Finite Group Databasebeta

← Group #287321

Character table — Group #287321

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222444444444444444444444444888888888888888881616161616161616161616163232
order12222222444444444444444488888888888888882244444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-111111111-1-1
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1-11111-1-1111111-1-111-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111
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
χ91111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11-1
χ101111111111111111-1-111-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-11
χ111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-111111111-1-111-1-1-1-1111-1
χ121111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1111111-1-111-1-11111-1-1-11
χ131111111111111111-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-11
χ141111111111111111-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1111111-1-111-1-11111-1-1-1-1-11
χ161111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1111111-1-1-1-111-1-1-1-111111-1
χ17222222222-222-2-22-222-2-222-2-200000000000000002222-2-2-2-2-20000000000000000000000
χ18222222222-222-2-22-222-2-222-2-20000000000000000-2-2-2-222-2220000000000000000000000
χ19222222222-222-2-22-2-2-2-2-2-2-222000000000000000022-2-2222-2-20000000000000000000000
χ20222222222-222-2-22-2-2-2-2-2-2-2220000000000000000-2-222-2-22220000000000000000000000
χ2122222222-22-2-222-2222-2-2-2-2-2-22222-2-2-2-200000000000000200220000-2-200000000000000
χ2222222222-22-2-222-2222-2-2-2-2-2-2-2-2-2-2222200000000000000200-2-200002200000000000000
χ2322222222-22-2-222-22-2-2-2-222222222222200000000000000-200-2-20000-2-200000000000000
χ2422222222-22-2-222-22-2-2-2-22222-2-2-2-2-2-2-2-200000000000000-2002200002200000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-222000000002i2i2i2i−2i−2i−2i−2i000000-200002i2i−2i−2i0000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-22200000000−2i−2i−2i−2i2i2i2i2i000000-20000−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-2000000002i2i2i2i−2i−2i−2i−2i00000020000−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-200000000−2i−2i−2i−2i2i2i2i2i000000200002i2i−2i−2i0000000000000000
χ292-222-2-2-222-22-22-2-22002-200000000000022-2-222-2-2000000000000000002i−2i0000002i−2i0000
χ302-222-2-2-222-22-22-2-22002-200000000000022-2-222-2-200000000000000000−2i2i000000−2i2i0000
χ312-222-2-2-222-22-22-2-22002-2000000000000-2-222-2-222000000000000000002i−2i000000−2i2i0000
χ322-222-2-2-222-22-22-2-22002-2000000000000-2-222-2-22200000000000000000−2i2i0000002i−2i0000
χ332-222-2-2-22-22-22-222-2002-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000000002-22i−2i00000000
χ342-222-2-2-22-22-22-222-2002-20000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000-22−2i2i00000000
χ352-222-2-2-22-22-22-222-2002-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000002-2−2i2i00000000
χ362-222-2-2-22-22-22-222-2002-2000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000-222i−2i00000000
χ372-22-222-2-220-2-200202i−2i002i−2i00i2i2−i2−i222−2−22−22−22−22−22-22i−2i000002−2i2−i2i2−i2i2−i200000000000000
χ382-22-222-2-220-2-200202i−2i002i−2i00i2i2−i2−i222−2−2−22−22−22−22-22−2i2i000002−2−i2i2−i2i2i2−i200000000000000
