Finite Group Databasebeta

← Group #100415

Character table — Group #100415

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222222244444444444444444444444444444448888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-111-1-111-1-111-1-1-1-111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1-1-111-1-111-1-111-1-1-1-111111-1-1-1-1ii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−iii-1-111-11
χ1111111111-1-1-1-111-1-111-1-111-1-1-1-111111-1-1-1-1−i−iii−i−iiiiiii−i−i−i−i−i−iiiii−i−i-1-111-11
χ1211111111-1-1-1-111-1-111-1-111-1-1-1-111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii−i−iii11-1-11-1
χ1311111111-1-1-1-111-1-111-1-111-1-1-1-11-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−i−i−iii−i−iii11-1-1-11
χ1411111111-1-1-1-111-1-111-1-111-1-1-1-11-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii−i−iiiii−i−i-1-1111-1
χ1511111111-1-1-1-111-1-111-1-111-1-1-1-11-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−iii−i−i−i−iii-1-1111-1
χ1611111111-1-1-1-111-1-111-1-111-1-1-1-11-1-1-1-11111−i−iii−i−iii−i−i−i−iiiiiii−i−iii−i−i11-1-1-11
χ1722222222222222-2-222-2-2-2-222-2-2-222-2-222-2-2000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-222-2-2-2-2-222-2-222000000000000000000000000000000
χ19222222222222-2-222-2-22222-2-2-2-2-2000000002222-2-2-2-20000000000000000000000
χ20222222222222-2-222-2-22222-2-2-2-2-200000000-2-2-2-222220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22220000000000000000000000002-22-20000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-2222000000000000000000000000-22-220000000000
χ2322222222-2-2-2-222222222-2-2-2-222-222-2-2-2-222000000000000000000000000000000
χ2422222222-2-2-2-222222222-2-2-2-222-2-2-22222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-222-2-222-2-220000000000000000000000002i−2i−2i2i0000000000
χ2622222222-2-2-2-2-2-222-2-222-2-222-2-22000000000000000000000000−2i2i2i−2i0000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ29222-2-22-2-222-2-22200-2-200002-2000002-2002-20000000022−2−222−2−200002−22−2000000
χ30222-2-22-2-222-2-22200-2-200002-2000002-2002-200000000−2−222−2−2220000−22−22000000
χ31222-2-22-2-222-2-22200-2-200002-200000-2200-220000000022−2−222−2−20000−22−22000000
χ32222-2-22-2-222-2-22200-2-200002-200000-2200-2200000000−2−222−2−22200002−22−2000000
χ33222-2-22-2-2-2-2222200-2-20000-22000002-200-2200000000i2i2−i2−i2−i2−i2i2i20000i2−i2−i2i2000000
χ34222-2-22-2-2-2-2222200-2-20000-22000002-200-2200000000−i2−i2i2i2i2i2−i2−i20000−i2i2i2−i2000000
χ35222-2-22-2-2-2-2222200-2-20000-2200000-22002-200000000i2i2−i2−i2−i2−i2i2i20000−i2i2i2−i2000000
χ36222-2-22-2-2-2-2222200-2-20000-2200000-22002-200000000−i2−i2i2i2i2i2−i2−i20000i2−i2−i2i2000000
χ3722-2-22-22-22-22-200-2-200222-200000000000002-22-20000i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i200
χ3822-2-22-22-22-22-200-2-200222-200000000000002-22-20000−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i200
χ3922-2-22-22-22-22-200-2-200222-20000000000000-22-220000i2−i2i2−i2i2−i2i2−i200000000−i2i2−i2i200
χ4022-2-22-22-22-22-200-2-200222-20000000000000-22-220000−i2i2−i2i2−i2i2−i2i200000000i2−i2i2−i200
χ4122-2-22-22-2-22-22002200-2-22-200000000000002i−2i−2i2i00002−22−2−22−2200000000−i2i2i2−i200
χ4222-2-22-22-2-22-22002200-2-22-200000000000002i−2i−2i2i0000−22−222−22−200000000i2−i2−i2i200
χ4322-2-22-22-2-22-22002200-2-22-20000000000000−2i2i2i−2i00002−22−2−22−2200000000i2−i2−i2i200
χ4422-2-22-22-2-22-22002200-2-22-20000000000000−2i2i2i−2i0000−22−222−22−200000000−i2i2i2−i200
χ45444-4-44-4-444-4-4-4-400440000-4400000000000000000000000000000000000000000
χ46444-4-44-4-4-4-444-4-4004400004-400000000000000000000000000000000000000000
χ4744-44-4-4-444-4-4400000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ4844-44-4-4-444-4-440000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ4944-44-4-4-44-444-400000000000000000000000000000002-2-22-222-200000000000000
χ5044-44-4-4-44-444-40000000000000000000000000000000-222-22-2-2200000000000000
χ5144-4-44-44-44-44-4004400-4-4-440000000000000000000000000000000000000000000
χ5244-4-44-44-4-44-4400-4-40044-440000000000000000000000000000000000000000000
χ534-44-44-4-440000004i−4i004i−4i00000000000000000002+2i−2−2i2−2i−2+2i0000000000000000000000
χ544-44-44-4-440000004i−4i004i−4i0000000000000000000−2−2i2+2i−2+2i2−2i0000000000000000000000
χ554-44-44-4-44000000−4i4i00−4i4i00000000000000000002−2i−2+2i2+2i−2−2i0000000000000000000000
χ564-44-44-4-44000000−4i4i00−4i4i0000000000000000000−2+2i2−2i−2−2i2+2i0000000000000000000000
χ574-4-4444-4-400004-44i−4i4-4−4i4i00004i−4i000000000000000000000000000000000000000
χ584-4-4444-4-400004-4−4i4i4-44i−4i0000−4i4i000000000000000000000000000000000000000
χ594-4-4444-4-40000-444i−4i-44−4i4i0000−4i4i000000000000000000000000000000000000000
χ604-4-4444-4-40000-44−4i4i-444i−4i00004i−4i000000000000000000000000000000000000000
χ614-4-4-4-444400004-400-440000000004-4000000000000000000000000000000000000
χ624-4-4-4-444400004-400-44000000000-44000000000000000000000000000000000000
χ634-4-4-4-44440000-44004-400000000000004-400000000000000000000000000000000
χ644-4-4-4-44440000-44004-40000000000000-4400000000000000000000000000000000
χ658-888-8-88-8000000000000000000000000000000000000000000000000000000000

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