Finite Group Databasebeta

← Group #278955

Character table — Group #278955

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111111122222222444444444444448888888888888888888888888888881616161632323232
order12222222444444442244448888888822444444448888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11-1-11-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11-1-11-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-1111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ91111111111111111-1-111-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-11-1
χ101111111111111111-1-111-1-11111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-11
χ111111111111111111-1-111-1-111111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-11-11
χ121111111111111111-1-111-1-111111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1111-11-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-111111111-1-1-1-11111-1-1-1-1-1-1111-1-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-111-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-111-111-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-11-1-11
χ17222222222-2-2222-2-222-2-2-2-22222-2-2-2-20000200-200-2-200002200000000000000000000
χ18222222222-2-2222-2-222-2-2-2-2-2-2-2-222220000200-200220000-2-200000000000000000000
χ19222222222-2-2222-2-2-2-2-2-2222222-2-2-2-20000-200200220000-2-200000000000000000000
χ20222222222-2-2222-2-2-2-2-2-222-2-2-2-222220000-200200-2-200002200000000000000000000
χ2122222222-222-2-2-22222-2-222000000002222-2-2-2-2-2-20000000000000000000000000000
χ2222222222-222-2-2-22222-2-22200000000-2-2-2-2-222-2220000000000000000000000000000
χ2322222222-222-2-2-222-2-2-2-2-2-20000000022-2-22-2-22220000000000000000000000000000
χ2422222222-222-2-2-222-2-2-2-2-2-200000000-2-2222222-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2000000000000-200200002i2i−2i−2i002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2000000000000-20020000−2i−2i2i2i00−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222000000000000200-200002i2i−2i−2i00−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222000000000000200-20000−2i−2i2i2i002i2i−2i−2i0000000000000000
χ292-222-22-2-202-20002-22-2002-2i2i2−i2−i2i2i2−i2−i2000002i−2i02i−2ii2−i22−22−2i2−i22−22−20000000000000000
χ302-222-22-2-202-20002-22-2002-2i2i2−i2−i2i2i2−i2−i200000−2i2i0−2i2ii2−i2−22−22i2−i2−22−220000000000000000
χ312-222-22-2-202-20002-22-2002-2−i2−i2i2i2−i2−i2i2i2000002i−2i02i−2i−i2i2−22−22−i2i2−22−220000000000000000
χ322-222-22-2-202-20002-22-2002-2−i2−i2i2i2−i2−i2i2i200000−2i2i0−2i2i−i2i22−22−2−i2i22−22−20000000000000000
χ332-222-22-2-202-20002-2-2200-22i2i2−i2−i2i2i2−i2−i2000002i−2i0−2i2i−i2i2−22−22−i2i22−22−20000000000000000
χ342-222-22-2-202-20002-2-2200-22i2i2−i2−i2i2i2−i2−i200000−2i2i02i−2i−i2i22−22−2−i2i2−22−220000000000000000
χ352-222-22-2-202-20002-2-2200-22−i2−i2i2i2−i2−i2i2i2000002i−2i0−2i2ii2−i22−22−2i2−i2−22−220000000000000000
χ362-222-22-2-202-20002-2-2200-22−i2−i2i2i2−i2−i2i2i200000−2i2i02i−2ii2−i2−22−22i2−i22−22−20000000000000000
χ372-222-22-2-20-22000-222-200-22i2i2−i2−i2−i2−i2i2i22-22-2000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ382-222-22-2-20-22000-222-200-22i2i2−i2−i2−i2−i2i2i2-22-22000000−i2i2−i2i2i2−i2i2−i2−i2i2i2−i20000000000000000
χ392-222-22-2-20-22000-222-200-22−i2−i2i2i2i2i2−i2−i22-22-2000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ402-222-22-2-20-22000-222-200-22−i2−i2i2i2i2i2−i2−i2-22-22000000i2−i2i2−i2−i2i2−i2i2i2−i2−i2i20000000000000000
χ412-222-22-2-20-22000-22-22002-2i2i2−i2−i2−i2−i2i2i22-2-22000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000
χ422-222-22-2-20-22000-22-22002-2i2i2−i2−i2−i2−i2i2i2-222-2000000i2−i2i2−i2−i2i2−i2i2−i2i2i2−i20000000000000000
χ432-222-22-2-20-22000-22-22002-2−i2−i2i2i2i2i2−i2−i22-2-22000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000
χ442-222-22-2-20-22000-22-22002-2−i2−i2i2i2i2i2−i2−i2-222-2000000−i2i2−i2i2i2−i2i2−i2i2−i2−i2i20000000000000000
χ452-2-2-2222-2-2222-22-2-2002-2002-22-22-22-200000000000000000000002i2i−2i−2i00002i−2i000000
χ462-2-2-2222-2-2222-22-2-2002-2002-22-22-22-20000000000000000000000−2i−2i2i2i0000−2i2i000000
χ472-2-2-2222-2-2222-22-2-2002-200-22-22-22-2200000000000000000000002i2i−2i−2i0000−2i2i000000
χ482-2-2-2222-2-2222-22-2-2002-200-22-22-22-220000000000000000000000−2i−2i2i2i00002i−2i000000
χ492-2-2-2222-2-2-2-22-222200-22002-22-2-22-220000000000000000000000000022-2-2002-20000
χ502-2-2-2222-2-2-2-22-222200-22002-22-2-22-2200000000000000000000000000-2-22200-220000
χ512-2-2-2222-2-2-2-22-222200-2200-22-222-22-20000000000000000000000000022-2-200-220000
χ522-2-2-2222-2-2-2-22-222200-2200-22-222-22-200000000000000000000000000-2-222002-20000
χ5344-444-4-4-44004-4-40000000000000000000000000000000000000022−2222−22000000000000
χ5444-444-4-4-44004-4-400000000000000000000000000000000000000−2222−2222000000000000
χ5544-444-4-4-4-400-4440000000000000000000000000000000000000000002i2−2i22i2−2i200000000
χ5644-444-4-4-4-400-444000000000000000000000000000000000000000000−2i22i2−2i22i200000000
χ5744-4-4-44-4404-4000-440000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ5844-4-4-44-4404-4000-44000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ5944-4-4-44-440-440004-40000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ6044-4-4-44-440-440004-4000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ614-44-44-4-44400-4-440000000000000000000000000000000000000000002i2−2i2−2i22i200000000
χ624-44-44-4-44400-4-44000000000000000000000000000000000000000000−2i22i22i2−2i200000000
χ634-44-44-4-44-40044-4000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ644-44-44-4-44-40044-400000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ654-4-4-4444-4444-44-4-4-400-44000000000000000000000000000000000000000000000000
χ664-4-4-4444-44-4-4-44-444004-4000000000000000000000000000000000000000000000000
χ67888-8-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-8-888000000000000000000000000000000000000000000000000000000000000

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