Finite Group Databasebeta

← Group #296234

Character table — Group #296234

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444488888888888888888888888888888161616161616161616163232
order12222222444444444444444422444444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-11-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1111111
χ5111111111111111111111111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1
χ7111111111111111111111111-1-1-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ8111111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ911111111111111111-1-1-1-1-1-1111-1-1-111-1-111111111-1-1-1-11111-1-1-1-11-1-11-1-111-1-11-1
χ1011111111111111111-1-1-1-1-1-1111-1-1-111-1-11111-1-1-1-11111-1-1-1-111111-1-11-1-1-1-111-11
χ1111111111111111111-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-11
χ1211111111111111111-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-11-1
χ1311111111111111111-1-1-1-1-1-11-1-111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1111-1
χ1411111111111111111-1-1-1-1-1-11-1-111-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-11
χ1511111111111111111-1-1-1-1-1-11-1-111-1-1-11111111111-1-1-1-1-1-1-1-11111-111-1-1-111-1-1-11
χ1611111111111111111-1-1-1-1-1-11-1-111-1-1-1111111-1-1-1-111111111-1-1-1-1-111-1-1-1-1-1111-1
χ172222222222-2-222-2-2-22222-2-2-20000-222-2-200000000000000000000020-200000000
χ182222222222-2-222-2-2-22222-2-2-20000-2-2-222000000000000000000000-20200000000
χ192222222222-2-222-2-2-2-2-2-2-222-2000022222000000000000000000000-20-200000000
χ202222222222-2-222-2-2-2-2-2-2-222-200002-2-2-2-200000000000000000000020200000000
χ2122222222-2-222-2-222-222-2-2-2-2-222-2-22000000000000000000000000-202000000000
χ2222222222-2-222-2-222-222-2-2-2-2-2-2-222200000000000000000000000020-2000000000
χ2322222222-2-222-2-222-2-2-22222-22222-2000000000000000000000000-20-2000000000
χ2422222222-2-222-2-222-2-2-22222-2-2-2-2-2-2000000000000000000000000202000000000
χ2522222222-2-2-2-2-2-2-2-2222-2-22220000-2000022-2-2000000000000000000002-2000000
χ2622222222-2-2-2-2-2-2-2-2222-2-22220000-20000-2-22200000000000000000000-22000000
χ2722222222-2-2-2-2-2-2-2-22-2-222-2-2200002000022-2-200000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-22-2-222-2-22000020000-2-222000000000000000000002-2000000
χ29222-22-2-2-22-22-22-22-2-200000020000000002i−2i2i−2i000022-2-200000000000000002i−2i00
χ30222-22-2-2-22-22-22-22-2-200000020000000002i−2i2i−2i0000-2-2220000000000000000−2i2i00
χ31222-22-2-2-22-22-22-22-2-20000002000000000−2i2i−2i2i000022-2-20000000000000000−2i2i00
χ32222-22-2-2-22-22-22-22-2-20000002000000000−2i2i−2i2i0000-2-22200000000000000002i−2i00
χ33222-22-2-2-2-22-22-22-22-200000020000000002i−2i−2i2i22-2-20000000000000000002i−2i0000
χ34222-22-2-2-2-22-22-22-22-200000020000000002i−2i−2i2i-2-222000000000000000000−2i2i0000
χ35222-22-2-2-2-22-22-22-22-20000002000000000−2i2i2i−2i22-2-2000000000000000000−2i2i0000
χ36222-22-2-2-2-22-22-22-22-20000002000000000−2i2i2i−2i-2-2220000000000000000002i−2i0000
χ372-2-2222-2-2002-200-220002i−2i2i−2i02-22i−2i0000000002−22−2i2−i2i2−i222−2−2i2i2−i2−i2000000000000
χ382-2-2222-2-2002-200-220002i−2i2i−2i02-22i−2i000000000−22−22−i2i2−i2i2−2−222−i2−i2i2i2000000000000
χ392-2-2222-2-2002-200-220002i−2i2i−2i0-22−2i2i0000000002−22−2i2−i2i2−i2−2−222−i2−i2i2i2000000000000
χ402-2-2222-2-2002-200-220002i−2i2i−2i0-22−2i2i000000000−22−22−i2i2−i2i222−2−2i2i2−i2−i2000000000000
χ412-2-2222-2-2002-200-22000−2i2i−2i2i02-2−2i2i0000000002−22−2−i2i2−i2i222−2−2−i2−i2i2i2000000000000
χ422-2-2222-2-2002-200-22000−2i2i−2i2i02-2−2i2i000000000−22−22i2−i2i2−i2−2−222i2i2−i2−i2000000000000
χ432-2-2222-2-2002-200-22000−2i2i−2i2i0-222i−2i0000000002−22−2−i2i2−i2i2−2−222i2i2−i2−i2000000000000
χ442-2-2222-2-2002-200-22000−2i2i−2i2i0-222i−2i000000000−22−22i2−i2i2−i222−2−2−i2−i2i2i2000000000000
χ45444-44-4-4-44-4-444-4-444000000-400000000000000000000000000000000000000000
χ46444-44-4-4-4-444-4-444-44000000-400000000000000000000000000000000000000000
χ4744-44-4-44-44400-4-40000000000000004-40000000000000000000000000000000000
χ4844-44-4-44-44400-4-4000000000000000-440000000000000000000000000000000000
χ4944-44-4-44-4-4-40044000000000000000004i−4i00000000000000000000000000000000
χ5044-44-4-44-4-4-4004400000000000000000−4i4i00000000000000000000000000000000
χ5144-4-4-44-444-400-44000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ5244-4-4-44-444-400-4400000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ5344-4-4-44-44-44004-400000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ5444-4-4-44-44-44004-40000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ554-44-4-444-40000000004i−4i000000000000000000000000002i−2i−2i2i2-2-22000000000000
χ564-44-4-444-40000000004i−4i00000000000000000000000000−2i2i2i−2i-222-2000000000000
χ574-44-4-444-4000000000−4i4i000000000000000000000000002i−2i−2i2i-222-2000000000000
χ584-44-4-444-4000000000−4i4i00000000000000000000000000−2i2i2i−2i2-2-22000000000000
χ594-4-4444-4-400-44004-40004i−4i−4i4i000000000000000000000000000000000000000000
χ604-4-4444-4-400-44004-4000−4i4i4i−4i000000000000000000000000000000000000000000
χ614-4-4-44-444004400-4-400000000000000000000000002i2−2i2−2i22i200000000000000000000
χ624-4-4-44-444004400-4-40000000000000000000000000−2i22i22i2−2i200000000000000000000
χ634-4-4-44-44400-4-4004400000000000000000000022−22−2222000000000000000000000000
χ644-4-4-44-44400-4-40044000000000000000000000−222222−22000000000000000000000000
χ658-888-8-8-88000000000000000000000000000000000000000000000000000000000

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