Finite Group Databasebeta

← Group #315192

Character table — Group #315192

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444448888888844888888888888888888884444444488888888444488882444
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
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-11-11-1
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-11-11
χ111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1-11-11
χ121111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-1111-11-1
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11-11-1-1-1111-1-11
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11-1111-1-1-111-1
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111-11-1-1-111-111-1
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-11-1111-1-11-1-11
χ17222222222-2-22-2-22222222222-2-200000000-2-2-2-200000000000000000000000022-2-200000000
χ18222222222-2-22-2-22222222222-2-200000000-2-2-2-2000000000000000000000000-2-22200000000
χ19222222222-2-22-2-222-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000002-2-2200000000
χ20222222222-2-22-2-222-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000-222-200000000
χ2122222222-222-222-2-200000000-2-22222-2-2-2-200000000000022-2-222-2-200000000000000000000
χ2222222222-222-222-2-200000000-2-22222-2-2-2-2000000000000-2-222-2-22200000000000000000000
χ2322222222-222-222-2-200000000-2-2-2-2-2-2222200000000000022-2-2-2-22200000000000000000000
χ2422222222-222-222-2-200000000-2-2-2-2-2-22222000000000000-2-22222-2-200000000000000000000
χ2522-22-2-22-202-202-200i2i2i2i2−i2−i2−i2−i20000002i2i−2i−2ii2i2−i2−i22222−2−2−2−2002-22i−2i0022−2−2i2i2−i2−i2000000000000
χ2622-22-2-22-202-202-200i2i2i2i2−i2−i2−i2−i20000002i2i−2i−2ii2i2−i2−i22222−2−2−2−200-22−2i2i00−2−222−i2−i2i2i2000000000000
χ2722-22-2-22-202-202-200i2i2i2i2−i2−i2−i2−i2000000−2i−2i2i2ii2i2−i2−i2−2−2−2−22222002-2−2i2i00−2−222i2i2−i2−i2000000000000
χ2822-22-2-22-202-202-200i2i2i2i2−i2−i2−i2−i2000000−2i−2i2i2ii2i2−i2−i2−2−2−2−2222200-222i−2i0022−2−2−i2−i2i2i2000000000000
χ2922-22-2-22-202-202-200−i2−i2−i2−i2i2i2i2i20000002i2i−2i−2i−i2−i2i2i2−2−2−2−22222002-22i−2i00−2−222−i2−i2i2i2000000000000
χ3022-22-2-22-202-202-200−i2−i2−i2−i2i2i2i2i20000002i2i−2i−2i−i2−i2i2i2−2−2−2−2222200-22−2i2i0022−2−2i2i2−i2−i2000000000000
χ3122-22-2-22-202-202-200−i2−i2−i2−i2i2i2i2i2000000−2i−2i2i2i−i2−i2i2i22222−2−2−2−2002-2−2i2i0022−2−2−i2−i2i2i2000000000000
χ3222-22-2-22-202-202-200−i2−i2−i2−i2i2i2i2i2000000−2i−2i2i2i−i2−i2i2i22222−2−2−2−200-222i−2i00−2−222i2i2−i2−i2000000000000
χ332-222-2-2-220-2202-200i2i2−i2−i2i2i2−i2−i20000002-22-2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i22i−2i00002i−2i2−22−22−22−2000000000000
χ342-222-2-2-220-2202-200i2i2−i2−i2i2i2−i2−i20000002-22-2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2−2i2i0000−2i2i−22−22−22−22000000000000
χ352-222-2-2-220-2202-200i2i2−i2−i2i2i2−i2−i2000000-22-22i2−i2i2−i2−i2−i2i2i2−i2−i2i2i22i−2i0000−2i2i−22−222−22−2000000000000
χ362-222-2-2-220-2202-200i2i2−i2−i2i2i2−i2−i2000000-22-22i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2−2i2i00002i−2i2−22−2−22−22000000000000
χ372-222-2-2-220-2202-200−i2−i2i2i2−i2−i2i2i20000002-22-2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i22i−2i00002i−2i−22−22−22−22000000000000
χ382-222-2-2-220-2202-200−i2−i2i2i2−i2−i2i2i20000002-22-2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2−2i2i0000−2i2i2−22−22−22−2000000000000
χ392-222-2-2-220-2202-200−i2−i2i2i2−i2−i2i2i2000000-22-22−i2i2−i2i2i2i2−i2−i2i2i2−i2−i22i−2i0000−2i2i2−22−2−22−22000000000000
χ402-222-2-2-220-2202-200−i2−i2i2i2−i2−i2i2i2000000-22-22−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2−2i2i00002i−2i−22−222−22−2000000000000
