Finite Group Databasebeta

← Group #344165

Character table — Group #344165

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444444444444444488888888161616161616161616161616161616163232
order12222222444444444488888888888888888888888844444444444444448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-11-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-11-1-1-11-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-111
χ51111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-111-1-111111-1-1-1-1-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-111-1-11111-11
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1111-1-1-1-111-1-1-1-1-11
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-111-1-11111111-1
χ9111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11-11-1-1111-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111-1-1-1-1-1-1-1-1-1111-1
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-1111111-1-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1111111-1-111-11
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1111111-1-111-1-111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-111-1-1-1-1-1-1-11111-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-1-1-1-11-1-111-1-1-1-11111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-111-11111-1-111-1-1-1-1
χ17222222222-2-22-222-2-2-222220000-2-2-2-2000000000000000022-2-202000-2000000000000
χ18222222222-2-22-222-2-2-222220000-2-2-2-20000000000000000-2-2220-20002000000000000
χ19222222222-2-22-222-2-2-2-2-2-2-200002222000000000000000022220-2000-2000000000000
χ20222222222-2-22-222-2-2-2-2-2-2-2000022220000000000000000-2-2-2-2020002000000000000
χ2122222222-222-22-2-22-2-2000022220000-2-2-2-20000000022-2-2000020-2000000000000000
χ2222222222-222-22-2-22-2-2000022220000-2-2-2-200000000-2-2220000-202000000000000000
χ2322222222-222-22-2-22-2-20000-2-2-2-2000022220000000022220000-20-2000000000000000
χ2422222222-222-22-2-22-2-20000-2-2-2-20000222200000000-2-2-2-20000202000000000000000
χ252-222-2-22-22-2-2-222-222-200000000000000002i2i2i2i−2i−2i−2i−2i000000000002-202i−2i0000000000
χ262-222-2-22-22-2-2-222-222-200000000000000002i2i2i2i−2i−2i−2i−2i00000000000-220−2i2i0000000000
χ272-222-2-22-22-2-2-222-222-20000000000000000−2i−2i−2i−2i2i2i2i2i000000000002-20−2i2i0000000000
χ282-222-2-22-22-2-2-222-222-20000000000000000−2i−2i−2i−2i2i2i2i2i00000000000-2202i−2i0000000000
χ292-22-222-2-2-200202-20000000i2i2−i2−i22i2i−2i−2ii2i2−i2−i222−2−222−2−200002-22i−2i000000000000i2−i22−200
χ302-22-222-2-2-200202-20000000i2i2−i2−i22i2i−2i−2ii2i2−i2−i222−2−222−2−20000-22−2i2i000000000000−i2i2−2200
χ312-22-222-2-2-200202-20000000i2i2−i2−i2−2i−2i2i2ii2i2−i2−i2−2−222−2−22200002-2−2i2i000000000000i2−i2−2200
χ322-22-222-2-2-200202-20000000i2i2−i2−i2−2i−2i2i2ii2i2−i2−i2−2−222−2−2220000-222i−2i000000000000−i2i22−200
χ332-22-222-2-2-200202-20000000−i2−i2i2i22i2i−2i−2i−i2−i2i2i2−2−222−2−22200002-22i−2i000000000000−i2i2−2200
χ342-22-222-2-2-200202-20000000−i2−i2i2i22i2i−2i−2i−i2−i2i2i2−2−222−2−2220000-22−2i2i000000000000i2−i22−200
χ352-22-222-2-2-200202-20000000−i2−i2i2i2−2i−2i2i2i−i2−i2i2i222−2−222−2−200002-2−2i2i000000000000−i2i22−200
χ362-22-222-2-2-200202-20000000−i2−i2i2i2−2i−2i2i2i−i2−i2i2i222−2−222−2−20000-222i−2i000000000000i2−i2−2200
χ372-2-222-2-2202-20200-20022−2−200002−22−22i−2i2i−2ii2−i2i2−i2i2−i2i2−i22-22i−2i0000000000002−2i2−i2000000
χ382-2-222-2-2202-20200-20022−2−200002−22−22i−2i2i−2ii2−i2i2−i2i2−i2i2−i2-22−2i2i000000000000−22−i2i2000000
χ392-2-222-2-2202-20200-20022−2−200002−22−2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i22-2−2i2i0000000000002−2−i2i2000000
χ402-2-222-2-2202-20200-20022−2−200002−22−2−2i2i−2i2i−i2i2−i2i2−i2i2−i2i2-222i−2i000000000000−22i2−i2000000
χ412-2-222-2-2202-20200-200−2−2220000−22−222i−2i2i−2i−i2i2−i2i2−i2i2−i2i22-22i−2i000000000000−22−i2i2000000
χ422-2-222-2-2202-20200-200−2−2220000−22−222i−2i2i−2i−i2i2−i2i2−i2i2−i2i2-22−2i2i0000000000002−2i2−i2000000
χ432-2-222-2-2202-20200-200−2−2220000−22−22−2i2i−2i2ii2−i2i2−i2i2−i2i2−i22-2−2i2i000000000000−22i2−i2000000
χ442-2-222-2-2202-20200-200−2−2220000−22−22−2i2i−2i2ii2−i2i2−i2i2−i2i2−i2-222i−2i0000000000002−2−i2i2000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ46444-4-4-4-4440040-4-40004-44-40000000000000000000000000000000000000000000000
χ47444-4-4-4-4440040-4-4000-44-440000000000000000000000000000000000000000000000
χ48444-4-4-4-44-400-404400000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ49444-4-4-4-44-400-40440000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5044-44-44-4-404-40-40040000004i−4i4i−4i000000000000000000000000000000000000000000
χ5144-44-44-4-404-40-4004000000−4i4i−4i4i000000000000000000000000000000000000000000
χ5244-44-44-4-40-440400-400000000000000000022−2222−22−2222−222200000000000000000000000000
χ5344-44-44-4-40-440400-4000000000000000000−2222−222222−2222−2200000000000000000000000000
χ5444-4-44-44-40000000000000000002i2−2i2−2i22i222−22−2222−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ5544-4-44-44-40000000000000000002i2−2i2−2i22i2−222222−222i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ5644-4-44-44-4000000000000000000−2i22i22i2−2i222−22−22222i−2i−2i2i2i−2i−2i2i00000000000000000000000000
χ5744-4-44-44-4000000000000000000−2i22i22i2−2i2−222222−22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000
χ584-444-4-44-4444-4-44-4-4-4400000000000000000000000000000000000000000000000000
χ594-444-4-44-4-4444-4-44-44-400000000000000000000000000000000000000000000000000
χ604-444-4-44-4-4-4-444-444-4400000000000000000000000000000000000000000000000000
χ614-44-444-4-4400-40-4400000002i22i2−2i2−2i20000−2i2−2i22i22i20000000000000000000000000000000000
χ624-44-444-4-4400-40-440000000−2i2−2i22i22i200002i22i2−2i2−2i20000000000000000000000000000000000
χ634-4-444-4-440-440-4004002222−22−220000−2222−222200000000000000000000000000000000000000
χ644-4-444-4-440-440-400400−22−222222000022−2222−2200000000000000000000000000000000000000
χ654-4-4-4-4444000000000022−22−222222−22−2222000000002-2-22-222-200000000000000000000000000
χ664-4-4-4-4444000000000022−22−2222−222222−2200000000-222-22-2-2200000000000000000000000000
χ674-4-4-4-44440000000000−222222−2222−22−222200000000-222-22-2-2200000000000000000000000000
χ684-4-4-4-44440000000000−222222−22−222222−22000000002-2-22-222-200000000000000000000000000

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