Finite Group Databasebeta

← Group #149772

Character table — Group #149772

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111222222444488888888888888881616161616163232323232323232
order12222222224444444444448888888844444488888888
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111111111-1-1-1-1-1-1ii−i−iii−i−i
χ6111111111111111111-1-1-1-111111111-1-1-1-1-1-1−i−iii−i−iii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ911111-1-1-1-111-1-1111-1-111111111-1-1-1-1-1-111-1-11-11-11-11-1
χ1011111-1-1-1-111-1-1111-1-111111111-1-1-1-1-1-111-1-1-11-11-11-11
χ1111111-1-1-1-111-1-1111-1-11111-1-1-1-11111-1-1-1-1111-11-1-11-11
χ1211111-1-1-1-111-1-1111-1-11111-1-1-1-11111-1-1-1-111-11-111-11-1
χ1311111-1-1-1-111-1-1111-1-1-1-1-1-11111-1-1-1-111-1-111i−i−iii−i−ii
χ1411111-1-1-1-111-1-1111-1-1-1-1-1-11111-1-1-1-111-1-111−iii−i−iii−i
χ1511111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1i−i−ii−iii−i
χ1611111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1−iii−ii−i−ii
χ1722222222222222-2-2-2-222-2-2000000002-2000000000000
χ1822222222222222-2-2-2-2-2-22200000000-22000000000000
χ1922222-2-2-2-222-2-22-2-22222-2-200000000-22000000000000
χ2022222-2-2-2-222-2-22-2-222-2-222000000002-2000000000000
χ212-2-22-200002200-22-2002i−2i2i−2i00002i2i−2i−2i00002-200000000
χ222-2-22-200002200-22-2002i−2i2i−2i0000−2i−2i2i2i0000-2200000000
χ232-2-22-200002200-22-200−2i2i−2i2i00002i2i−2i−2i0000-2200000000
χ242-2-22-200002200-22-200−2i2i−2i2i0000−2i−2i2i2i00002-200000000
χ252-2-22-200002200-2-22002i−2i−2i2i2i2i−2i−2i0000002-20000000000
χ262-2-22-200002200-2-22002i−2i−2i2i−2i−2i2i2i000000-220000000000
χ272-2-22-200002200-2-2200−2i2i2i−2i2i2i−2i−2i000000-220000000000
χ282-2-22-200002200-2-2200−2i2i2i−2i−2i−2i2i2i0000002-20000000000
χ294444444444-4-4-4-4000000000000000000000000000000
χ3044444-4-4-4-44-444-4000000000000000000000000000000
χ314444-444-4-4-40000000000002-22-22-22-200000000000000
χ324444-444-4-4-4000000000000-22-22-22-2200000000000000
χ334444-4-4-444-40000000000002-22-2-22-2200000000000000
χ344444-4-4-444-4000000000000-22-222-22-200000000000000
χ354-4-4440000-404-40000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ364-4-4440000-404-4000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ374-4-4440000-40-440000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ384-4-4440000-40-44000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ394-4-44-400004-4004004-400000000000000000000000000
χ404-4-44-400004-400400-4400000000000000000000000000
χ4188-8-80008-800000000000000000000000000000000000
χ4288-8-8000-8800000000000000000000000000000000000
χ438-88-808-80000000000000000000000000000000000000
χ448-88-80-880000000000000000000000000000000000000

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