Finite Group Databasebeta

← Group #247182

Character table — Group #247182

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444224444444444444444444888888888888888822444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111111-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ7111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1
χ91111111111-1-1-1-1111111-1-1-1-111111111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-11111-1-111-1-1
χ101111111111-1-1-1-1111111-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-111-1-111-1-111
χ111111111111-1-1-1-1111111-1-1-1-1111111-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-11-1-111-1-1-1-111
χ121111111111-1-1-1-1111111-1-1-1-1111111-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-11-1-1-1-11111-1-1
χ131111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-11111-1-11111-1-1-1-11111-1-1-1-1111-1-1-1-1-111-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111111-1-1-111-1-111-1-1
χ151111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1111-1-11111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-111111-1-1-1-111
χ1722222222222222-2-222-2-222-2-20000-2-222-200000022000000000000000000-2-20000000000
χ1822222222222222-2-222-2-222-2-20000-2-2-2-2-2000000-2-2000000000000000000220000000000
χ192222222222-2-2-2-2-2-222-2-2-2-2220000-2-2222000000-2-2000000000000000000-220000000000
χ202222222222-2-2-2-2-2-222-2-2-2-2220000-2-2-2-22000000220000000000000000002-20000000000
χ2122222222-2-2222222-2-222-2-2222222-2-200-2-2-222-2-200000000000000000000000000000000
χ2222222222-2-2222222-2-222-2-222-2-2-2-2-2-200-222-2-22200000000000000000000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-20000220020000000000000000000000002-2002-200000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-2000022002000000000000000000000000-2200-2200000000
χ2522222222-2-2-2-2-2-222-2-22222-2-22222-2-2002-2-2-2-22200000000000000000000000000000000
χ2622222222-2-2-2-2-2-222-2-22222-2-2-2-2-2-2-2-20022222-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-20000000000000000000000002-200-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200002200-2000000000000000000000000-22002-200000000
χ292-222-2-22-2002i2i−2i−2i2-2002-2002i−2i2i2i−2i−2i00000002-2000000000000i2i2−i2−i222−2−200000000002−2i2−i2
χ302-222-2-22-2002i2i−2i−2i2-2002-2002i−2i2i2i−2i−2i00000002-2000000000000−i2−i2i2i2−2−2220000000000−22−i2i2
χ312-222-2-22-2002i2i−2i−2i2-2002-2002i−2i−2i−2i2i2i0000000-22000000000000i2i2−i2−i222−2−20000000000−22−i2i2
χ322-222-2-22-2002i2i−2i−2i2-2002-2002i−2i−2i−2i2i2i0000000-22000000000000−i2−i2i2i2−2−22200000000002−2i2−i2
χ332-222-2-22-200−2i−2i2i2i2-2002-200−2i2i2i2i−2i−2i0000000-22000000000000i2i2−i2−i2−2−22200000000002−2−i2i2
χ342-222-2-22-200−2i−2i2i2i2-2002-200−2i2i2i2i−2i−2i0000000-22000000000000−i2−i2i2i222−2−20000000000−22i2−i2
χ352-222-2-22-200−2i−2i2i2i2-2002-200−2i2i−2i−2i2i2i00000002-2000000000000i2i2−i2−i2−2−2220000000000−22i2−i2
χ362-222-2-22-200−2i−2i2i2i2-2002-200−2i2i−2i−2i2i2i00000002-2000000000000−i2−i2i2i222−2−200000000002−2−i2i2
χ372-22-222-2-2-2-22-22-20022002-2000000002i−2i00000002i−2i22−2−222−2−2i2−i2i2−i2i2−i2i2−i200000000000000
