Finite Group Databasebeta

← Group #348995

Character table — Group #348995

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
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1
χ91111111111111111-1-1-1-1-1-111111-1-1-1-1111-1-111-1-111-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-1-1-111111-1-1-1-1111-1-111-1-111-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-111111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-111111111-1-1-1-111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-111111-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-11111-1-11-1
χ131111111111111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-11
χ141111111111111111-1-1-1-1-1-11-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1
χ151111111111111111-1-1-1-1-1-11-1-1-1-111111-1-111-1-111-1-111-11111-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-1-1-11-1-1-1-111111-1-111-1-111-1-111-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ1722222222222-2-2-22-222-2-2-2-2-22222-2-2-2-2-20000-2-2220000200000000000000000000000000
χ1822222222222-2-2-22-222-2-2-2-2-2-2-2-2-22222-2000022-2-20000200000000000000000000000000
χ1922222222222-2-2-22-2-2-22222-222222222-20000-2-2-2-20000-200000000000000000000000000
χ2022222222222-2-2-22-2-2-22222-2-2-2-2-2-2-2-2-2-2000022220000-200000000000000000000000000
χ2122222222-2-2-2222-222222-2-2-200000000-222-2-20000-2-222-200000000000000000000000000
χ2222222222-2-2-2222-222222-2-2-200000000-2-2-222000022-2-2-200000000000000000000000000
χ2322222222-2-2-2222-22-2-2-2-222-200000000-222220000-2-2-2-2200000000000000000000000000
χ2422222222-2-2-2222-22-2-2-2-222-200000000-2-2-2-2-200002222200000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2222000000002000000000000-222-2-222-2-2000000000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-2222000000002000000000000-2-2-222-2-222000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-22000000002000000000000222-2-2-2-222000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-220000000020000000000002-2-22222-2-2000000000000000000
χ292-2222-2-2-22-2-200020002-22-202i2i−2i−2i2i2i−2i−2i000000000000000000000022−2−222−2−2i2−i2i2−i2000000
χ302-2222-2-2-22-2-200020002-22-202i2i−2i−2i2i2i−2i−2i0000000000000000000000−2−222−2−222−i2i2−i2i2000000
χ312-2222-2-2-22-2-200020002-22-20−2i−2i2i2i−2i−2i2i2i000000000000000000000022−2−222−2−2−i2i2−i2i2000000
χ322-2222-2-2-22-2-200020002-22-20−2i−2i2i2i−2i−2i2i2i0000000000000000000000−2−222−2−222i2−i2i2−i2000000
χ332-2222-2-2-22-2-20002000-22-2202i2i−2i−2i−2i−2i2i2i000000000000000000000022−2−2−2−222i2−i2−i2i2000000
χ342-2222-2-2-22-2-20002000-22-2202i2i−2i−2i−2i−2i2i2i0000000000000000000000−2−22222−2−2−i2i2i2−i2000000
χ352-2222-2-2-22-2-20002000-22-220−2i−2i2i2i2i2i−2i−2i000000000000000000000022−2−2−2−222−i2i2i2−i2000000
χ362-2222-2-2-22-2-20002000-22-220−2i−2i2i2i2i2i−2i−2i0000000000000000000000−2−22222−2−2i2−i2−i2i2000000
χ372-2-22-22-2222-222-2-2-2000000-22i−2i2i−2i00002002i−2i2i−2i00002i−2i000002-22-2000000000000000000
χ382-2-22-22-2222-222-2-2-2000000-22i−2i2i−2i0000200−2i2i2i−2i0000−2i2i00000-22-22000000000000000000
χ392-2-22-22-2222-222-2-2-2000000-2−2i2i−2i2i00002002i−2i−2i2i00002i−2i00000-22-22000000000000000000
χ402-2-22-22-2222-222-2-2-2000000-2−2i2i−2i2i0000200−2i2i−2i2i0000−2i2i000002-22-2000000000000000000
χ412-2-22-22-2222-2-2-22-2200000022i−2i2i−2i0000-22-200−2i2i002-20002i−2i2i−2i0000000000000000000000
χ422-2-22-22-2222-2-2-22-2200000022i−2i2i−2i0000-2-2200−2i2i00-22000−2i2i−2i2i0000000000000000000000
χ432-2-22-22-2222-2-2-22-220000002−2i2i−2i2i0000-22-2002i−2i002-2000−2i2i−2i2i0000000000000000000000
χ442-2-22-22-2222-2-2-22-220000002−2i2i−2i2i0000-2-22002i−2i00-220002i−2i2i−2i0000000000000000000000
χ452-2-22-22-22-2-2222-22-2000000200002-22-2-2002i−2i002-200−2i2i02i−2i−2i2i0000000000000000000000
χ462-2-22-22-22-2-2222-22-2000000200002-22-2-200−2i2i002-2002i−2i0−2i2i2i−2i0000000000000000000000
χ472-2-22-22-22-2-2222-22-200000020000-22-22-2002i−2i00-2200−2i2i0−2i2i2i−2i0000000000000000000000
χ482-2-22-22-22-2-2222-22-200000020000-22-22-200−2i2i00-22002i−2i02i−2i−2i2i0000000000000000000000
χ492-2-22-22-22-2-22-2-2222000000-200002-22-222-20000-22-2200000002-2-22000000000000000000
χ502-2-22-22-22-2-22-2-2222000000-200002-22-22-220000-222-20000000-222-2000000000000000000
χ512-2-22-22-22-2-22-2-2222000000-20000-22-2222-200002-2-220000000-222-2000000000000000000
χ522-2-22-22-22-2-22-2-2222000000-20000-22-222-2200002-22-200000002-2-22000000000000000000
χ53444-4-4-4-440004-440-4000000000000000000000000000000000000022−2222−2200000000000000
χ54444-4-4-4-440004-440-40000000000000000000000000000000000000−2222−222200000000000000
χ55444-4-4-4-44000-44-404000000000000000000000000000000000000000002i2−2i22i2−2i20000000000
χ56444-4-4-4-44000-44-40400000000000000000000000000000000000000000−2i22i2−2i22i20000000000
χ5744-44-4-44-44-44000-4000000004-4-4400000000000000000000000000000000000000000000
χ5844-44-4-44-44-44000-400000000-444-400000000000000000000000000000000000000000000
χ5944-44-4-44-4-44-400040000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ6044-44-4-44-4-44-40004000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ614-4444-4-4-4-444000-40004-4-440000000000000000000000000000000000000000000000000
χ624-4444-4-4-4-444000-4000-444-40000000000000000000000000000000000000000000000000
χ634-44-4-444-4000000004i−4i000000000000000000000000000000000002-2-222i−2i−2i2i0000000000
χ644-44-4-444-4000000004i−4i00000000000000000000000000000000000-222-2−2i2i2i−2i0000000000
χ654-44-4-444-400000000−4i4i000000000000000000000000000000000002-2-22−2i2i2i−2i0000000000
χ664-44-4-444-400000000−4i4i00000000000000000000000000000000000-222-22i−2i−2i2i0000000000
χ674-4-4-44-4440004-4-40400000000000000000000000000000000000000000000000000022−2200
χ684-4-4-44-4440004-4-404000000000000000000000000000000000000000000000000000−222200
χ694-4-4-44-444000-4440-400000000000000000000000000000000000000000000000002i2−2i20000
χ704-4-4-44-444000-4440-40000000000000000000000000000000000000000000000000−2i22i20000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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