Finite Group Databasebeta

← Group #284661

Character table — Group #284661

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888822444444222444448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-11-1-1-1-1-11-1-1-1-1-11111-1-1
χ3111111111111111111111111111111111111111111-1-111-1-111-1-1-11-1-1-111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11111-1-1-111-1-1-1-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111-1-1-11111-1-1-1-1-1-11-1
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-1-1-11111111-1
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1111-1-11111-11
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-111111-11-1-1-1-111-1-1-1-1
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-1-111-1-1-1-1-1-11111
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1111-11111-1-111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1111-1-111-1-1-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-111-1-1-1-11-1-111-1-111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-11-111-1-111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-11111-1-11111-1-11-1
χ17222222222-2-22-222-2-2-222220000-2-2-2-20000000000002200-2-200200000-200000000000
χ18222222222-2-22-222-2-2-222220000-2-2-2-2000000000000-2-2002200-200000200000000000
χ19222222222-2-22-222-2-2-2-2-2-2-2000022220000000000002200-2-200-200000200000000000
χ20222222222-2-22-222-2-2-2-2-2-2-200002222000000000000-2-2002200200000-200000000000
χ2122222222-222-22-2-22-2-2000022220000-2-2-2-200000000002200-2-2000-200020000000000
χ2222222222-222-22-2-22-2-2000022220000-2-2-2-20000000000-2-200220002000-20000000000
χ2322222222-222-22-2-22-2-20000-2-2-2-2000022220000000000220022000-2000-20000000000
χ2422222222-222-22-2-22-2-20000-2-2-2-2000022220000000000-2-200-2-2000200020000000000
χ252-22-2-2-222222-2-22-2-2-2200002i2i−2i−2i00002i2i−2i−2i000000000000000002-202i−2i000000000000
χ262-22-2-2-222222-2-22-2-2-2200002i2i−2i−2i00002i2i−2i−2i00000000000000000-220−2i2i000000000000
χ272-22-2-2-222222-2-22-2-2-220000−2i−2i2i2i0000−2i−2i2i2i000000000000000002-20−2i2i000000000000
χ282-22-2-2-222222-2-22-2-2-220000−2i−2i2i2i0000−2i−2i2i2i00000000000000000-2202i−2i000000000000
χ292-22-2-2-222-2222-2-22-22-200002i2i−2i−2i0000−2i−2i2i2i000000002-2002-2000000000000002i−2i0000
χ302-22-2-2-222-2222-2-22-22-200002i2i−2i−2i0000−2i−2i2i2i00000000-2200-2200000000000000−2i2i0000
χ312-22-2-2-222-2222-2-22-22-20000−2i−2i2i2i00002i2i−2i−2i000000002-2002-200000000000000−2i2i0000
χ322-22-2-2-222-2222-2-22-22-20000−2i−2i2i2i00002i2i−2i−2i00000000-2200-22000000000000002i−2i0000
χ332-22-2-2-222-2-2-222-222-2200000000000000002222-2-2-2-22-200-2200000000000000002-200
χ342-22-2-2-222-2-2-222-222-2200000000000000002222-2-2-2-2-22002-20000000000000000-2200
χ352-22-2-2-222-2-2-222-222-220000000000000000-2-2-2-222222-200-220000000000000000-2200
χ362-22-2-2-222-2-2-222-222-220000000000000000-2-2-2-22222-22002-200000000000000002-200
χ372-2-222-22-202-20200-20022−2−2000022−2−22i−2i2i−2ii2i2−i2−i2i2i2−i2−i2002i−2i002-2000000002−2i2−i2000000
χ382-2-222-22-202-20200-20022−2−2000022−2−22i−2i2i−2ii2i2−i2−i2i2i2−i2−i200−2i2i00-2200000000−22−i2i2000000
χ392-2-222-22-202-20200-20022−2−2000022−2−2−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2002i−2i00-2200000000−22i2−i2000000
χ402-2-222-22-202-20200-20022−2−2000022−2−2−2i2i−2i2i−i2−i2i2i2−i2−i2i2i200−2i2i002-2000000002−2−i2i2000000
χ412-2-222-22-202-20200-200−2−2220000−2−2222i−2i2i−2i−i2−i2i2i2−i2−i2i2i2002i−2i002-200000000−22−i2i2000000
χ422-2-222-22-202-20200-200−2−2220000−2−2222i−2i2i−2i−i2−i2i2i2−i2−i2i2i200−2i2i00-22000000002−2i2−i2000000
χ432-2-222-22-202-20200-200−2−2220000−2−222−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2002i−2i00-22000000002−2−i2i2000000
χ442-2-222-22-202-20200-200−2−2220000−2−222−2i2i−2i2ii2i2−i2−i2i2i2−i2−i200−2i2i002-200000000−22i2−i2000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-44-4-4-440040-4-40004-44-40000000000000000000000000000000000000000000000
χ47444-44-4-4-440040-4-4000-44-440000000000000000000000000000000000000000000000
χ48444-44-4-4-4-400-404400000000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000
χ49444-44-4-4-4-400-40440000000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000
χ5044-44-4-4-44000000000000002i2−2i22i2−2i22i2−2i22i2−2i200002-2-22-222-200000000000000000000000000
χ5144-44-4-4-44000000000000002i2−2i22i2−2i2−2i22i2−2i22i20000-222-22-2-2200000000000000000000000000
χ5244-44-4-4-4400000000000000−2i22i2−2i22i22i2−2i22i2−2i20000-222-22-2-2200000000000000000000000000
χ5344-44-4-4-4400000000000000−2i22i2−2i22i2−2i22i2−2i22i200002-2-22-222-200000000000000000000000000
χ5444-4-4-444-404-40-4004000000000000004-4-440000000000000000000000000000000000
χ5544-4-4-444-404-40-400400000000000000-444-40000000000000000000000000000000000
χ5644-4-4-444-40-440400-40000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5744-4-4-444-40-440400-4000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ584-444-44-4-4400-40-4400000000000000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000
χ594-444-44-4-4400-40-440000000000000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000
χ604-444-44-4-4-400404-4000000000004i−4i−4i4i00000000000000000000000000000000000000
χ614-444-44-4-4-400404-400000000000−4i4i4i−4i00000000000000000000000000000000000000
χ624-44-4-4-4444-4-4-444-444-400000000000000000000000000000000000000000000000000
χ634-4-444-44-40-440-4004002222−22−220000−22−22222200000000000000000000000000000000000000
χ644-4-444-44-40-440-400400−22−22222200002222−22−2200000000000000000000000000000000000000
χ654-4-4-444-44000000000022−22−222222−22−2222000000002-2-222-2-2200000000000000000000000000
χ664-4-4-444-44000000000022−22−2222−222222−2200000000-222-2-222-200000000000000000000000000
χ674-4-4-444-440000000000−222222−2222−22−222200000000-222-2-222-200000000000000000000000000
χ684-4-4-444-440000000000−222222−22−222222−22000000002-2-222-2-2200000000000000000000000000

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