Finite Group Databasebeta

← Group #309810

Character table — Group #309810

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1111111111111111111-11-1-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-111-1-11111-1-111-1
χ71111111111111111111111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-11
χ91111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11
χ101111111111111111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1111
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-11111-1-11111-1-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1111-1-111-1-111-1-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1111
χ172222222222-2-222-2-20000-2-2222222-2-2220000-2-2000000000000-200000000000000
χ182222222222-2-222-2-20000-2-22222-2-222-2-20000-2-2000000000000200000000000000
χ192222222222-2-222-2-20000-2-2-2-2-2-22222-2-2000022000000000000-200000000000000
χ202222222222-2-222-2-20000-2-2-2-2-2-2-2-2-2-222000022000000000000200000000000000
χ2122222222-2-222-2-2222222-2-2000000000022-2-20022-2-2000000000-20000000000000
χ2222222222-2-222-2-2222222-2-20000000000-2-2-2-200-2-22200000000020000000000000
χ2322222222-2-222-2-222-2-2-2-2-2-20000000000222200-2-222000000000-20000000000000
χ2422222222-2-222-2-222-2-2-2-2-2-20000000000-2-2220022-2-200000000020000000000000
χ252-22-22-22-222-2-2-2-2222i2i−2i−2i-220000000000002i−2i00000000000000002i−2i000000002-20
χ262-22-22-22-222-2-2-2-2222i2i−2i−2i-220000000000002i−2i0000000000000000−2i2i00000000-220
χ272-22-22-22-222-2-2-2-222−2i−2i2i2i-22000000000000−2i2i00000000000000002i−2i00000000-220
χ282-22-22-22-222-2-2-2-222−2i−2i2i2i-22000000000000−2i2i0000000000000000−2i2i000000002-20
χ292-22-22-22-2-2-22222-2-20000-220000002i−2i2i−2i000000000022-2-200000000002i−2i0000000
χ302-22-22-22-2-2-22222-2-20000-220000002i−2i2i−2i0000000000-2-2220000000000−2i2i0000000
χ312-22-22-22-2-2-22222-2-20000-22000000−2i2i−2i2i000000000022-2-20000000000−2i2i0000000
χ322-22-22-22-2-2-22222-2-20000-22000000−2i2i−2i2i0000000000-2-22200000000002i−2i0000000
χ332-22-22-22-2-2-2-2-222222i2i−2i−2i2-20000002i−2i−2i2i00−2i2i0000000000000000002-2000000000
χ342-22-22-22-2-2-2-2-222222i2i−2i−2i2-2000000−2i2i2i−2i00−2i2i000000000000000000-22000000000
χ352-22-22-22-2-2-2-2-22222−2i−2i2i2i2-20000002i−2i−2i2i002i−2i000000000000000000-22000000000
χ362-22-22-22-2-2-2-2-22222−2i−2i2i2i2-2000000−2i2i2i−2i002i−2i0000000000000000002-2000000000
χ372-2-22-222-2002-2002-22-22-200i2i2−i2−i20000002-200i2−i22-200i2−i2i2−i2i2i2−i2−i200000000i2−i200000
χ382-2-22-222-2002-2002-22-22-200i2i2−i2−i2000000-2200i2−i2-2200i2−i2i2−i2−i2−i2i2i200000000−i2i200000
χ392-2-22-222-2002-2002-22-22-200−i2−i2i2i20000002-200−i2i22-200−i2i2−i2i2−i2−i2i2i200000000−i2i200000
χ402-2-22-222-2002-2002-22-22-200−i2−i2i2i2000000-2200−i2i2-2200−i2i2−i2i2i2i2−i2−i200000000i2−i200000
χ412-2-22-222-2002-2002-2-22-2200i2i2−i2−i20000002-200i2−i2-2200−i2i2−i2i2−i2−i2i2i200000000i2−i200000
χ422-2-22-222-2002-2002-2-22-2200i2i2−i2−i2000000-2200i2−i22-200−i2i2−i2i2i2i2−i2−i200000000−i2i200000
χ432-2-22-222-2002-2002-2-22-2200−i2−i2i2i20000002-200−i2i2-2200i2−i2i2−i2i2i2−i2−i200000000−i2i200000
χ442-2-22-222-2002-2002-2-22-2200−i2−i2i2i2000000-2200−i2i22-200i2−i2i2−i2−i2−i2i2i200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-44-4-44-4004-40000000000004-40000000000000000000000000000000000000
χ47444-4-44-4-44-4004-4000000000000-440000000000000000000000000000000000000
χ48444-4-44-4-4-4400-44000000000000000000000000000000000000000000000022−22000
χ49444-4-44-4-4-4400-440000000000000000000000000000000000000000000000−2222000
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
χ5444-4-4-4-444004-400-44000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ5544-4-4-4-444004-400-4400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ5644-4-4-4-44400-44004-44i−4i−4i4i000000000000000000000000000000000000000000000
χ5744-4-4-4-44400-44004-4−4i4i4i−4i000000000000000000000000000000000000000000000
χ584-444-4-4-444-400-44000000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ594-444-4-4-444-400-4400000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ604-444-4-4-44-44004-4000000004i−4i−4i4i000000000000000000000000000000000000000
χ614-444-4-4-44-44004-400000000−4i4i4i−4i000000000000000000000000000000000000000
χ624-44-44-44-44444-4-4-4-400004-40000000000000000000000000000000000000000000
χ634-4-44-444-400-4400-440000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ644-4-44-444-400-4400-44000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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