χ412-2-2222-2-22-2-2-2222-200000000-222i2i−2i−2i2i−2i−2i2i000000000000000000002-2-222i−2i−2i2i000000000000
χ422-2-2222-2-22-2-2-2222-200000000-222i2i−2i−2i2i−2i−2i2i00000000000000000000-222-2−2i2i2i−2i000000000000
χ432-2-2222-2-22-2-2-2222-200000000-22−2i−2i2i2i−2i2i2i−2i000000000000000000002-2-22−2i2i2i−2i000000000000
χ442-2-2222-2-22-2-2-2222-200000000-22−2i−2i2i2i−2i2i2i−2i00000000000000000000-222-22i−2i−2i2i000000000000
χ452-2-2222-2-2-2222-2-2-2222-2-2-2-222-2200000000-222-200000000000000000000000000002i−2i2i−2i0000
χ462-2-2222-2-2-2222-2-2-2222-2-2-2-222-2200000000-222-20000000000000000000000000000−2i2i−2i2i0000
χ472-2-2222-2-2-2222-2-2-22-2-22222-2-2-22000000002-2-2200000000000000000000000000002i−2i−2i2i0000
χ482-2-2222-2-2-2222-2-2-22-2-22222-2-2-22000000002-2-220000000000000000000000000000−2i2i2i−2i0000
χ492-2-2222-2-2-2-2-2222-2222-2-2-2-2222-22i2i−2i−2i−2i2i2i−2i2-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ502-2-2222-2-2-2-2-2222-2222-2-2-2-2222-2−2i−2i2i2i2i−2i−2i2i2-2-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ512-2-2222-2-2-2-2-2222-22-2-22222-2-22-22i2i−2i−2i−2i2i2i−2i-222-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ522-2-2222-2-2-2-2-2222-22-2-22222-2-22-2−2i−2i2i2i2i−2i−2i2i-222-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ5344444444-4-4-4-4-4-4-4-40000000044000000000000000000000000000000000000000000000000
χ54444-4-44-4-4400400-4-44-44-44-44-400000000000000000000000000000000000000000000000000
χ55444-4-44-4-4400400-4-4-44-44-44-4400000000000000000000000000000000000000000000000000
χ56444-4-44-4-4-400-4004400000000000000000000002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000
χ57444-4-44-4-4-400-400440000000000000000000000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000
χ5844-44-4-44-40-440-44002i22i22i22i2−2i2−2i2−2i2−2i20000000000−2i2−2i22i22i2000000000000000000000000000000000000
χ5944-44-4-44-40-440-4400−2i2−2i2−2i2−2i22i22i22i22i200000000002i22i2−2i2−2i2000000000000000000000000000000000000
χ6044-4-44-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i20022−2222−22000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ6144-4-44-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i200−2222−222200000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ6244-4-44-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i20022−2222−2200000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ6344-4-44-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i200−2222−2222000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ644-444-4-4-4404-40-44002i22i2−2i2−2i22i22i2−2i2−2i20000000000−2i22i2−2i22i2000000000000000000000000000000000000
χ654-444-4-4-4404-40-4400−2i2−2i22i22i2−2i2−2i22i22i200000000002i2−2i22i2−2i2000000000000000000000000000000000000
χ664-44-44-44-4000000002i2−2i2−2i22i22i2−2i2−2i22i2002i2−2i2−2i22i200000000-222-2-222-20000000000000000000000000000
χ674-44-44-44-4000000002i2−2i2−2i22i22i2−2i2−2i22i200−2i22i22i2−2i2000000002-2-222-2-220000000000000000000000000000
χ684-44-44-44-400000000−2i22i22i2−2i2−2i22i22i2−2i2002i2−2i2−2i22i2000000002-2-222-2-220000000000000000000000000000
χ694-44-44-44-400000000−2i22i22i2−2i2−2i22i22i2−2i200−2i22i22i2−2i200000000-222-2-222-20000000000000000000000000000
χ704-4-4444-4-4444-4-4-44-4000000004-4000000000000000000000000000000000000000000000000
χ714-4-4-4-4444400-400-44000000000000000000000022−22−2222−222222−220000000000000000000000000000
χ724-4-4-4-4444400-400-440000000000000000000000−222222−2222−22−22220000000000000000000000000000
χ734-4-4-4-4444-4004004-44-4-44-444-400000000000000000000000000000000000000000000000000
χ744-4-4-4-4444-4004004-4-444-44-4-4400000000000000000000000000000000000000000000000000

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