Finite Group Databasebeta

← Group #255469

Character table — Group #255469

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444444444444444888888888888888844444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1
χ3111111111111111111111111111111-1-1111-1-1111111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111-1-111-1-1-1-11111111111111111-1-11-1-1-1-11-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-11111
χ71111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111
χ81111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111-111-1-1-1-1
χ91111111111-1-1-1-1111111-1-11111-1-11111-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-111111-1-1
χ101111111111-1-1-1-1111111-1-11111-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-111
χ111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-111
χ121111111111-1-1-1-1111111-1-11111-1-111-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111111-1-1-111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-111-1-11-1-111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-11-1-111-11111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-111111111-1-1-1-1111-1-1-1-1-111-1-111
χ1722222222222222-2-222-2-2220000-2-2-2-222-200220000000000000000000000-20000-2000000
χ1822222222222222-2-222-2-2220000-2-2-2-2-2-2-200-2-20000000000000000000000200002000000
χ192222222222-2-2-2-2-2-222-2-2-2-2000022-2-222200-2-2000000000000000000000020000-2000000
χ202222222222-2-2-2-2-2-222-2-2-2-2000022-2-2-2-2200220000000000000000000000-200002000000
χ2122222222-2-2222222-2-222-2-2222222-2-200-2-2-200-2-222000000000000000000000000000000
χ2222222222-2-2222222-2-222-2-2-2-2-2-222-2-200-2220022-2-2000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-20000-2-2220020000000000000000000000000002-20002-20000
χ2422222222-2-22222-2-2-2-2-2-2-2-20000-2-222002000000000000000000000000000-22000-220000
χ2522222222-2-2-2-2-2-222-2-222222222-2-2-2-20022200-2-2-2-2000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2-2-2002-2-2002222000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200-20000000000000000000000000002-2000-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200-2000000000000000000000000000-220002-20000
χ292-2222-2-2-2-2-222-2-20022002-2000000002-20002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000
χ302-2222-2-2-2-2-222-2-20022002-2000000002-20002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000
χ312-2222-2-2-2-2-222-2-20022002-200000000-22000-220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000
χ322-2222-2-2-2-2-222-2-20022002-200000000-22000-220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000
χ332-2222-2-2-2-2-2-2-222002200-22000000002-2000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ342-2222-2-2-2-2-2-2-222002200-22000000002-2000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ352-2222-2-2-2-2-2-2-222002200-2200000000-220002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ362-2222-2-2-2-2-2-2-222002200-2200000000-220002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ372-22-2-22-222-20000222-2-2-20022-2-2002-200000002-20000002i−2i2i−2i00000000000002i−2i0000000
χ382-22-2-22-222-20000222-2-2-20022-2-2002-200000002-2000000−2i2i−2i2i0000000000000−2i2i0000000
χ392-22-2-22-222-20000222-2-2-200-2-222002-20000000-220000002i−2i2i−2i0000000000000−2i2i0000000
χ402-22-2-22-222-20000222-2-2-200-2-222002-20000000-22000000−2i2i−2i2i00000000000002i−2i0000000
χ412-22-2-22-22-22000022-22-2-20022-2-200-220000000-22002i−2i2i−2i0000000000002i−2i000000000000
χ422-22-2-22-22-22000022-22-2-20022-2-200-220000000-2200−2i2i−2i2i000000000000−2i2i000000000000
χ432-22-2-22-22-22000022-22-2-200-2-22200-2200000002-2002i−2i2i−2i000000000000−2i2i000000000000
χ442-22-2-22-22-22000022-22-2-200-2-22200-2200000002-200−2i2i−2i2i0000000000002i−2i000000000000
χ452-2-2-2222-2002i−2i2i−2i2-2002-2002-22-22i−2i000000000002i−2i000000002−22−2i2−i2i2−i200000000002−2i2−i2
χ462-2-2-2222-2002i−2i2i−2i2-2002-2002-22-22i−2i000000000002i−2i00000000−22−22−i2i2−i2i20000000000−22−i2i2
χ472-2-2-2222-2002i−2i2i−2i2-2002-200-22-222i−2i00000000000−2i2i000000002−22−2i2−i2i2−i20000000000−22−i2i2
χ482-2-2-2222-2002i−2i2i−2i2-2002-200-22-222i−2i00000000000−2i2i00000000−22−22−i2i2−i2i200000000002−2i2−i2
χ492-2-2-2222-200−2i2i−2i2i2-2002-2002-22-2−2i2i00000000000−2i2i000000002−22−2−i2i2−i2i200000000002−2−i2i2
χ502-2-2-2222-200−2i2i−2i2i2-2002-2002-22-2−2i2i00000000000−2i2i00000000−22−22i2−i2i2−i20000000000−22i2−i2
χ512-2-2-2222-200−2i2i−2i2i2-2002-200-22-22−2i2i000000000002i−2i000000002−22−2−i2i2−i2i20000000000−22i2−i2
χ522-2-2-2222-200−2i2i−2i2i2-2002-200-22-22−2i2i000000000002i−2i00000000−22−22i2−i2i2−i200000000002−2−i2i2
χ53444-4-4-44-44-4000000-440000000000000000000000022−22−222200000000000000000000000000
χ54444-4-4-44-44-4000000-4400000000000000000000000−222222−2200000000000000000000000000
χ55444-4-4-44-4-440000004-400000000000000000000000000022−22−22220000000000000000000000
χ56444-4-4-44-4-440000004-4000000000000000000000000000−222222−220000000000000000000000
χ5744-44-44-4-40000004-400-44004-4-44000000000000000000000000000000000000000000000
χ5844-44-44-4-40000004-400-4400-444-4000000000000000000000000000000000000000000000
χ5944-44-44-4-4000000-44004-400000000000004-4000000000000000000000000000000000000
χ6044-44-44-4-4000000-44004-40000000000000-44000000000000000000000000000000000000
χ6144-4-44-4-44004i−4i−4i4i000000000000000000000000000000000002i−2i−2i2i-222-200000000000000
χ6244-4-44-4-44004i−4i−4i4i00000000000000000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ6344-4-44-4-4400−4i4i4i−4i000000000000000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ6444-4-44-4-4400−4i4i4i−4i00000000000000000000000000000000000−2i2i2i−2i-222-200000000000000
χ654-4444-4-4-44444-4-400-4-400-440000000000000000000000000000000000000000000000000
χ664-4444-4-4-444-4-44400-4-4004-40000000000000000000000000000000000000000000000000
χ674-44-4-44-444-40000-4-44-44400000000-4400000000000000000000000000000000000000000
χ684-44-4-44-44-440000-4-4-4444000000004-400000000000000000000000000000000000000000
χ694-4-4-4444-4004i−4i4i−4i-4400-44000000−4i4i0000000000000000000000000000000000000000000
χ704-4-4-4444-400−4i4i−4i4i-4400-440000004i−4i0000000000000000000000000000000000000000000
χ718-8-88-8-888000000000000000000000000000000000000000000000000000000000000000

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