-222-2-22000000002-200002i2i−2i−2i−2i2i2i−2i0000000000000000−2i2i2i−2i-222-2000000000000
χ472-22-2-22-222-2-222-2-22000000002-20000−2i−2i2i2i2i−2i−2i2i00000000000000002i−2i−2i2i-222-2000000000000
χ482-22-2-22-222-2-222-2-22000000002-20000−2i−2i2i2i2i−2i−2i2i0000000000000000−2i2i2i−2i2-2-22000000000000
χ492-22-2-22-22-222-2-222-22i2i−2i−2i−2i−2i2i2i2-2−2i2i2i−2i0000000000000000000000000000000000002i−2i2-20000
χ502-22-2-22-22-222-2-222-22i2i−2i−2i−2i−2i2i2i2-2−2i2i2i−2i000000000000000000000000000000000000−2i2i-220000
χ512-22-2-22-22-222-2-222-2−2i−2i2i2i2i2i−2i−2i2-22i−2i−2i2i0000000000000000000000000000000000002i−2i-220000
χ522-22-2-22-22-222-2-222-2−2i−2i2i2i2i2i−2i−2i2-22i−2i−2i2i000000000000000000000000000000000000−2i2i2-20000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ544444-4-4-4-44040-40-4022222222−22−22−22−2200−22−22222200000000000000000000000000000000000000000000
χ554444-4-4-4-44040-40-40−22−22−22−2222222222002222−22−2200000000000000000000000000000000000000000000
χ5644-4-44-4-44040-40-40400000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000
χ5744-4-44-4-44040-40-4040000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000
χ5844-4-44-4-440-404040-44i−4i4i−4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ5944-4-44-4-440-404040-4−4i4i−4i4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ6044-4-4-444-4000000002i2−2i22i2−2i2−2i22i2−2i22i200000022−2222−2200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ6144-4-4-444-4000000002i2−2i22i2−2i2−2i22i2−2i22i2000000−2222−22220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ6244-4-4-444-400000000−2i22i2−2i22i22i2−2i22i2−2i200000022−2222−220000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ6344-4-4-444-400000000−2i22i2−2i22i22i2−2i22i2−2i2000000−2222−222200002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ644-44-44-44-440-40-40402i22i2−2i2−2i22i22i2−2i2−2i200−2i22i2−2i22i200000000000000000000000000000000000000000000
χ654-44-44-44-440-40-4040−2i2−2i22i22i2−2i2−2i22i22i2002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ664-44-4-44-44-4-444-4-44400000000-44000000000000000000000000000000000000000000000000
χ674-4-4444-4-40000000022−22−222222−22−22220000002i2−2i2−2i22i20000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ684-4-4444-4-40000000022−22−222222−22−2222000000−2i22i22i2−2i200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ694-4-4444-4-400000000−222222−22−222222−220000002i2−2i2−2i22i200002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ704-4-4444-4-400000000−222222−22−222222−22000000−2i22i22i2−2i20000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ714-4-44-4-44404040-40-400000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000
χ724-4-44-4-44404040-40-40000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000
χ734-4-44-4-4440-40-404044-4-44-444-400000000000000000000000000000000000000000000000000
χ744-4-44-4-4440-40-40404-444-44-4-4400000000000000000000000000000000000000000000000000

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