Finite Group Databasebeta

← Group #286755

Character table — Group #286755

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444488888888888888884444444448888888844448888888824
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ9111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-11-1
χ10111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-11
χ11111111111111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111-11
χ12111111111111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-11-1
χ13111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-1111-1
χ14111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-111-1-11111-1-1-1-1111-1
χ17222222222-2-222-22-2-2-22222-2-20000000022222222-2000000000000-2-2-2-200000000000000
χ18222222222-2-222-22-2-2-22222-2-200000000-2-2-2-2-2-2-2-2-2000000000000222200000000000000
χ19222222222-2-222-22-2-2-2-2-2-2-222000000002222-2-2-2-22000000000000-2-22200000000000000
χ20222222222-2-222-22-2-2-2-2-2-2-22200000000-2-2-2-22222200000000000022-2-200000000000000
χ2122222222-222-2-22-22-2-222-2-2-2-20000000000000000222-2-222-2-20000000000000000000000
χ2222222222-222-2-22-22-2-222-2-2-2-200000000000000002-2-222-2-2220000000000000000000000
χ2322222222-222-2-22-22-2-2-2-222220000000000000000-222-2-2-2-2220000000000000000000000
χ2422222222-222-2-22-22-2-2-2-222220000000000000000-2-2-22222-2-20000000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2222i2i2i2i−2i−2i−2i−2i00000000-2000000002i2i−2i−2i000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-222−2i−2i−2i−2i2i2i2i2i00000000-200000000−2i−2i2i2i000000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-222-2-22i2i2i2i−2i−2i−2i−2i00000000200000000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-222-2-2−2i−2i−2i−2i2i2i2i2i000000002000000002i2i−2i−2i000000000000000000
χ29222-2-2-2-2222-22-2-2-222-200000022-2-222-2-200000000000000000000000002i−2i002i−2i00000000
χ30222-2-2-2-2222-22-2-2-222-200000022-2-222-2-20000000000000000000000000−2i2i00−2i2i00000000
χ31222-2-2-2-2222-22-2-2-222-2000000-2-222-2-22200000000000000000000000002i−2i00−2i2i00000000
χ32222-2-2-2-2222-22-2-2-222-2000000-2-222-2-2220000000000000000000000000−2i2i002i−2i00000000
χ33222-2-2-2-22-2-22-2222-22-20000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000002-2002i−2i000000
χ34222-2-2-2-22-2-22-2222-22-20000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000-2200−2i2i000000
χ35222-2-2-2-22-2-22-2222-22-2000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000002-200−2i2i000000
χ36222-2-2-2-22-2-22-2222-22-2000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000-22002i−2i000000
χ372-2-2-222-2202200-20-200002-22-2i2−i2i2−i2i2−i2i2−i222−2−222−2−20002i−2i2i−2i00i2−i2i2−i22−22−200000000000000
χ382-2-2-222-2202200-20-200002-22-2i2−i2i2−i2i2−i2i2−i2−2−222−2−222000−2i2i−2i2i00i2−i2i2−i2−22−2200000000000000
χ392-2-2-222-2202200-20-200002-22-2−i2i2−i2i2−i2i2−i2i222−2−222−2−2000−2i2i−2i2i00−i2i2−i2i22−22−200000000000000
χ402-2-2-222-2202200-20-200002-22-2−i2i2−i2i2−i2i2−i2i2−2−222−2−2220002i−2i2i−2i00−i2i2−i2i2−22−2200000000000000
χ412-2-2-222-2202200-20-20000-22-22i2−i2i2−i2i2−i2i2−i222−2−2−2−2220002i−2i−2i2i00−i2i2−i2i22−2−2200000000000000
χ422-2-2-222-2202200-20-20000-22-22i2−i2i2−i2i2−i2i2−i2−2−22222−2−2000−2i2i2i−2i00−i2i2−i2i2−222−200000000000000
χ432-2-2-222-2202200-20-20000-22-22−i2i2−i2i2−i2i2−i2i222−2−2−2−222000−2i2i2i−2i00i2−i2i2−i22−2−2200000000000000
χ442-2-2-222-2202200-20-20000-22-22−i2i2−i2i2−i2i2−i2i2−2−22222−2−20002i−2i−2i2i00i2−i2i2−i2−222−200000000000000
χ452-2-2-222-220-2-20020200002-2-222−22−2−22−2222−2−222−2−202-200002-2−222−2−22−2200000000000000
χ462-2-2-222-220-2-20020200002-2-222−22−2−22−22−2−222−2−2220-220000-22−222−22−22−200000000000000
χ472-2-2-222-220-2-20020200002-2-22−22−222−22−222−2−222−2−20-220000-222−2−22−22−2200000000000000
χ482-2-2-222-220-2-20020200002-2-22−22−222−22−2−2−222−2−22202-200002-22−2−222−22−200000000000000
χ492-2-2-222-220-2-2002020000-222-22−22−2−22−2222−2−2−2−22202-20000-222−2−22−222−200000000000000
χ502-2-2-222-220-2-2002020000-222-22−22−2−22−22−2−22222−2−20-2200002-22−2−222−2−2200000000000000
χ512-2-2-222-220-2-2002020000-222-2−22−222−22−222−2−2−2−2220-2200002-2−222−2−222−200000000000000
χ522-2-2-222-220-2-2002020000-222-2−22−222−22−2−2−22222−2−202-20000-22−222−22−2−2200000000000000
χ53444-4-4-4-444-444-44-4-4-4400000000000000000000000000000000000000000000000000000
χ54444-4-4-4-44-44-4-44-444-4400000000000000000000000000000000000000000000000000000
χ5544-444-4-4-4400-440-4000000000000000004-44-400000000000000000000000000000000000
χ5644-444-4-4-4400-440-400000000000000000-44-4400000000000000000000000000000000000
χ5744-444-4-4-4-4004-4040000000000000000000004i−4i4i−4i0000000000000000000000000000000
χ5844-444-4-4-4-4004-404000000000000000000000−4i4i−4i4i0000000000000000000000000000000
χ5944-4-4-444-4400-4-404000000000000000000000000000000000000000000000000002i2−2i20000
χ6044-4-4-444-4400-4-40400000000000000000000000000000000000000000000000000−2i22i20000
χ6144-4-4-444-4-400440-400000000000000000000000000000000000000000000000000002i2−2i200
χ6244-4-4-444-4-400440-40000000000000000000000000000000000000000000000000000−2i22i200
χ634-44-44-44-400000000004i−4i00000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000
χ644-44-44-44-400000000004i−4i000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000
χ654-44-44-44-40000000000−4i4i00000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000
χ664-44-44-44-40000000000−4i4i000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000
χ674-4-44-4-44404-40040-4000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ684-4-44-4-44404-40040-400000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ694-4-44-4-4440-4400-4040000000022−22−2222−222222−22000000000000000000000000000000000000000
χ704-4-44-4-4440-4400-40400000000−222222−2222−22−2222000000000000000000000000000000000000000
χ718-888-88-8-8000000000000000000000000000000000000000000000000000000000000000

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