Finite Group Databasebeta

← Group #309971

Character table — Group #309971

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1
χ411111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-1-1-1-11111-1-11
χ51111111111111111111111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11-1-1111-1-111-1-1-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-11111-1
χ71111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-1-1
χ81111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1111
χ91111111111111111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-1111
χ101111111111111111-1-1-1-11111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-11-1-11111-1-1-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-11111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111111-1-1-1-1111-1-111-1-11
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-111111-1-111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111111111111-1-1-111-1-1-1-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-1-111111
χ1722222222222-2-2-2-220000-2-22222222200-2-200-2-200000000000000000-2000000000
χ1822222222222-2-2-2-220000-2-22222-2-2-2-2002200-2-2000000000000000002000000000
χ1922222222222-2-2-2-220000-2-2-2-2-2-222-2-20022002200000000000000000-2000000000
χ2022222222222-2-2-2-220000-2-2-2-2-2-2-2-22200-2-20022000000000000000002000000000
χ2122222222-2-2-22222-22222-2-200000000-2-200220022-2-200000000-200000000000000
χ2222222222-2-2-22222-22222-2-200000000-2-200-2-200-2-22200000000200000000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-20000000022002200-2-22200000000-200000000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2000000002200-2-20022-2-200000000200000000000000
χ252-222-2-2-222-2-222-2-220000-220000002i−2i002i−2i0000000022-2-200000002i−2i0000000000
χ262-222-2-2-222-2-222-2-220000-220000002i−2i002i−2i00000000-2-2220000000−2i2i0000000000
χ272-222-2-2-222-2-222-2-220000-22000000−2i2i00−2i2i0000000022-2-20000000−2i2i0000000000
χ282-222-2-2-222-2-222-2-220000-22000000−2i2i00−2i2i00000000-2-22200000002i−2i0000000000
χ292-222-2-2-222-2-2-2-22222i2i−2i−2i2-20000002i−2i2i−2i−2i2i00000000000000000000002-20000000
χ302-222-2-2-222-2-2-2-22222i2i−2i−2i2-2000000−2i2i2i−2i2i−2i0000000000000000000000-220000000
χ312-222-2-2-222-2-2-2-2222−2i−2i2i2i2-20000002i−2i−2i2i−2i2i0000000000000000000000-220000000
χ322-222-2-2-222-2-2-2-2222−2i−2i2i2i2-2000000−2i2i−2i2i2i−2i00000000000000000000002-20000000
χ332-222-2-2-22-222-2-222-22i2i−2i−2i-2200000000−2i2i00000000000000000002i−2i00000002-2000
χ342-222-2-2-22-222-2-222-22i2i−2i−2i-2200000000−2i2i0000000000000000000−2i2i0000000-22000
χ352-222-2-2-22-222-2-222-2−2i−2i2i2i-22000000002i−2i00000000000000000002i−2i0000000-22000
χ362-222-2-2-22-222-2-222-2−2i−2i2i2i-22000000002i−2i0000000000000000000−2i2i00000002-2000
χ372-22-2-222-20002-22-202i−2i2i−2i00i2i2−i2−i2000000002i−2ii2−i22-2002−22−2i2i2−i2−i20000000000002−20
χ382-22-2-222-20002-22-202i−2i2i−2i00i2i2−i2−i200000000−2i2ii2−i2-22002−22−2−i2−i2i2i2000000000000−220
χ392-22-2-222-20002-22-202i−2i2i−2i00−i2−i2i2i2000000002i−2i−i2i22-200−22−22−i2−i2i2i2000000000000−220
χ402-22-2-222-20002-22-202i−2i2i−2i00−i2−i2i2i200000000−2i2i−i2i2-2200−22−22i2i2−i2−i20000000000002−20
χ412-22-2-222-20002-22-20−2i2i−2i2i00i2i2−i2−i2000000002i−2ii2−i2-2200−22−22−i2−i2i2i20000000000002−20
χ422-22-2-222-20002-22-20−2i2i−2i2i00i2i2−i2−i200000000−2i2ii2−i22-200−22−22i2i2−i2−i2000000000000−220
χ432-22-2-222-20002-22-20−2i2i−2i2i00−i2−i2i2i2000000002i−2i−i2i2-22002−22−2i2i2−i2−i2000000000000−220
χ442-22-2-222-20002-22-20−2i2i−2i2i00−i2−i2i2i200000000−2i2i−i2i22-2002−22−2−i2−i2i2i20000000000002−20
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-40004-4-4400000000000000000000000000022−22−22220000000000000000000
χ47444-44-4-4-40004-4-44000000000000000000000000000−222222−220000000000000000000
χ48444-44-4-4-4000-444-404-4-44000000000000000000000000000000000000000000000
χ49444-44-4-4-4000-444-40-444-4000000000000000000000000000000000000000000000
χ5044-44-4-44-444-40000-400000000004-40000000000000000000000000000000000000
χ5144-44-4-44-444-40000-40000000000-440000000000000000000000000000000000000
χ5244-44-4-44-4-4-44000040000000000000000000000000000000000000000002i2−2i200000
χ5344-44-4-44-4-4-4400004000000000000000000000000000000000000000000−2i22i200000
χ5444-4-4-44-44000000000000002i2−2i22i2−2i2000000000000002i2−2i200002-22-2000000000000000
χ5544-4-4-44-44000000000000002i2−2i22i2−2i200000000000000−2i22i20000-22-22000000000000000
χ5644-4-4-44-4400000000000000−2i22i2−2i22i2000000000000002i2−2i20000-22-22000000000000000
χ5744-4-4-44-4400000000000000−2i22i2−2i22i200000000000000−2i22i200002-22-2000000000000000
χ584-444-4-4-44-44444-4-4-400004-40000000000000000000000000000000000000000000
χ594-44-4-444-4000-44-4400000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ604-44-4-444-4000-44-440000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ614-4-4444-4-44-440000-40000004-4-44000000000000000000000000000000000000000
χ624-4-4444-4-44-440000-4000000-444-4000000000000000000000000000000000000000
χ634-4-4444-4-4-44-4000040000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ644-4-4444-4-4-44-400004000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ658-8-8-88-888000000000000000000000000000000000000000000000000000000000

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