Finite Group Databasebeta

← Group #307018

Character table — Group #307018

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1111111111111111111-1-11-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11-1-1111-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111111-1-1-1
χ91111111111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-11
χ101111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111111-1-1-111-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-111-1111-1-111-1-111-1
χ17222222222-22-22-22-20000-2-2222222-2-222000000-2-2000000000000000-2000000000
χ18222222222-22-22-22-20000-2-22222-2-222-2-2000000-2-20000000000000002000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-222-2-2-2-2000000220000000000000002000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2-2-2222200000022000000000000000-2000000000
χ2122222222-22-22-22-222222-2-20000000000-2-222-2-200000022000000-2000000000000
χ2222222222-22-22-22-222222-2-20000000000-2-2-2-222000000-2-20000002000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000000000222222000000-2-2000000-2000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000000022-2-2-2-2000000220000002000000000000
χ252-22-22-2-222-2-222-2-2222-2-2-2200000000002-200000000000000002i−2i000000002i−2i000
χ262-22-22-2-222-2-222-2-2222-2-2-2200000000002-20000000000000000−2i2i00000000−2i2i000
χ272-22-22-2-222-2-222-2-22-2-222-220000000000-2200000000000000002i−2i00000000−2i2i000
χ282-22-22-2-222-2-222-2-22-2-222-220000000000-220000000000000000−2i2i000000002i−2i000
χ292-22-22-2-22-222-2-222-20000-2200002i−2i2i−2i000000000022-2-20000000000002i−2i0000000
χ302-22-22-2-22-222-2-222-20000-2200002i−2i2i−2i0000000000-2-222000000000000−2i2i0000000
χ312-22-22-2-22-222-2-222-20000-220000−2i2i−2i2i000000000022-2-2000000000000−2i2i0000000
χ322-22-22-2-22-222-2-222-20000-220000−2i2i−2i2i0000000000-2-2220000000000002i−2i0000000
χ332-22-22-2-22-2-222-2-22222-2-22-200002i−2i−2i2i00-2200000000000000000002i−2i0000000000
χ342-22-22-2-22-2-222-2-22222-2-22-20000−2i2i2i−2i00-220000000000000000000−2i2i0000000000
χ352-22-22-2-22-2-222-2-222-2-2222-200002i−2i−2i2i002-20000000000000000000−2i2i0000000000
χ362-22-22-2-22-2-222-2-222-2-2222-20000−2i2i2i−2i002-200000000000000000002i−2i0000000000
χ372-2-2-2222-202020-20-22-22-20022−2−2000000002i−2i002−22−22−22i−2ii2i2−i2−i200000000i2−i200000
χ382-2-2-2222-202020-20-22-22-20022−2−200000000−2i2i002−22−22−2−2i2i−i2−i2i2i200000000−i2i200000
χ392-2-2-2222-202020-20-22-22-200−2−222000000002i−2i00−22−22−222i−2i−i2−i2i2i200000000−i2i200000
χ402-2-2-2222-202020-20-22-22-200−2−22200000000−2i2i00−22−22−22−2i2ii2i2−i2−i200000000i2−i200000
χ412-2-2-2222-202020-20-2-22-220022−2−2000000002i−2i002−2−22−22−2i2i−i2−i2i2i200000000i2−i200000
χ422-2-2-2222-202020-20-2-22-220022−2−200000000−2i2i002−2−22−222i−2ii2i2−i2−i200000000−i2i200000
χ432-2-2-2222-202020-20-2-22-2200−2−222000000002i−2i00−222−22−2−2i2ii2i2−i2−i200000000−i2i200000
χ442-2-2-2222-202020-20-2-22-2200−2−22200000000−2i2i00−222−22−22i−2i−i2−i2i2i200000000i2−i200000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-44-4-440-40-4040000000000000004-4000000000000000000000000000000000
χ47444-4-44-4-440-40-404000000000000000-44000000000000000000000000000000000
χ48444-4-44-4-4-404040-40000000000000000000000000000000000000000000000022−220
χ49444-4-44-4-4-404040-400000000000000000000000000000000000000000000000−22220
χ5044-444-4-4-4040-40-40400000000000000000000000022−22−2222000000000000000000000
χ5144-444-4-4-4040-40-404000000000000000000000000−222222−22000000000000000000000
χ5244-444-4-4-40-404040-44-4-44000000000000000000000000000000000000000000000
χ5344-444-4-4-40-404040-4-444-4000000000000000000000000000000000000000000000
χ5444-4-4-4-444000000000000002i2−2i22i2−2i2000000000022−22000000002i−2i2i−2i000000000000000
χ5544-4-4-4-444000000000000002i2−2i22i2−2i20000000000−222200000000−2i2i−2i2i000000000000000
χ5644-4-4-4-44400000000000000−2i22i2−2i22i2000000000022−2200000000−2i2i−2i2i000000000000000
χ5744-4-4-4-44400000000000000−2i22i2−2i22i20000000000−2222000000002i−2i2i−2i000000000000000
χ584-444-4-44-44040-40-4000000000000000000000000000000022−22−2222000000000000000
χ594-444-4-44-44040-40-40000000000000000000000000000000−222222−22000000000000000
χ604-444-4-44-4-40-4040400000004i−4i−4i4i000000000000000000000000000000000000000
χ614-444-4-44-4-40-404040000000−4i4i4i−4i000000000000000000000000000000000000000
χ624-44-44-4-4444-4-444-4-400004-40000000000000000000000000000000000000000000
χ634-4-4-4444-40-40-404040000002222−22−22000000000000−22220000000000000000000000000
χ644-4-4-4444-40-40-40404000000−22−22222200000000000022−220000000000000000000000000
χ658-8-88-88-88000000000000000000000000000000000000000000000000000000000

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