Finite Group Databasebeta

← Group #296755

Character table — Group #296755

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444444444444422224444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ91111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-1-11111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-111-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1111-1-111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-111111-111-1-1-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-11-111-1-111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11111-11-1-11111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111-1-1111-1
χ172222222222-2-222-2-222-2-2-2-2222222-2-2220000-2-2-2-20000000000000000000000000000
χ182222222222-2-222-2-222-2-2-2-222-2-2-2-2-2-2-2-2000022220000000000000000000000000000
χ192222222222-2-222-2-2-2-22222-2-22222-2-2-2-2000022-2-20000000000000000000000000000
χ202222222222-2-222-2-2-2-22222-2-2-2-2-2-2-2-2220000-2-2220000000000000000000000000000
χ2122222222-2-222-2-2222222-2-2-2-20000-2-20022-2-200000000000000000000-220000000000
χ2222222222-2-222-2-2222222-2-2-2-20000-2-200-2-222000000000000000000002-20000000000
χ2322222222-2-222-2-222-2-2-2-222220000-2-200222200000000000000000000-2-20000000000
χ2422222222-2-222-2-222-2-2-2-222220000-2-200-2-2-2-200000000000000000000220000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-2-200002200000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-2-20000220000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-22200002200000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2220000220000000000000000000000000000-222-2000000
χ29222-2-2-2-222-2002-200002i−2i2i−2i0022-2-2000000002i−2i00i2i2−i2−i222−2−2i2i2−i2−i222−2−2000000000000
χ30222-2-2-2-222-2002-200002i−2i2i−2i0022-2-2000000002i−2i00−i2−i2i2i2−2−222−i2−i2i2i2−2−222000000000000
χ31222-2-2-2-222-2002-200002i−2i2i−2i00-2-22200000000−2i2i00i2i2−i2−i222−2−2−i2−i2i2i2−2−222000000000000
χ32222-2-2-2-222-2002-200002i−2i2i−2i00-2-22200000000−2i2i00−i2−i2i2i2−2−222i2i2−i2−i222−2−2000000000000
χ33222-2-2-2-222-2002-20000−2i2i−2i2i0022-2-200000000−2i2i00i2i2−i2−i2−2−222i2i2−i2−i2−2−222000000000000
χ34222-2-2-2-222-2002-20000−2i2i−2i2i0022-2-200000000−2i2i00−i2−i2i2i222−2−2−i2−i2i2i222−2−2000000000000
χ35222-2-2-2-222-2002-20000−2i2i−2i2i00-2-222000000002i−2i00i2i2−i2−i2−2−222−i2−i2i2i222−2−2000000000000
χ36222-2-2-2-222-2002-20000−2i2i−2i2i00-2-222000000002i−2i00−i2−i2i2i222−2−2i2i2−i2−i2−2−222000000000000
χ372-2222-2-2-2-2-22-2222-2000000002i−2i2i−2i2-2000000002i−2i00002i−2i2i−2i00002-22-2000000000000
χ382-2222-2-2-2-2-22-2222-2000000002i−2i2i−2i2-2000000002i−2i0000−2i2i−2i2i0000-22-22000000000000
χ392-2222-2-2-2-2-22-2222-200000000−2i2i−2i2i2-200000000−2i2i00002i−2i2i−2i0000-22-22000000000000
χ402-2222-2-2-2-2-22-2222-200000000−2i2i−2i2i2-200000000−2i2i0000−2i2i−2i2i00002-22-2000000000000
χ412-2222-2-2-2-2-2-2222-22000000002i−2i2i−2i-2200000000−2i2i2i−2i2i−2i00002-22-20000000000000000
χ422-2222-2-2-2-2-2-2222-22000000002i−2i2i−2i-2200000000−2i2i−2i2i−2i2i0000-22-220000000000000000
χ432-2222-2-2-2-2-2-2222-2200000000−2i2i−2i2i-22000000002i−2i2i−2i2i−2i0000-22-220000000000000000
χ442-2222-2-2-2-2-2-2222-2200000000−2i2i−2i2i-22000000002i−2i−2i2i−2i2i00002-22-20000000000000000
χ452-22-2-222-2-22002-2002i−2i00002i−2i2i−2i−2i2i002-2000000002−2−22i2−i2−i2i2−i2i2i2−i22−2−22000000000000
χ462-22-2-222-2-22002-2002i−2i00002i−2i2i−2i−2i2i002-200000000−222−2−i2i2i2−i2i2−i2−i2i2−222−2000000000000
χ472-22-2-222-2-22002-2002i−2i00002i−2i−2i2i2i−2i00-22000000002−2−22i2−i2−i2i2i2−i2−i2i2−222−2000000000000
χ482-22-2-222-2-22002-2002i−2i00002i−2i−2i2i2i−2i00-2200000000−222−2−i2i2i2−i2−i2i2i2−i22−2−22000000000000
χ492-22-2-222-2-22002-200−2i2i0000−2i2i2i−2i−2i2i00-22000000002−2−22−i2i2i2−i2−i2i2i2−i2−222−2000000000000
χ502-22-2-222-2-22002-200−2i2i0000−2i2i2i−2i−2i2i00-2200000000−222−2i2−i2−i2i2i2−i2−i2i22−2−22000000000000
χ512-22-2-222-2-22002-200−2i2i0000−2i2i−2i2i2i−2i002-2000000002−2−22−i2i2i2−i2i2−i2−i2i22−2−22000000000000
χ522-22-2-222-2-22002-200−2i2i0000−2i2i−2i2i2i−2i002-200000000−222−2i2−i2−i2i2−i2i2i2−i2−222−2000000000000
χ53444-4-4-4-44-4400-4400004i−4i−4i4i0000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4400-440000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ5544-4-444-4-4004400-4-400000000000000004-40000000000000000000000000000000000
χ5644-4-444-4-4004400-4-40000000000000000-440000000000000000000000000000000000
χ5744-4-444-4-400-4-400440000000000000000004i−4i00000000000000000000000000000000
χ5844-4-444-4-400-4-40044000000000000000000−4i4i00000000000000000000000000000000
χ594-4444-4-4-4444-4-4-44-4000000000000-4400000000000000000000000000000000000000
χ604-4444-4-4-444-44-4-4-440000000000004-400000000000000000000000000000000000000
χ614-44-4-444-44-400-44004i−4i0000−4i4i00000000000000000000000000000000000000000000
χ624-44-4-444-44-400-4400−4i4i00004i−4i00000000000000000000000000000000000000000000
χ634-4-4-44-444004-400-4400000000000000000000000000000000000000000000000022−2200
χ644-4-4-44-444004-400-44000000000000000000000000000000000000000000000000−222200
χ654-4-4-44-44400-44004-4000000000000000000000000000000000000000000000022−220000
χ664-4-4-44-44400-44004-40000000000000000000000000000000000000000000000−22220000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-88-88-88000000000000000000000000000000000000000000000000000000000000

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