Finite Group Databasebeta

← Group #315346

Character table — Group #315346

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444444488888888888844444444444488888888888888888844884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1
χ81111111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ9111111111111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-1-1-1-11-11
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-1111-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-111-1
χ17222222222-222-2-2-22-2-20000222200002222-2-200-2-200-2-2000000000000000000000000
χ18222222222-222-2-2-22-2-2000022220000-2-2-2-222002200-2-2000000000000000000000000
χ19222222222-222-2-2-22-2-20000-2-2-2-2000022-2-2-2-200220022000000000000000000000000
χ20222222222-222-2-2-22-2-20000-2-2-2-20000-2-2222200-2-20022000000000000000000000000
χ2122222222-22-2-2222-2-2-222220000-2-2-2-20000002200-2-2000000000000000000-22000000
χ2222222222-22-2-2222-2-2-222220000-2-2-2-2000000-2-200220000000000000000002-2000000
χ2322222222-22-2-2222-2-2-2-2-2-2-2000022220000002200-2-20000000000000000002-2000000
χ2422222222-22-2-2222-2-2-2-2-2-2-200002222000000-2-20022000000000000000000-22000000
χ252222-2-2-2-2202-2000-20022−2−222-2-222−2−22-22-2000000000022−2−222−2−2000022−2−200000000
χ262222-2-2-2-2202-2000-20022−2−222-2-222−2−2-22-220000000000−2−222−2−222000022−2−200000000
χ272222-2-2-2-2202-2000-20022−2−2-2-22222−2−22-2-22000000000022−2−2−2−2220000−2−22200000000
χ282222-2-2-2-2202-2000-20022−2−2-2-22222−2−2-222-20000000000−2−22222−2−20000−2−22200000000
χ292222-2-2-2-2202-2000-200−2−22222-2-2−2−2222-22-20000000000−2−222−2−2220000−2−22200000000
χ302222-2-2-2-2202-2000-200−2−22222-2-2−2−222-22-22000000000022−2−222−2−20000−2−22200000000
χ312222-2-2-2-2202-2000-200−2−222-2-222−2−2222-2-220000000000−2−22222−2−2000022−2−200000000
χ322222-2-2-2-2202-2000-200−2−222-2-222−2−222-222-2000000000022−2−2−2−222000022−2−200000000
χ332-2-222-22-222-2-2-22-22-2200002i−2i2i−2i00000000000000002i−2i2-22-22i−2i2i−2i0000000000000000
χ342-2-222-22-222-2-2-22-22-2200002i−2i2i−2i00000000000000002i−2i-22-22−2i2i−2i2i0000000000000000
χ352-2-222-22-222-2-2-22-22-220000−2i2i−2i2i0000000000000000−2i2i2-22-2−2i2i−2i2i0000000000000000
χ362-2-222-22-222-2-2-22-22-220000−2i2i−2i2i0000000000000000−2i2i-22-222i−2i2i−2i0000000000000000
χ372-2-222-22-22-2-2-22-2222-22-22-22i−2i2i−2i2-22-2000000000000−2i2i0000000000002i−2i2i−2i00000000
χ382-2-222-22-22-2-2-22-2222-22-22-2−2i2i−2i2i2-22-20000000000002i−2i000000000000−2i2i−2i2i00000000
χ392-2-222-22-22-2-2-22-2222-2-22-222i−2i2i−2i-22-22000000000000−2i2i000000000000−2i2i−2i2i00000000
χ402-2-222-22-22-2-2-22-2222-2-22-22−2i2i−2i2i-22-220000000000002i−2i0000000000002i−2i2i−2i00000000
χ412-2-222-22-2-2-2222-22-2-222-22-20000-22-2200000000000000000000002i2i−2i−2i0000002i−2i0000
χ422-2-222-22-2-2-2222-22-2-222-22-20000-22-220000000000000000000000−2i−2i2i2i000000−2i2i0000
χ432-2-222-22-2-2-2222-22-2-22-22-2200002-22-200000000000000000000002i2i−2i−2i000000−2i2i0000
χ442-2-222-22-2-2-2222-22-2-22-22-2200002-22-20000000000000000000000−2i−2i2i2i0000002i−2i0000
χ452-2-22-22-2220-22000-2002−2−222i−2i−2i2i2−2−2200002-2002i−2i00002−2−22i2−i2−i2i20000i2−i2−i2i200000000
χ462-2-22-22-2220-22000-2002−2−222i−2i−2i2i2−2−220000-2200−2i2i0000−222−2−i2i2i2−i20000i2−i2−i2i200000000
χ472-2-22-22-2220-22000-2002−2−22−2i2i2i−2i2−2−2200002-200−2i2i00002−2−22−i2i2i2−i20000−i2i2i2−i200000000
χ482-2-22-22-2220-22000-2002−2−22−2i2i2i−2i2−2−220000-22002i−2i0000−222−2i2−i2−i2i20000−i2i2i2−i200000000
χ492-2-22-22-2220-22000-200−222−22i−2i−2i2i−222−200002-2002i−2i0000−222−2−i2i2i2−i20000−i2i2i2−i200000000
χ502-2-22-22-2220-22000-200−222−22i−2i−2i2i−222−20000-2200−2i2i00002−2−22i2−i2−i2i20000−i2i2i2−i200000000
χ512-2-22-22-2220-22000-200−222−2−2i2i2i−2i−222−200002-200−2i2i0000−222−2i2−i2−i2i20000i2−i2−i2i200000000
χ522-2-22-22-2220-22000-200−222−2−2i2i2i−2i−222−20000-22002i−2i00002−2−22−i2i2i2−i20000i2−i2−i2i200000000
χ5344444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000000
χ544444-4-4-4-4-40-440004002222−22−220000−22−22222200000000000000000000000000000000000000
χ554444-4-4-4-4-40-44000400−22−22222200002222−22−2200000000000000000000000000000000000000
χ5644-4-44-4-440400-4-440000000000000000000004i−4i000000000000000000000000000000
χ5744-4-44-4-440400-4-44000000000000000000000−4i4i000000000000000000000000000000
χ5844-4-44-4-440-40044-400000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ5944-4-44-4-440-40044-40000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ604-44-444-4-404004-4-4000000000000000000000000000000000000022−22−2222000000000000
χ614-44-444-4-404004-4-40000000000000000000000000000000000000−222222−22000000000000
χ624-44-444-4-40-400-44400000000000000000000000004i−4i00000000000000000000000000
χ634-44-444-4-40-400-4440000000000000000000000000−4i4i00000000000000000000000000
χ644-4-444-44-4-4444-44-4-44-400000000000000000000000000000000000000000000000000
χ654-4-44-44-44-404-400040022−22−22220000−222222−2200000000000000000000000000000000000000
χ664-4-44-44-44-404-4000400−222222−22000022−22−222200000000000000000000000000000000000000
χ6788-8-8-888-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-8-888000000000000000000000000000000000000000000000000000000000000

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