χ382-22-222-2-2-2-22-22-20022002-2000000002i−2i00000002i−2i−2−222−2−222−i2i2−i2i2−i2i2−i2i200000000000000
χ392-22-222-2-2-2-22-22-20022002-200000000−2i2i0000000−2i2i22−2−222−2−2−i2i2−i2i2−i2i2−i2i200000000000000
χ402-22-222-2-2-2-22-22-20022002-200000000−2i2i0000000−2i2i−2−222−2−222i2−i2i2−i2i2−i2i2−i200000000000000
χ412-22-222-2-2-2-2-22-22002200-22000000002i−2i0000000−2i2i22−2−2−2−222i2−i2i2−i2−i2i2−i2i200000000000000
χ422-22-222-2-2-2-2-22-22002200-22000000002i−2i0000000−2i2i−2−22222−2−2−i2i2−i2i2i2−i2i2−i200000000000000
χ432-22-222-2-2-2-2-22-22002200-2200000000−2i2i00000002i−2i22−2−2−2−222−i2i2−i2i2i2−i2i2−i200000000000000
χ442-22-222-2-2-2-2-22-22002200-2200000000−2i2i00000002i−2i−2−22222−2−2i2−i2i2−i2−i2i2−i2i200000000000000
χ452-2-2-22-2222-20000-2-22-22200002-22-22-20002-200000000002-22-200000000000000002-20000
χ462-2-2-22-2222-20000-2-22-22200002-22-22-20002-20000000000-22-220000000000000000-220000
χ472-2-2-22-2222-20000-2-22-2220000-22-222-2000-2200000000002-22-20000000000000000-220000
χ482-2-2-22-2222-20000-2-22-2220000-22-222-2000-220000000000-22-2200000000000000002-20000
χ492-2-2-22-222-220000-2-2-222200002-22-2-22000-220000002-22-20000000000000000002-2000000
χ502-2-2-22-222-220000-2-2-222200002-22-2-22000-22000000-22-22000000000000000000-22000000
χ512-2-2-22-222-220000-2-2-22220000-22-22-220002-20000002-22-2000000000000000000-22000000
χ522-2-2-22-222-220000-2-2-22220000-22-22-220002-2000000-22-220000000000000000002-2000000
χ53444-4-4-4-44004i−4i−4i4i000000000000000000000000000000000002-2-22−2i2i2i−2i00000000000000
χ54444-4-4-4-44004i−4i−4i4i00000000000000000000000000000000000-222-22i−2i−2i2i00000000000000
χ55444-4-4-4-4400−4i4i4i−4i000000000000000000000000000000000002-2-222i−2i−2i2i00000000000000
χ56444-4-4-4-4400−4i4i4i−4i00000000000000000000000000000000000-222-2−2i2i2i−2i00000000000000
χ5744-444-4-4-44-4000000-440000000000000000000000022−22−222200000000000000000000000000
χ5844-444-4-4-44-4000000-4400000000000000000000000−222222−2200000000000000000000000000
χ5944-444-4-4-4-440000004-400000000000000000000000000022−22−22220000000000000000000000
χ6044-444-4-4-4-440000004-4000000000000000000000000000−222222−220000000000000000000000
χ6144-4-4-444-40000004-400-44000000000000000004i−4i00000000000000000000000000000000
χ6244-4-4-444-40000004-400-4400000000000000000−4i4i00000000000000000000000000000000
χ6344-4-4-444-4000000-44004-400004i−4i−4i4i0000000000000000000000000000000000000000000
χ6444-4-4-444-4000000-44004-40000−4i4i4i−4i0000000000000000000000000000000000000000000
χ654-444-4-44-4004i4i−4i−4i-4400-4400−4i4i00000000000000000000000000000000000000000000000
χ664-444-4-44-400−4i−4i4i4i-4400-44004i−4i00000000000000000000000000000000000000000000000
χ674-44-444-4-4444-44-400-4-400-440000000000000000000000000000000000000000000000000
χ684-44-444-4-444-44-4400-4-4004-40000000000000000000000000000000000000000000000000
χ694-4-4-44-4444-40000444-4-4-400000000-4400000000000000000000000000000000000000000
χ704-4-4-44-444-44000044-44-4-4000000004-400000000000000000000000000000000000000000
χ718-8-88-88-88000000000000000000000000000000000000000000000000000000000000000

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