Finite Group Databasebeta

← Group #309960

Character table — Group #309960

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111-1-1111111111111111-1-1-1-1-1-1-111-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-1111
χ71111111111111111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-1111-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11111111-1-1-1
χ911111111111111111-1-1-1-111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-11
χ1011111111111111111-1-1-1-111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-11-1-1-1-11111-1
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111111111-1
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-11111-111-1-1-1-1-1-11
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111111-1-1-111-1-1-1-111-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-111-1-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-111111-1-111-1-111-1
χ172222222222-2-222-2-2-22222-20000-2-2000022000022-2-200000000-200000000000000
χ182222222222-2-222-2-2-22222-20000-2-20000-2-20000-2-22200000000200000000000000
χ192222222222-2-222-2-2-2-2-2-2-2-20000220000220000-2-22200000000-200000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-20000220000-2-2000022-2-200000000200000000000000
χ2122222222-2-222-2-222-20000-2222200222200-2-2-2-200000000000000000-2000000000
χ2222222222-2-222-2-222-20000-2222200-2-2-2-20022-2-2000000000000000002000000000
χ2322222222-2-222-2-222-20000-2-2-2-2-20022-2-200-2-222000000000000000002000000000
χ2422222222-2-222-2-222-20000-2-2-2-2-200-2-22200222200000000000000000-2000000000
χ252-222-2-2-222-2002-20002i2i−2i−2i0i2i2−i2−i20000002i−2i00i2−i22-20022−2−2i2i2−i2−i2000000002−200000
χ262-222-2-2-222-2002-20002i2i−2i−2i0i2i2−i2−i2000000−2i2i00i2−i2-220022−2−2−i2−i2i2i200000000−2200000
χ272-222-2-2-222-2002-20002i2i−2i−2i0−i2−i2i2i20000002i−2i00−i2i22-200−2−222−i2−i2i2i200000000−2200000
χ282-222-2-2-222-2002-20002i2i−2i−2i0−i2−i2i2i2000000−2i2i00−i2i2-2200−2−222i2i2−i2−i2000000002−200000
χ292-222-2-2-222-2002-2000−2i−2i2i2i0i2i2−i2−i20000002i−2i00i2−i2-2200−2−222−i2−i2i2i2000000002−200000
χ302-222-2-2-222-2002-2000−2i−2i2i2i0i2i2−i2−i2000000−2i2i00i2−i22-200−2−222i2i2−i2−i200000000−2200000
χ312-222-2-2-222-2002-2000−2i−2i2i2i0−i2−i2i2i20000002i−2i00−i2i2-220022−2−2i2i2−i2−i200000000−2200000
χ322-222-2-2-222-2002-2000−2i−2i2i2i0−i2−i2i2i2000000−2i2i00−i2i22-20022−2−2−i2−i2i2i2000000002−200000
χ332-22-22-22-222-2-2-2-222-2000020000002i−2i00002i−2i0000002-22-200000000002i−2i0000000
χ342-22-22-22-222-2-2-2-222-2000020000002i−2i00002i−2i000000-22-220000000000−2i2i0000000
χ352-22-22-22-222-2-2-2-222-200002000000−2i2i0000−2i2i0000002-22-20000000000−2i2i0000000
χ362-22-22-22-222-2-2-2-222-200002000000−2i2i0000−2i2i000000-22-2200000000002i−2i0000000
χ372-22-22-22-2-2-22222-2-2-22i−2i2i−2i200002i−2i000000000000000000000002i−2i00000002-2000
χ382-22-22-22-2-2-22222-2-2-22i−2i2i−2i200002i−2i00000000000000000000000−2i2i0000000-22000
χ392-22-22-22-2-2-22222-2-2-2−2i2i−2i2i20000−2i2i000000000000000000000002i−2i0000000-22000
χ402-22-22-22-2-2-22222-2-2-2−2i2i−2i2i20000−2i2i00000000000000000000000−2i2i00000002-2000
χ412-22-22-22-2-2-2-2-2222222i−2i2i−2i-20000−2i2i2i−2i0000−2i2i000000000000000002-20000000000
χ422-22-22-22-2-2-2-2-2222222i−2i2i−2i-20000−2i2i−2i2i00002i−2i00000000000000000-220000000000
χ432-22-22-22-2-2-2-2-222222−2i2i−2i2i-200002i−2i2i−2i0000−2i2i00000000000000000-220000000000
χ442-22-22-22-2-2-2-2-222222−2i2i−2i2i-200002i−2i−2i2i00002i−2i000000000000000002-20000000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000
χ46444-4-44-4-44-400-44000000000000000000000000000022−22−22220000000000000000000
χ47444-4-44-4-44-400-440000000000000000000000000000−222222−220000000000000000000
χ48444-4-44-4-4-44004-40004-4-4400000000000000000000000000000000000000000000
χ49444-4-44-4-4-44004-4000-444-400000000000000000000000000000000000000000000
χ5044-444-4-4-40000000000000022−2222−220000000000000022−2200002-22-2000000000000000
χ5144-444-4-4-40000000000000022−2222−2200000000000000−22220000-22-22000000000000000
χ5244-444-4-4-400000000000000−2222−22220000000000000022−220000-22-22000000000000000
χ5344-444-4-4-400000000000000−2222−222200000000000000−222200002-22-2000000000000000
χ5444-4-4-4-444004-4004-4000000000000004i−4i000000000000000000000000000000000
χ5544-4-4-4-444004-4004-400000000000000−4i4i000000000000000000000000000000000
χ5644-4-4-4-44400-4400-4400000000000000000000000000000000000000000000002i2−2i20
χ5744-4-4-4-44400-4400-440000000000000000000000000000000000000000000000−2i22i20
χ584-444-4-4-44-4400-44000000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ594-444-4-4-44-4400-4400000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ604-44-44-44-44444-4-4-4-440000-40000000000000000000000000000000000000000000
χ614-4-44-444-4004-400-440000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ624-4-44-444-4004-400-44000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ634-4-44-444-400-44004-40000004i−4i−4i4i000000000000000000000000000000000000000
χ644-4-44-444-400-44004-4000000−4i4i4i−4i000000000000000000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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