Finite Group Databasebeta

← Group #336827

Character table — Group #336827

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888222244444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-111-1-111111111-1-1-1-111111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111-1-1111111-1-1-1-111111111-11-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-1111111-1
χ71111111111111111111111-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111111111-1-1-1-1-1-111-1-111-1-11
χ9111111111111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1
χ11111111111111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-11-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11-1-11111-111
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1111-11
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-11-1-111-1-11-11
χ1722222222222-2-2-2-22-2-20000222222002200-2-20000-2-2000000000000-20000000000
χ1822222222222-2-2-2-22-2-200002222-2-200-2-200220000-2-200000000000020000000000
χ1922222222222-2-2-2-22-2-20000-2-2-2-22200-2-20022000022000000000000-20000000000
χ2022222222222-2-2-2-22-2-20000-2-2-2-2-2-2002200-2-200002200000000000020000000000
χ2122222222-2-2-22222-2-2-222220000002200-2-20022-2-2000000000000000-2000000000
χ2222222222-2-2-22222-2-2-22222000000-2-2002200-2-2-2-20000000000000002000000000
χ2322222222-2-2-22222-2-2-2-2-2-2-20000002200-2-200-2-2220000000000000002000000000
χ2422222222-2-2-22222-2-2-2-2-2-2-2000000-2-20022002222000000000000000-2000000000
χ252-222-22-2-2-2-2222-2-222-20000000000000000000000002i2i−2i−2i22-2-20000002i−2i0000000
χ262-222-22-2-2-2-2222-2-222-20000000000000000000000002i2i−2i−2i-2-222000000−2i2i0000000
χ272-222-22-2-2-2-2222-2-222-2000000000000000000000000−2i−2i2i2i22-2-2000000−2i2i0000000
χ282-222-22-2-2-2-2222-2-222-2000000000000000000000000−2i−2i2i2i-2-2220000002i−2i0000000
χ292-22-22-22-20002-22-20002i2i−2i−2ii2i2−i2−i2002-20000002i−2i00i2−i20000i2−i2i2−i222−2−20000002−2000
χ302-22-22-22-20002-22-20002i2i−2i−2ii2i2−i2−i200-22000000−2i2i00i2−i20000−i2i2−i2i222−2−2000000−22000
χ312-22-22-22-20002-22-20002i2i−2i−2i−i2−i2i2i2002-20000002i−2i00−i2i20000−i2i2−i2i2−2−222000000−22000
χ322-22-22-22-20002-22-20002i2i−2i−2i−i2−i2i2i200-22000000−2i2i00−i2i20000i2−i2i2−i2−2−2220000002−2000
χ332-22-22-22-20002-22-2000−2i−2i2i2ii2i2−i2−i2002-2000000−2i2i00i2−i20000i2−i2i2−i2−2−222000000−22000
χ342-22-22-22-20002-22-2000−2i−2i2i2ii2i2−i2−i200-220000002i−2i00i2−i20000−i2i2−i2i2−2−2220000002−2000
χ352-22-22-22-20002-22-2000−2i−2i2i2i−i2−i2i2i2002-2000000−2i2i00−i2i20000−i2i2−i2i222−2−20000002−2000
χ362-22-22-22-20002-22-2000−2i−2i2i2i−i2−i2i2i200-220000002i−2i00−i2i20000i2−i2i2−i222−2−2000000−22000
χ372-2-22-2-2222-220000-2002−22−22i−2i2i−2i2-2002i−2i0000002−200i2−i2i2−i20000i2−i2i2−i200002−200000
χ382-2-22-2-2222-220000-2002−22−22i−2i2i−2i-2200−2i2i0000002−200−i2i2−i2i20000i2−i2i2−i20000−2200000
χ392-2-22-2-2222-220000-2002−22−2−2i2i−2i2i2-200−2i2i0000002−200−i2i2−i2i20000−i2i2−i2i200002−200000
χ402-2-22-2-2222-220000-2002−22−2−2i2i−2i2i-22002i−2i0000002−200i2−i2i2−i20000−i2i2−i2i20000−2200000
χ412-2-22-2-2222-220000-200−22−222i−2i2i−2i2-2002i−2i000000−2200−i2i2−i2i20000−i2i2−i2i20000−2200000
χ422-2-22-2-2222-220000-200−22−222i−2i2i−2i-2200−2i2i000000−2200i2−i2i2−i20000−i2i2−i2i200002−200000
χ432-2-22-2-2222-220000-200−22−22−2i2i−2i2i2-200−2i2i000000−2200i2−i2i2−i20000i2−i2i2−i20000−2200000
χ442-2-22-2-2222-220000-200−22−22−2i2i−2i2i-22002i−2i000000−2200−i2i2−i2i20000i2−i2i2−i200002−200000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ46444-4-4-4-440004-4-4400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ47444-4-4-4-440004-4-440000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ48444-4-4-4-44000-444-4000000000000000004i−4i0000000000000000000000000000000
χ49444-4-4-4-44000-444-400000000000000000−4i4i0000000000000000000000000000000
χ5044-444-4-4-44-4-4000040000000000000000004i−4i00000000000000000000000000000
χ5144-444-4-4-44-4-400004000000000000000000−4i4i00000000000000000000000000000
χ5244-444-4-4-4-4440000-40000000000000000000000000022−22−22220000000000000000000
χ5344-444-4-4-4-4440000-400000000000000000000000000−222222−220000000000000000000
χ5444-4-4-444-400000000002i2−2i2−2i22i222−22−2222000000000000000000000000−2i2i2i−2i00000000000
χ5544-4-4-444-400000000002i2−2i2−2i22i2−222222−220000000000000000000000002i−2i−2i2i00000000000
χ5644-4-4-444-40000000000−2i22i22i2−2i222−22−22220000000000000000000000002i−2i−2i2i00000000000
χ5744-4-4-444-40000000000−2i22i22i2−2i2−222222−22000000000000000000000000−2i2i2i−2i00000000000
χ584-444-44-4-444-444-4-4-4-4400000000000000000000000000000000000000000000000
χ594-444-44-4-444-4-4-444-44-400000000000000000000000000000000000000000000000
χ604-444-44-4-4-4-44-4-4444-4400000000000000000000000000000000000000000000000
χ614-44-44-44-4000-44-4400000002i22i2−2i2−2i200000000000000−2i22i200000000000000000000000
χ624-44-44-44-4000-44-440000000−2i2−2i22i22i2000000000000002i2−2i200000000000000000000000
χ634-4-44-4-444-44-4000040022−2222−220000000000000000−22220000000000000000000000000
χ644-4-44-4-444-44-40000400−2222−2222000000000000000022−220000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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