Finite Group Databasebeta

← Group #149751

Character table — Group #149751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888888888881616161616161616161616161632323232
order12222222244444444222244444444444448888888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-111111111-1-1-1-1
χ411111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ6111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ7111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ8111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ911111-1-11-11-1-11111111-1-111-1-111-1-1-1-111-111-1-111-1-111-1-11-11-1
χ1011111-1-11-11-1-11111111-1-111-1-111-1-1-1-111-111-1-1-1-111-1-111-11-11
χ1111111-1-11-11-1-111111-1-11111-1-1-1-111-1-111-1-1-11111-1-111-1-1-11-11
χ1211111-1-11-11-1-111111-1-11111-1-1-1-111-1-111-1-1-111-1-111-1-1111-11-1
χ1311111-1-11-11-1-1-1-11-1-111-1-111-1-111-1-111-1-11-1-111ii−i−i−i−iiii−i−ii
χ1411111-1-11-11-1-1-1-11-1-111-1-111-1-111-1-111-1-11-1-111−i−iiiii−i−i−iii−i
χ1511111-1-11-11-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1111-1-1ii−i−i−i−iii−iii−i
χ1611111-1-11-11-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1111-1-1−i−iiiii−i−ii−i−ii
χ17222222222222222220000-2-2-2-2000022-2-2-20000000000000000
χ18222222222222-2-22-2-20000-2-2-2-20000-2-22220000000000000000
χ1922222-2-22-22-2-2222220000-2-2220000-2-2-2-220000000000000000
χ2022222-2-22-22-2-2-2-22-2-20000-2-22200002222-20000000000000000
χ212-2-22200-202002i−2i-22i−2i002-22-200002-2002i−2i0002i−2i000000000000
χ222-2-22200-202002i−2i-22i−2i00-222-20000-22002i−2i000−2i2i000000000000
χ232-2-22200-202002i−2i-22i−2i2-200-22002-20000−2i2i02i−2i00000000000000
χ242-2-22200-202002i−2i-22i−2i-2200-2200-220000−2i2i0−2i2i00000000000000
χ252-2-22200-20200−2i2i-2−2i2i002-22-200002-200−2i2i000−2i2i000000000000
χ262-2-22200-20200−2i2i-2−2i2i00-222-20000-2200−2i2i0002i−2i000000000000
χ272-2-22200-20200−2i2i-2−2i2i2-200-22002-200002i−2i0−2i2i00000000000000
χ282-2-22200-20200−2i2i-2−2i2i-2200-2200-2200002i−2i02i−2i00000000000000
χ29444444444-4-4-400-400000000000000000000000000000000000
χ3044444-4-44-4-44400-400000000000000000000000000000000000
χ314444-444-4-40000000022220000-2-2-2-2000000000000000000000
χ324444-444-4-400000000-2-2-2-200002222000000000000000000000
χ334444-4-4-4-440000000022-2-20000-2-222000000000000000000000
χ344444-4-4-4-4400000000-2-222000022-2-2000000000000000000000
χ3544-4-404-400000220-2-20000000000002-200000002−22−22−22−20000
χ3644-4-404-400000220-2-20000000000002-20000000−22−22−22−220000
χ3744-4-404-400000-2-2022000000000000-220000000i2−i2i2−i2−i2i2−i2i20000
χ3844-4-404-400000-2-2022000000000000-220000000−i2i2−i2i2i2−i2i2−i20000
χ3944-4-40-4400000220-2-2000000000000-2200000002−2−222−2−220000
χ4044-4-40-4400000220-2-2000000000000-220000000−222−2−222−20000
χ4144-4-40-4400000-2-20220000000000002-20000000i2−i2−i2i2−i2i2i2−i20000
χ4244-4-40-4400000-2-20220000000000002-20000000−i2i2i2−i2i2−i2−i2i20000
χ434-4-44400-40-400004000000004-40000000000000000000000000
χ444-4-44400-40-40000400000000-440000000000000000000000000
χ454-4-44-4004004-4000002-22-20000-22-22000000000000000000000
χ464-4-44-4004004-400000-22-2200002-22-2000000000000000000000
χ474-4-44-400400-44000002-2-220000-222-2000000000000000000000
χ484-4-44-400400-4400000-222-200002-2-22000000000000000000000
χ498-88-8000000004i−4i0−4i4i000000000000000000000000000000000
χ508-88-800000000−4i4i04i−4i000000000000000000000000000000000

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