Finite Group Databasebeta

← Group #348899

Character table — Group #348899

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444448888888888888888888888888888816161616161616163232
order12222222444444444444444444444444224444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-111111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ1722222222222-2-2-2-2222-2-2-2-22222-2-2-2-2-2-20000-2-2220000000020000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-2-2-2-22222-2000022-2-20000000020000000000000000000000
χ1922222222222-2-2-2-22-2-222222222-22222-20000-2-2-2-200000000-20000000000000000000000
χ2022222222222-2-2-2-22-2-22222-2-2-2-2-2-2-2-2-2-20000222200000000-20000000000000000000000
χ2122222222-2-2-22222-22222-2-20000-20000-222-2-20000-2-2220000-20000000000000000000000
χ2222222222-2-2-22222-22222-2-20000-20000-2-2-222000022-2-20000-20000000000000000000000
χ2322222222-2-2-22222-2-2-2-2-2220000-20000-222220000-2-2-2-2000020000000000000000000000
χ2422222222-2-2-22222-2-2-2-2-2220000-20000-2-2-2-2-200002222000020000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222000020000200000000000022-2-2-222-2-2000000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2220000200002000000000000-2-222-2-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-2000020000200000000000022-2-22-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-20000200002000000000000-2-222222-2-2000000000000000000
χ292-2222-2-2-22-2-200002002-22-22i2i−2i−2i02i2i−2i−2i000000000000000000000022−2−222−2−2i2−i2i2−i2000000
χ302-2222-2-2-22-2-200002002-22-22i2i−2i−2i02i2i−2i−2i0000000000000000000000−2−222−2−222−i2i2−i2i2000000
χ312-2222-2-2-22-2-200002002-22-2−2i−2i2i2i0−2i−2i2i2i000000000000000000000022−2−222−2−2−i2i2−i2i2000000
χ322-2222-2-2-22-2-200002002-22-2−2i−2i2i2i0−2i−2i2i2i0000000000000000000000−2−222−2−222i2−i2i2−i2000000
χ332-2222-2-2-22-2-20000200-22-222i2i−2i−2i0−2i−2i2i2i000000000000000000000022−2−2−2−222i2−i2−i2i2000000
χ342-2222-2-2-22-2-20000200-22-222i2i−2i−2i0−2i−2i2i2i0000000000000000000000−2−22222−2−2−i2i2i2−i2000000
χ352-2222-2-2-22-2-20000200-22-22−2i−2i2i2i02i2i−2i−2i000000000000000000000022−2−2−2−222−i2i2i2−i2000000
χ362-2222-2-2-22-2-20000200-22-22−2i−2i2i2i02i2i−2i−2i0000000000000000000000−2−22222−2−2i2−i2−i2i2000000
χ372-2-22-22-2222-222-2-2-20000002i−2i2i−2i-200002002i−2i2i−2i00002i−2i2-22-200000000000000000000000
χ382-2-22-22-2222-222-2-2-20000002i−2i2i−2i-20000200−2i2i2i−2i0000−2i2i-22-2200000000000000000000000
χ392-2-22-22-2222-222-2-2-2000000−2i2i−2i2i-200002002i−2i−2i2i00002i−2i-22-2200000000000000000000000
χ402-2-22-22-2222-222-2-2-2000000−2i2i−2i2i-20000200−2i2i−2i2i0000−2i2i2-22-200000000000000000000000
χ412-2-22-22-2222-2-2-222-20000002i−2i2i−2i20000-22-200−2i2i002-200000002i−2i2i−2i000000000000000000
χ422-2-22-22-2222-2-2-222-20000002i−2i2i−2i20000-2-2200−2i2i00-220000000−2i2i−2i2i000000000000000000
χ432-2-22-22-2222-2-2-222-2000000−2i2i−2i2i20000-22-2002i−2i002-20000000−2i2i−2i2i000000000000000000
χ442-2-22-22-2222-2-2-222-2000000−2i2i−2i2i20000-2-22002i−2i00-2200000002i−2i2i−2i000000000000000000
χ452-2-22-22-22-2-2222-2-22000000000022-22-2-2002i−2i002-200−2i2i000002i−2i−2i2i000000000000000000
χ462-2-22-22-22-2-2222-2-22000000000022-22-2-200−2i2i002-2002i−2i00000−2i2i2i−2i000000000000000000
χ472-2-22-22-22-2-2222-2-2200000000002-22-22-2002i−2i00-2200−2i2i00000−2i2i2i−2i000000000000000000
χ482-2-22-22-22-2-2222-2-2200000000002-22-22-200−2i2i00-22002i−2i000002i−2i−2i2i000000000000000000
χ492-2-22-22-22-2-22-2-22220000000000-22-22-222-20000-22-22002-2-2200000000000000000000000
χ502-2-22-22-22-2-22-2-22220000000000-22-22-22-220000-222-200-222-200000000000000000000000
χ512-2-22-22-22-2-22-2-22220000000000-2-22-2222-200002-2-2200-222-200000000000000000000000
χ522-2-22-22-22-2-22-2-22220000000000-2-22-222-2200002-22-2002-2-2200000000000000000000000
χ53444-4-44-4-40004-44-4000000000000000000000000000000000000000000000000000022−2200
χ54444-4-44-4-40004-44-40000000000000000000000000000000000000000000000000000−222200
χ55444-4-44-4-4000-44-440000000000000000000000000000000000000000000000000022−220000
χ56444-4-44-4-4000-44-4400000000000000000000000000000000000000000000000000−22220000
χ5744-44-4-44-44-440000-40000004-4-44000000000000000000000000000000000000000000000
χ5844-44-4-44-44-440000-4000000-444-4000000000000000000000000000000000000000000000
χ5944-44-4-44-4-44-400004000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ6044-44-4-44-4-44-40000400000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ6144-4-44-4-44000000004-4000000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000
χ6244-4-44-4-44000000004-400000000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000
χ6344-4-44-4-4400000000-44000000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000
χ6444-4-44-4-4400000000-4400000000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000
χ654-4444-4-4-4-4440000-4004-4-440000000000000000000000000000000000000000000000000
χ664-4444-4-4-4-4440000-400-444-40000000000000000000000000000000000000000000000000
χ674-4-4-4444-40004-4-44000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ684-4-4-4444-40004-4-4400000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ694-4-4-4444-4000-444-40000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ704-4-4-4444-4000-444-4000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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