Finite Group Databasebeta

← Group #296973

Character table — Group #296973

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444444442244444444888888888888888844444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ4111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ51111111111111111111111-1-11-1-1111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ71111111111111111111111-1-11-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ81111111111111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ91111111111111111-1-1-1-11111-1-1-111-1111111-1-1-1-11111-1-1-1-11-1-1-111-1-111-1-11-1
χ101111111111111111-1-1-1-11111-1-1-111-111-1-1-1-11111-1-1-1-111111-1-1-111-1-1-1-111-11
χ111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-111-1-111-1-1111-1
χ121111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-111-1-11111-1-1-11
χ131111111111111111-1-1-1-111-1-1-11111-1111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1-111-11
χ141111111111111111-1-1-1-111-1-1-11111-111-1-1-1-11111-1-1-1-11111-11-1-1-1-11111-1-11-1
χ151111111111111111-1-1-1-111-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111111-1-111-1-1-11
χ161111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111111-1-1-1-1111-1
χ172222222222-2-2-222-22222-2-222-22200-2000000000000000000-2-2000000000000
χ182222222222-2-2-222-22222-2-2-2-2-2-2-200-200000000000000000022000000000000
χ192222222222-2-2-222-2-2-2-2-2-2-2222-2-2002000000000000000000-22000000000000
χ202222222222-2-2-222-2-2-2-2-2-2-2-2-22220020000000000000000002-2000000000000
χ2122222222-2-2222-2-2222-2-2-2-20020022-2-2-20000000000000000002-20000000000
χ2222222222-2-2222-2-2222-2-2-2-200200-2-2-222000000000000000000-220000000000
χ2322222222-2-2222-2-22-2-222-2-200-200222-2-2000000000000000000-220000000000
χ2422222222-2-2222-2-22-2-222-2-200-200-2-22220000000000000000002-20000000000
χ2522222222-2-2-2-2-2-2-2-222-2-22200-20000200000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-22200-2000020000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220020000-200000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220020000-20000000000000000000000-222-2000000
χ2922-222-2-2-22-22-2-22-2200002-2000002i−2i02i−2i00002i2i−2i−2i000022-2-200000000000000
χ3022-222-2-2-22-22-2-22-2200002-2000002i−2i02i−2i0000−2i−2i2i2i0000-2-22200000000000000
χ3122-222-2-2-22-22-2-22-2200002-200000−2i2i0−2i2i00002i2i−2i−2i0000-2-22200000000000000
χ3222-222-2-2-22-22-2-22-2200002-200000−2i2i0−2i2i0000−2i−2i2i2i000022-2-200000000000000
χ3322-222-2-2-2-222-2-2-2220000-22000002i−2i0−2i2i2i2i−2i−2i000022-2-2000000000000000000
χ3422-222-2-2-2-222-2-2-2220000-22000002i−2i0−2i2i−2i−2i2i2i0000-2-222000000000000000000
χ3522-222-2-2-2-222-2-2-2220000-2200000−2i2i02i−2i2i2i−2i−2i0000-2-222000000000000000000
χ3622-222-2-2-2-222-2-2-2220000-2200000−2i2i02i−2i−2i−2i2i2i000022-2-2000000000000000000
χ3722-2-2-222-2-2-20002202-22-2002-202-20000000000000i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i200
χ3822-2-2-222-2-2-20002202-22-2002-202-20000000000000−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i200
χ3922-2-2-222-2-2-20002202-22-200-220-220000000000000i2−i2i2−i2i2−i2i2−i200000000−i2i2−i2i200
χ4022-2-2-222-2-2-20002202-22-200-220-220000000000000−i2i2−i2i2−i2i2−i2i200000000i2−i2i2−i200
χ4122-2-2-222-2-2-2000220-22-22002-20-220000000000000i2−i2i2−i2−i2i2−i2i200000000i2−i2−i2i200
χ4222-2-2-222-2-2-2000220-22-22002-20-220000000000000−i2i2−i2i2i2−i2i2−i200000000−i2i2i2−i200
χ4322-2-2-222-2-2-2000220-22-2200-2202-20000000000000i2−i2i2−i2−i2i2−i2i200000000−i2i2i2−i200
χ4422-2-2-222-2-2-2000220-22-2200-2202-20000000000000−i2i2−i2i2i2−i2i2−i200000000i2−i2−i2i200
χ45444-4-4-4-444-4000-4400000000000000000000000002i2−2i2−2i22i2000000000000000000
χ46444-4-4-4-444-4000-440000000000000000000000000−2i22i22i2−2i2000000000000000000
χ47444-4-4-4-44-440004-4000000000000000000000000000002i2−2i2−2i22i200000000000000
χ48444-4-4-4-44-440004-400000000000000000000000000000−2i22i22i2−2i200000000000000
χ4944-444-4-4-44-4-4444-4-40000-440000000000000000000000000000000000000000
χ5044-444-4-4-4-44-444-44-400004-40000000000000000000000000000000000000000
χ5144-4-4-444-444000-4-404-4-44000000000000000000000000000000000000000000
χ5244-4-4-444-444000-4-40-444-4000000000000000000000000000000000000000000
χ534-444-44-4-40044-400-40000000000000000000022−2222−220000000000000000000000
χ544-444-44-4-40044-400-400000000000000000000−2222−22220000000000000000000000
χ554-444-44-4-400-4-4400400000000000000002i2−2i22i2−2i200000000000000000000000000
χ564-444-44-4-400-4-440040000000000000000−2i22i2−2i22i200000000000000000000000000
χ574-4-44-4-444004-4400-4000000000000000000002i2−2i2−2i22i20000000000000000000000
χ584-4-44-4-444004-4400-400000000000000000000−2i22i22i2−2i20000000000000000000000
χ594-4-44-4-44400-44-4004000000000000000022−22−222200000000000000000000000000
χ604-4-44-4-44400-44-40040000000000000000−222222−2200000000000000000000000000
χ618-88-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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