χ392-22-222-2-220-2-200202i−2i002i−2i00−i2−i2i2i2−2−2222−22−22−22−2-22−2i2i00000−22i2−i2i2−i2−i2i200000000000000
χ402-22-222-2-220-2-200202i−2i002i−2i00−i2−i2i2i2−2−222−22−22−22−222-22i−2i00000−22−i2i2−i2i2−i2i200000000000000
χ412-22-222-2-220-2-20020−2i2i00−2i2i00i2i2−i2−i2−2−2222−22−22−22−2-222i−2i00000−22−i2i2−i2i2i2−i200000000000000
χ422-22-222-2-220-2-20020−2i2i00−2i2i00i2i2−i2−i2−2−222−22−22−22−222-2−2i2i00000−22i2−i2i2−i2i2−i200000000000000
χ432-22-222-2-220-2-20020−2i2i00−2i2i00−i2−i2i2i222−2−22−22−22−22−22-2−2i2i000002−2−i2i2−i2i2−i2i200000000000000
χ442-22-222-2-220-2-20020−2i2i00−2i2i00−i2−i2i2i222−2−2−22−22−22−22-222i−2i000002−2i2−i2i2−i2−i2i200000000000000
χ452-22-222-2-2-202200-202i−2i00−2i2i00i2i2−i2−i2−2−222i2−i2i2−i2−i2i2−i2i200002-202i−2i2−2−222−2−i2i200000000000000
χ462-22-222-2-2-202200-202i−2i00−2i2i00i2i2−i2−i2−2−222−i2i2−i2i2i2−i2i2−i20000-220−2i2i2−22−2−22−i2i200000000000000
χ472-22-222-2-2-202200-202i−2i00−2i2i00−i2−i2i2i222−2−2i2−i2i2−i2−i2i2−i2i20000-220−2i2i−22−222−2i2−i200000000000000
χ482-22-222-2-2-202200-202i−2i00−2i2i00−i2−i2i2i222−2−2−i2i2−i2i2i2−i2i2−i200002-202i−2i−222−2−22i2−i200000000000000
χ492-22-222-2-2-202200-20−2i2i002i−2i00i2i2−i2−i222−2−2i2−i2i2−i2−i2i2−i2i200002-20−2i2i−222−2−22−i2i200000000000000
χ502-22-222-2-2-202200-20−2i2i002i−2i00i2i2−i2−i222−2−2−i2i2−i2i2i2−i2i2−i20000-2202i−2i−22−222−2−i2i200000000000000
χ512-22-222-2-2-202200-20−2i2i002i−2i00−i2−i2i2i2−2−222i2−i2i2−i2−i2i2−i2i20000-2202i−2i2−22−2−22i2−i200000000000000
χ522-22-222-2-2-202200-20−2i2i002i−2i00−i2−i2i2i2−2−222−i2i2−i2i2i2−i2i2−i200002-20−2i2i2−2−222−2i2−i200000000000000
χ53444-4-4-44-440-4400-40000000000000000022−22−222222−22−22220000000000000000000000000000000
χ54444-4-4-44-440-4400-400000000000000000−222222−22−222222−220000000000000000000000000000000
χ55444-4-4-44-4-404-4004000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000
χ56444-4-4-44-4-404-400400000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000
χ5744-4-44-4-440400-4-404000000004i−4i4i−4i0000000000000000000000000000000000000000000
χ5844-4-44-4-440400-4-40400000000−4i4i−4i4i0000000000000000000000000000000000000000000
χ5944-4-44-4-440-400440-40000000000004i−4i4i−4i000000000000000000000000000000000000000
χ6044-4-44-4-440-400440-4000000000000−4i4i−4i4i000000000000000000000000000000000000000
χ614-444-4-4-44444-4-44-4-400-44000000000000000000000000000000000000000000000000000
χ624-444-4-4-44-4-4-444-44400-44000000000000000000000000000000000000000000000000000
χ634-4-444-44-4000000000000004i−4i22−22−22222i2−2i2−2i22i2000000000000000000000000000000000000000
χ644-4-444-44-4000000000000004i−4i−222222−22−2i22i22i2−2i2000000000000000000000000000000000000000
χ654-4-444-44-400000000000000−4i4i22−22−2222−2i22i22i2−2i2000000000000000000000000000000000000000
χ664-4-444-44-400000000000000−4i4i−222222−222i2−2i2−2i22i2000000000000000000000000000000000000000
χ674-4-4-4-444404004-40-40000000000000000000000000000000000000000000000000002i2−2i200
χ684-4-4-4-444404004-40-4000000000000000000000000000000000000000000000000000−2i22i200
χ694-4-4-4-44440-400-44040000000000000000000000000000000000000000000000022−22000000
χ704-4-4-4-44440-400-440400000000000000000000000000000000000000000000000−2222000000
χ7188-88-88-8-8000000000000000000000000000000000000000000000000000000000000000

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