Finite Group Databasebeta

← Group #139521

Character table — Group #139521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222222444444888888888881616161616161616161616161616161632323232
order12222222222244442444444444422444444444444448888
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ4111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-1111-1-1111111-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111-1-1-1-1111-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-111
χ7111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111
χ8111111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1
χ91111111111-1-111-1-1-1111-11111-1-111-11-1-1-1-1ii−i−iii−i−ii−ii−i
χ101111111111-1-111-1-1-1111-11111-1-111-11-1-1-1-1−i−iii−i−iii−ii−ii
χ111111111111-1-111-1-1-1111-1-1-1-1-1-1-1-1-1-111111ii−i−iii−i−i−ii−ii
χ121111111111-1-111-1-1-1111-1-1-1-1-1-1-1-1-1-111111−i−iii−i−iiii−ii−i
χ131111111111-1-1-1-111-111-111111-1-1-1-11-1-1-111ii−i−i−i−iiii−i−ii
χ141111111111-1-1-1-111-111-111111-1-1-1-11-1-1-111−i−iiiii−i−i−iii−i
χ151111111111-1-1-1-111-111-11-1-1-1-1-1-1111-111-1-1ii−i−i−i−iii−iii−i
χ161111111111-1-1-1-111-111-11-1-1-1-1-1-1111-111-1-1−i−iiiii−i−ii−i−ii
χ1722222222222222222-2-2220000-2-200-2-20000000000000000
χ18222222222222-2-2-2-22-2-2-2-20000-2-200220000000000000000
χ192222222222-2-222-2-2-2-2-22-2000022002-20000000000000000
χ202222222222-2-2-2-222-2-2-2-2200002200-220000000000000000
χ2122222-2-22-2-2220000-22-20000002-20000000000002-22-20000
χ2222222-2-22-2-2220000-22-20000002-2000000000000-22-220000
χ2322222-2-22-2-2220000-2-22000000-22000000002-22-200000000
χ2422222-2-22-2-2220000-2-22000000-2200000000-22-2200000000
χ2522222-2-22-2-2-2-2000022-2000000-220000000000002i−2i−2i2i0000
χ2622222-2-22-2-2-2-2000022-2000000-22000000000000−2i2i2i−2i0000
χ2722222-2-22-2-2-2-200002-220000002-2000000002i−2i−2i2i00000000
χ2822222-2-22-2-2-2-200002-220000002-200000000−2i2i2i−2i00000000
χ294444-44-4-44-40000440000-400000000000000000000000000
χ304444-44-4-44-40000-4-40000400000000000000000000000000
χ314444-4-44-4-44004400000-4000000000000000000000000000
χ324444-4-44-4-4400-4-4000004000000000000000000000000000
χ3344-4-4-4004004-40000000002i2i−2i−2i0000002i−2i00000000000000
χ3444-4-4-4004004-4000000000−2i−2i2i2i000000−2i2i00000000000000
χ3544-4-4-400400-440000000002i2i−2i−2i000000−2i2i00000000000000
χ3644-4-4-400400-44000000000−2i−2i2i2i0000002i−2i00000000000000
χ374-44-40400-4000004i−4i000002i−2i2i−2i000000002-2000000000000
χ384-44-40400-4000004i−4i00000−2i2i−2i2i00000000-22000000000000
χ394-44-40400-400000−4i4i000002i−2i2i−2i00000000-22000000000000
χ404-44-40400-400000−4i4i00000−2i2i−2i2i000000002-2000000000000
χ414-4-4400-4004004-400000002-2-22002-2000000000000000000
χ424-4-4400-4004004-40000000-222-200-22000000000000000000
χ434-4-4400-400400-4400000002-2-2200-22000000000000000000
χ444-4-4400-400400-440000000-222-2002-2000000000000000000
χ4588-8-8800-8000000000000000000000000000000000000000
χ468-88-80-800800000000000000000000000000000000000000
χ478-8-8800800-80000000000000000000000000000000000000

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