Finite Group Databasebeta

← Group #247153

Character table — Group #247153

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444444444444444444444444888888888888888822222444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1
χ3111111111111111111111111111111-1-11111111-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111-1-1-1-1-1-11111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ71111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-11111-1-1-1-1
χ911111111-1-1-1-111111111-1-11111-1-11111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1111-1-111-1-1
χ1011111111-1-1-1-111111111-1-11111-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-111111-1-1-1-111
χ1111111111-1-1-1-111111111-1-11111-1-111-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111111-1-1-1-1-111-1-111
χ1211111111-1-1-1-111111111-1-11111-1-111-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-11-1-111-1-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1111-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1-11-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-1-111111111-1-1-1-1-1-1-1-111111-1-111-111-1-111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-111111111-1-1-1-1111-1-1-111-1-1-1-111
χ1722222222222222-2-2-222-2220000-2-2-2-222-2000000220000000000000000-20000-200000000
χ1822222222222222-2-2-222-2220000-2-2-2-2-2-2-2000000-2-2000000000000000020000200000000
χ19222222222222-2-2222-2-22-2-2222222-2-200-222-2-2-2-200000000000000000000000000000000
χ20222222222222-2-2222-2-22-2-2-2-2-2-222-2-200-2-2-2222200000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-20000-2-2220020000000000000000000000000000002-22-20000
χ22222222222222-2-2-2-2-2-2-2-2-2-20000-2-222002000000000000000000000000000000-22-220000
χ2322222222-2-2-2-222-2-2-222-2-2-2000022-2-2222000000-2-2000000000000000020000-200000000
χ2422222222-2-2-2-222-2-2-222-2-2-2000022-2-2-2-22000000220000000000000000-20000200000000
χ2522222222-2-2-2-2-2-2222-2-22222222-2-2-2-2002-2-2-2-22200000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-2222-2-2-2-2-2-2-2-20022222-2-200000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200-20000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200-2000000000000000000000000000000-222-20000
χ292-222-2-2-2222-2-20022-200-2002i2i−2i−2i2-2000002i−2i00000000000000i2i2−i2−i2i2i2−i2−i200000000002−22−2
χ302-222-2-2-2222-2-20022-200-2002i2i−2i−2i2-2000002i−2i00000000000000−i2−i2i2i2−i2−i2i2i20000000000−22−22
χ312-222-2-2-2222-2-20022-200-200−2i−2i2i2i2-200000−2i2i00000000000000i2i2−i2−i2i2i2−i2−i20000000000−22−22
χ322-222-2-2-2222-2-20022-200-200−2i−2i2i2i2-200000−2i2i00000000000000−i2−i2i2i2−i2−i2i2i200000000002−22−2
χ332-222-2-2-22-2-2220022-200-2002i2i−2i−2i-2200000−2i2i00000000000000i2i2−i2−i2−i2−i2i2i200000000002−2−22
χ342-222-2-2-22-2-2220022-200-2002i2i−2i−2i-2200000−2i2i00000000000000−i2−i2i2i2i2i2−i2−i20000000000−222−2
χ352-222-2-2-22-2-2220022-200-200−2i−2i2i2i-22000002i−2i00000000000000i2i2−i2−i2−i2−i2i2i20000000000−222−2
χ362-222-2-2-22-2-2220022-200-200−2i−2i2i2i-22000002i−2i00000000000000−i2−i2i2i2i2i2−i2−i200000000002−2−22
χ372-22-222-2-22-22-222000-2-202-2000000002i−2i00000002i−2ii2i2−i2−i2i2i2−i2−i22−22−22−22−200000000000000
χ382-22-222-2-22-22-222000-2-202-2000000002i−2i00000002i−2i−i2−i2i2i2−i2−i2i2i2−22−22−22−2200000000000000
χ392-22-222-2-22-22-222000-2-202-200000000−2i2i0000000−2i2ii2i2−i2−i2i2i2−i2−i2−22−22−22−2200000000000000
χ402-22-222-2-22-22-222000-2-202-200000000−2i2i0000000−2i2i−i2−i2i2i2−i2−i2i2i22−22−22−22−200000000000000
χ412-22-222-2-2-22-2222000-2-20-22000000002i−2i0000000−2i2ii2i2−i2−i2−i2−i2i2i22−22−2−22−2200000000000000
χ422-22-222-2-2-22-2222000-2-20-22000000002i−2i0000000−2i2i−i2−i2i2i2i2i2−i2−i2−22−222−22−200000000000000
χ432-22-222-2-2-22-2222000-2-20-2200000000−2i2i00000002i−2ii2i2−i2−i2−i2−i2i2i2−22−222−22−200000000000000
χ442-22-222-2-2-22-2222000-2-20-2200000000−2i2i00000002i−2i−i2−i2i2i2i2i2−i2−i22−22−2−22−2200000000000000
χ452-2-2-2-222200002-22-2-22-22002-22-2002-2000002-2000000002-22-2000000000002-2000000000
χ462-2-2-2-222200002-22-2-22-22002-22-2002-2000002-200000000-22-2200000000000-22000000000
χ472-2-2-2-222200002-22-2-22-2200-22-22002-200000-22000000002-22-200000000000-22000000000
χ482-2-2-2-222200002-22-2-22-2200-22-22002-200000-2200000000-22-22000000000002-2000000000
χ492-2-2-2-22220000-222-2-2-222002-22-200-2200000-2200002-22-200000000000002-200000000000
χ502-2-2-2-22220000-222-2-2-222002-22-200-2200000-220000-22-220000000000000-2200000000000
χ512-2-2-2-22220000-222-2-2-22200-22-2200-22000002-200002-22-20000000000000-2200000000000
χ522-2-2-2-22220000-222-2-2-22200-22-2200-22000002-20000-22-2200000000000002-200000000000
χ53444-4-4-44-44-4-4400000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ54444-4-4-44-44-4-440000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ55444-4-4-44-4-444-400000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ56444-4-4-44-4-444-40000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ5744-44-44-4-400004-4000-44000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5844-44-44-4-400004-4000-4400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ5944-44-44-4-40000-440004-400000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ6044-44-44-4-40000-440004-40000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ6144-4-44-4-440000004-4400-4004i−4i−4i4i000000000000000000000000000000000000000000000
χ6244-4-44-4-440000004-4400-400−4i4i4i−4i000000000000000000000000000000000000000000000
χ6344-4-44-4-44000000-44-4004000000000000000004-400000000000000000000000000000000
χ6444-4-44-4-44000000-44-400400000000000000000-4400000000000000000000000000000000
χ654-444-4-4-4444-4-400-4-44004000000-440000000000000000000000000000000000000000000
χ664-444-4-4-44-4-44400-4-440040000004-40000000000000000000000000000000000000000000
χ674-44-444-4-44-44-4-4-4000440-440000000000000000000000000000000000000000000000000
χ684-44-444-4-4-44-44-4-40004404-40000000000000000000000000000000000000000000000000
χ694-4-4-4-444400004-4-4444-4-400000000-4400000000000000000000000000000000000000000
χ704-4-4-4-44440000-44-444-44-4000000004-400000000000000000000000000000000000000000
χ718-8-888-88-8000000000000000000000000000000000000000000000000000000000000000

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