Finite Group Databasebeta

← Group #152696

Character table — Group #152696

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222244444448888888881616161616161616161616161616161616161616163232
order12222222244444444444444424444888888888888888888
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-11-1-1-1-1-1-1-1-1-111111111-1-1
χ5111111111-1-111-1-1111-1-1-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ6111111111-1-111-1-1111-1-1-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ7111111111-1-111-1-1111-1-1-1-1-1-1-1-1-11-1iiii−i−i−i−i−i−i−i−iiiii11
χ8111111111-1-111-1-1111-1-1-1-1-1-1-1-1-11-1−i−i−i−iiiiiiiii−i−i−i−i11
χ911111-1-11-111111111-11-1-1-1-111-1-1-1111-1-111-1-111-1-111-1-11-1
χ1011111-1-11-111111111-11-1-1-1-111-1-1-11-1-111-1-111-1-111-1-1111-1
χ1111111-1-11-111111111-11-1-1-1-11-111-1-111-1-111-1-1-1-111-1-111-11
χ1211111-1-11-111111111-11-1-1-1-11-111-1-1-1-111-1-11111-1-111-1-1-11
χ1311111-1-11-1-1-111-1-111-1-11111-11-1-1-11ii−i−i−i−iiiii−i−i−i−iii-11
χ1411111-1-11-1-1-111-1-111-1-11111-11-1-1-11−i−iiiii−i−i−i−iiiii−i−i-11
χ1511111-1-11-1-1-111-1-111-1-11111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i1-1
χ1611111-1-11-1-1-111-1-111-1-11111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii1-1
χ17222222222222222-2-22-2-2-222-2000-20000000000000000000
χ18222222222-2-222-2-2-2-22222-2-22000-20000000000000000000
χ1922222-2-22-2222222-2-2-2-222-2-2-200020000000000000000000
χ2022222-2-22-2-2-222-2-2-2-2-22-2-222200020000000000000000000
χ212-2-22-200202-22-22-22-2020000-20000000000000002i−2i002i−2i00
χ222-2-22-200202-22-22-22-2020000-2000000000000000−2i2i00−2i2i00
χ232-2-22-200202-22-22-2-220-20000200000000000002-2002-20000
χ242-2-22-200202-22-22-2-220-2000020000000000000-2200-220000
χ252-2-22-20020-222-2-222-20-2000020000000000000002-200-2200
χ262-2-22-20020-222-2-222-20-200002000000000000000-22002-200
χ272-2-22-20020-222-2-22-22020000-200000000000002i−2i00−2i2i0000
χ282-2-22-20020-222-2-22-22020000-20000000000000−2i2i002i−2i0000
χ2944444444400-4-40000-400000000000000000000000000000
χ3044444-4-44-400-4-40000400000000000000000000000000000
χ314444-444-4-400000000000000022-20-2000000000000000000
χ324444-444-4-4000000000000000-2-2202000000000000000000
χ334444-4-4-4-440000000000000002-220-2000000000000000000
χ344444-4-4-4-44000000000000000-22-202000000000000000000
χ3544-4-404-4002200-2-20000002-20000002−22−22−22−20000000000
χ3644-4-404-4002200-2-20000002-2000000−22−22−22−220000000000
χ3744-4-404-400-2-20022000000-22000000i2−i2i2−i2−i2i2−i2i20000000000
χ3844-4-404-400-2-20022000000-22000000−i2i2−i2i2i2−i2i2−i20000000000
χ3944-4-40-44002200-2-2000000-220000002−2−222−2−220000000000
χ4044-4-40-44002200-2-2000000-22000000−222−2−222−20000000000
χ4144-4-40-4400-2-200220000002-2000000i2−i2−i2i2−i2i2i2−i20000000000
χ4244-4-40-4400-2-200220000002-2000000−i2i2i2−i2i2−i2−i2i20000000000
χ434-4-44-4004000-440000004-400000000000000000000000000
χ444-4-44-4004000-44000000-4400000000000000000000000000
χ458-88-8000004-400-4400000000000000000000000000000000
χ468-88-800000-44004-400000000000000000000000000000000
χ478-8-88800-8000000000000000000000000000000000000000

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