Finite Group Databasebeta

← Group #149777

Character table — Group #149777

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444444444444444444488881616161616163232323232323232
order12222222224444444444448888888888888888444422224488888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i
χ911111-1-1-1-111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11-11-11-1
χ1011111-1-1-1-111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-11-11-11
χ1111111-1-1-1-111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ1211111-1-1-1-111-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ1311111-1-1-1-111-1-11111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-111-1-11-1-111-1-11
χ1411111-1-1-1-111-1-11111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-111-1-1-111-1-111-1
χ1511111-1-1-1-111-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111i−i−ii−iii−i
χ1611111-1-1-1-111-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111−iii−ii−i−ii
χ172222222222222-2-2-2-2-2-2-2-22000000000000000022-2-200002-200000000
χ182222222222222-2-2-2-2-2-2-2-220000000000000000-2-2220000-2200000000
χ1922222-2-2-2-222-2-2-2-2-2-222222000000000000000022-2-20000-2200000000
χ2022222-2-2-2-222-2-2-2-2-2-2222220000000000000000-2-22200002-200000000
χ212-22-2-20000220022-2-20000-2000000002i2i2i2i−2i−2i−2i−2i2i−2i2i−2i002-20000000000
χ222-22-2-20000220022-2-20000-2000000002i2i2i2i−2i−2i−2i−2i−2i2i−2i2i00-220000000000
χ232-22-2-20000220022-2-20000-200000000−2i−2i−2i−2i2i2i2i2i2i−2i2i−2i00-220000000000
χ242-22-2-20000220022-2-20000-200000000−2i−2i−2i−2i2i2i2i2i−2i2i−2i2i002-20000000000
χ252-22-2-200002200-2-2220000-22i2i2i2i−2i−2i−2i−2i000000002i−2i−2i2i2-2000000000000
χ262-22-2-200002200-2-2220000-22i2i2i2i−2i−2i−2i−2i00000000−2i2i2i−2i-22000000000000
χ272-22-2-200002200-2-2220000-2−2i−2i−2i−2i2i2i2i2i000000002i−2i−2i2i-22000000000000
χ282-22-2-200002200-2-2220000-2−2i−2i−2i−2i2i2i2i2i00000000−2i2i2i−2i2-2000000000000
χ294444444444-4-4-400000000-40000000000000000000000000000000000
χ3044444-4-4-4-44-44400000000-40000000000000000000000000000000000
χ314444-444-4-4-400000000000022-2-222-2-222-2-222-2-2000000000000000000
χ324444-444-4-4-4000000000000-2-222-2-222-2-222-2-222000000000000000000
χ334444-4-4-444-400000000000022-2-222-2-2-2-222-2-222000000000000000000
χ344444-4-4-444-4000000000000-2-222-2-22222-2-222-2-2000000000000000000
χ3544-4-40004-400002-22-222-2-20002i2−2i2002i2−2i22i2−2i2002i2−2i200000000000000000000
χ3644-4-40004-400002-22-222-2-2000−2i22i200−2i22i2−2i22i200−2i22i200000000000000000000
χ3744-4-40004-40000-22-22-2-22202i2−2i2002i2−2i200002i2−2i2002i2−2i2000000000000000000
χ3844-4-40004-40000-22-22-2-2220−2i22i200−2i22i20000−2i22i200−2i22i2000000000000000000
χ3944-4-4000-4400002-22-2-2-2220002i2−2i2002i2−2i2−2i22i200−2i22i200000000000000000000
χ4044-4-4000-4400002-22-2-2-222000−2i22i200−2i22i22i2−2i2002i2−2i200000000000000000000
χ4144-4-4000-440000-22-2222-2-202i2−2i2002i2−2i20000−2i22i200−2i22i2000000000000000000
χ4244-4-4000-440000-22-2222-2-20−2i22i200−2i22i200002i2−2i2002i2−2i2000000000000000000
χ434-44-440000-404-40000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000
χ444-44-440000-404-4000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000
χ454-44-440000-40-440000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000
χ464-44-440000-40-44000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000
χ474-44-4-400004-40000004-44-440000000000000000000000000000000000
χ484-44-4-400004-4000000-44-4440000000000000000000000000000000000
χ494-4-4404-40000002-2-222-2-22022−2200−22220022−2200−222200000000000000000000
χ504-4-4404-40000002-2-222-2-220−22220022−2200−22220022−2200000000000000000000
χ514-4-4404-4000000-222-2-222-200022−2200−22220022−2200−2222000000000000000000
χ524-4-4404-4000000-222-2-222-2000−22220022−2200−22220022−22000000000000000000
χ534-4-440-440000002-2-22-222-2022−2200−222200−22220022−2200000000000000000000
χ544-4-440-440000002-2-22-222-20−22220022−220022−2200−222200000000000000000000
χ554-4-440-44000000-222-22-2-2200022−2200−222200−22220022−22000000000000000000
χ564-4-440-44000000-222-22-2-22000−22220022−220022−2200−2222000000000000000000

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