Finite Group Databasebeta

← Group #287839

Character table — Group #287839

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444488888888888888882222444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ9111111111111111111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11-1
χ10111111111111111111-1-1-1-1-1-1111111111111-1-1-1-111-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-11
χ11111111111111111111-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-111-11
χ12111111111111111111-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111111111-1-111-1-1-1-1-1-111111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111111111-1-1-1-1111111-1-1-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-11111-1-11111-1-1-1-11111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-11111-1-111-1-11111-1-1-1-1111-1
χ17222222222-222-2-22-2-2-222-2-22200000000222222220000-200000000-2-2-2-200000000000000
χ18222222222-222-2-22-2-2-222-2-22200000000-2-2-2-2-2-2-2-20000-200000000222200000000000000
χ19222222222-222-2-22-2-2-2-2-222-2-2000000002222-2-2-2-20000200000000-2-22200000000000000
χ20222222222-222-2-22-2-2-2-2-222-2-200000000-2-2-2-22222000020000000022-2-200000000000000
χ2122222222-22-2-222-22-2-222-2-2-2-2000000000000000022222-2-2-2-20000000000000000000000
χ2222222222-22-2-222-22-2-222-2-2-2-20000000000000000-2-2-2-2222220000000000000000000000
χ2322222222-22-2-222-22-2-2-2-22222000000000000000022-2-2-2-2-2220000000000000000000000
χ2422222222-22-2-222-22-2-2-2-222220000000000000000-2-222-222-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2222222-2-22i2i2i2i−2i−2i−2i−2i000000000000-200002i2i−2i−2i000000000000000000
χ2622222222-2-2-2-2-2-2-2-2222222-2-2−2i−2i−2i−2i2i2i2i2i000000000000-20000−2i−2i2i2i000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2-2-2222i2i2i2i−2i−2i−2i−2i00000000000020000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i000000000000200002i2i−2i−2i000000000000000000
χ29222-2-2-22-20200-2-20200002i−2i2i−2i22−2−222−2−222−2−2i2i2−i2−i22-2000002i−2ii2−i2i2−i22−2i2−i200000000000000
χ30222-2-2-22-20200-2-20200002i−2i2i−2i22−2−222−2−2−2−222−i2−i2i2i2-2200000−2i2ii2−i2i2−i2−22−i2i200000000000000
χ31222-2-2-22-20200-2-20200002i−2i2i−2i−2−222−2−22222−2−2i2i2−i2−i2-2200000−2i2i−i2i2−i2i22−2i2−i200000000000000
χ32222-2-2-22-20200-2-20200002i−2i2i−2i−2−222−2−222−2−222−i2−i2i2i22-2000002i−2i−i2i2−i2i2−22−i2i200000000000000
χ33222-2-2-22-20200-2-2020000−2i2i−2i2i22−2−222−2−222−2−2−i2−i2i2i22-200000−2i2i−i2i2−i2i22−2−i2i200000000000000
χ34222-2-2-22-20200-2-2020000−2i2i−2i2i22−2−222−2−2−2−222i2i2−i2−i2-22000002i−2i−i2i2−i2i2−22i2−i200000000000000
χ35222-2-2-22-20200-2-2020000−2i2i−2i2i−2−222−2−22222−2−2−i2−i2i2i2-22000002i−2ii2−i2i2−i22−2−i2i200000000000000
χ36222-2-2-22-20200-2-2020000−2i2i−2i2i−2−222−2−222−2−222i2i2−i2−i22-200000−2i2ii2−i2i2−i2−22i2−i200000000000000
χ37222-2-2-22-20-200220-200002i−2i−2i2ii2i2−i2−i2−i2−i2i2i222−2−2−i2−i2i2i2002-202i−2i00−222−2−22i2−i200000000000000
χ38222-2-2-22-20-200220-200002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2−2−222i2i2−i2−i200-220−2i2i00−222−22−2−i2i200000000000000
χ39222-2-2-22-20-200220-200002i−2i−2i2i−i2−i2i2i2i2i2−i2−i222−2−2−i2−i2i2i200-220−2i2i002−2−22−22i2−i200000000000000
χ40222-2-2-22-20-200220-200002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−2−222i2i2−i2−i2002-202i−2i002−2−222−2−i2i200000000000000
χ41222-2-2-22-20-200220-20000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i222−2−2i2i2−i2−i200-2202i−2i002−2−22−22−i2i200000000000000
χ42222-2-2-22-20-200220-20000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2−2−222−i2−i2i2i2002-20−2i2i002−2−222−2i2−i200000000000000
χ43222-2-2-22-20-200220-20000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i222−2−2i2i2−i2−i2002-20−2i2i00−222−2−22−i2i200000000000000
χ44222-2-2-22-20-200220-20000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2−2−222−i2−i2i2i200-2202i−2i00−222−22−2i2−i200000000000000
χ452-2-22-2-222222-22-2-2-22-20000002i−2i2i−2i2i−2i2i−2i00000000000000000000000002i−2i002-200000000
χ462-2-22-2-222222-22-2-2-22-20000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000−2i2i00-2200000000
χ472-2-22-2-222222-22-2-2-22-2000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000002i−2i00-2200000000
χ482-2-22-2-222222-22-2-2-22-2000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000−2i2i002-200000000
χ492-2-22-2-222-2-2-22-22222-20000002-22-2-22-220000000000000000000000000002-200002-20000
χ502-2-22-2-222-2-2-22-22222-20000002-22-2-22-22000000000000000000000000000-220000-220000
χ512-2-22-2-222-2-2-22-22222-2000000-22-222-22-20000000000000000000000000002-20000-220000
χ522-2-22-2-222-2-2-22-22222-2000000-22-222-22-2000000000000000000000000000-2200002-20000
χ5344-444-4-4-400000000004-400000000000022−2222−2222−2222−220000000000000000000000000000000
χ5444-444-4-4-400000000004-4000000000000−2222−2222−2222−22220000000000000000000000000000000
χ5544-444-4-4-40000000000-4400000000000022−2222−22−2222−22220000000000000000000000000000000
χ5644-444-4-4-40000000000-44000000000000−2222−222222−2222−220000000000000000000000000000000
χ5744-4-4-44-4440-4400-40000000000000000000004i−4i−4i4i0000000000000000000000000000000
χ5844-4-4-44-4440-4400-4000000000000000000000−4i4i4i−4i0000000000000000000000000000000
χ5944-4-4-44-44-404-4004000000000000000004-4-4400000000000000000000000000000000000
χ6044-4-4-44-44-404-400400000000000000000-444-400000000000000000000000000000000000
χ614-44-44-4-4440-4-400400000000000000000000000000000000000000000000000000002i2−2i200
χ624-44-44-4-4440-4-40040000000000000000000000000000000000000000000000000000−2i22i200
χ634-44-44-4-44-404400-40000000000000000000000000000000000000000000000002i2−2i2000000
χ644-44-44-4-44-404400-4000000000000000000000000000000000000000000000000−2i22i2000000
χ654-4-44-4-4444-44-4-44-44-4400000000000000000000000000000000000000000000000000000
χ664-4-44-4-444-44-444-44-4-4400000000000000000000000000000000000000000000000000000
χ674-4-4-4444-40400-440-4000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ684-4-4-4444-40400-440-400000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ694-4-4-4444-40-4004-4040000000022−22−2222−222222−22000000000000000000000000000000000000000
χ704-4-4-4444-40-4004-40400000000−222222−2222−22−2222000000000000000000000000000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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