Finite Group Databasebeta

← Group #307635

Character table — Group #307635

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882222444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ311111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-11111-1-1
χ51111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-111-1-111111111-1-11111-1-1-1-1-1-1-1-11-111-1-1-1-111-1-11-1
χ10111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-11111-1-1111-1
χ11111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111111111-111-1-1-1-1-1-111-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1111111-1-1-11
χ13111111111111111111-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-11111-1-1-11
χ15111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-11-1-111-1-111-1-11-1
χ16111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-111-1-1111-1
χ172222222222-2-222-2-2-2-22222222200000000-2-2000000000000-2-2000000000000
χ182222222222-2-222-2-2-2-22222-2-2-2-200000000-2-200000000000022000000000000
χ192222222222-2-222-2-2-2-2-2-2-2-222-2-20000000022000000000000-22000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-2-2-22200000000220000000000002-2000000000000
χ2122222222-2-222-2-222-2-20000000022-2-222-2-20022-2-20000000000000000000000
χ2222222222-2-222-2-222-2-20000000022-2-2-2-22200-2-2220000000000000000000000
χ2322222222-2-222-2-222-2-200000000-2-22222-2-200-2-2220000000000000000000000
χ2422222222-2-222-2-222-2-200000000-2-222-2-2220022-2-20000000000000000000000
χ2522-2-22-2-222222-2-2-2-2-2222-2-2000000002i−2i2i−2i2-20000000000000000002i−2i000000
χ2622-2-22-2-222222-2-2-2-2-2222-2-200000000−2i2i−2i2i2-2000000000000000000−2i2i000000
χ2722-2-22-2-222222-2-2-2-2-22-2-222000000002i−2i2i−2i-22000000000000000000−2i2i000000
χ2822-2-22-2-222222-2-2-2-2-22-2-22200000000−2i2i−2i2i-220000000000000000002i−2i000000
χ2922-2-22-2-2222-2-2-2-2222-222-2-2000000000000-22000000000000002i−2i2i−2i00000000
χ3022-2-22-2-2222-2-2-2-2222-222-2-2000000000000-2200000000000000−2i2i−2i2i00000000
χ3122-2-22-2-2222-2-2-2-2222-2-2-2220000000000002-2000000000000002i−2i−2i2i00000000
χ3222-2-22-2-2222-2-2-2-2222-2-2-2220000000000002-200000000000000−2i2i2i−2i00000000
χ3322-2-22-2-22-2-22222-2-22-20000000000002i−2i−2i2i00000022-2-22i2i−2i−2i00000000000000
χ3422-2-22-2-22-2-22222-2-22-20000000000002i−2i−2i2i000000-2-222−2i−2i2i2i00000000000000
χ3522-2-22-2-22-2-22222-2-22-2000000000000−2i2i2i−2i00000022-2-2−2i−2i2i2i00000000000000
χ3622-2-22-2-22-2-22222-2-22-2000000000000−2i2i2i−2i000000-2-2222i2i−2i−2i00000000000000
χ3722-2-2-222-22-2002-200002-22-22-22-20000000000i2−i2i2−i20000i2−i2i2−i200000000i2−i2i2−i200
χ3822-2-2-222-22-2002-200002-22-22-22-20000000000−i2i2−i2i20000−i2i2−i2i200000000−i2i2−i2i200
χ3922-2-2-222-22-2002-200002-22-2-22-220000000000i2−i2i2−i20000i2−i2i2−i200000000−i2i2−i2i200
χ4022-2-2-222-22-2002-200002-22-2-22-220000000000−i2i2−i2i20000−i2i2−i2i200000000i2−i2i2−i200
χ4122-2-2-222-22-2002-20000-22-222-2-220000000000i2−i2i2−i20000−i2i2−i2i200000000i2−i2−i2i200
χ4222-2-2-222-22-2002-20000-22-222-2-220000000000−i2i2−i2i20000i2−i2i2−i200000000−i2i2i2−i200
χ4322-2-2-222-22-2002-20000-22-22-222-20000000000i2−i2i2−i20000−i2i2−i2i200000000−i2i2i2−i200
χ4422-2-2-222-22-2002-20000-22-22-222-20000000000−i2i2−i2i20000i2−i2i2−i200000000i2−i2−i2i200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ464444-4-4-4-44-400-4400004-4-440000000000000000000000000000000000000000
χ474444-4-4-4-44-400-440000-444-40000000000000000000000000000000000000000
χ484444-4-4-4-4-44004-400000000000000000000000000000022−22−222200000000000000
χ494444-4-4-4-4-44004-4000000000000000000000000000000−222222−2200000000000000
χ5044-4-44-4-44-4-4-4-44444-4400000000000000000000000000000000000000000000
χ5144-4-4-444-4-4400-4400000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5244-4-4-444-4-4400-440000000000000000000000−2i22i22i2−2i20000000000000000000000
χ534-44-444-4-4004-4004-40000000000000000000000002i2−2i22i2−2i2000000000000000000
χ544-44-444-4-4004-4004-4000000000000000000000000−2i22i2−2i22i2000000000000000000
χ554-44-444-4-400-4400-440000000000004i−4i00000000000000000000000000000000
χ564-44-444-4-400-4400-44000000000000−4i4i00000000000000000000000000000000
χ574-4-444-44-4004-400-440000000000000000000000002i2−2i2−2i22i2000000000000000000
χ584-4-444-44-4004-400-44000000000000000000000000−2i22i22i2−2i2000000000000000000
χ594-4-444-44-400-44004-400000000004i−4i0000000000000000000000000000000000
χ604-4-444-44-400-44004-40000000000−4i4i0000000000000000000000000000000000
χ618-88-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-88-88-88000000000000000000000000000000000000000000000000000000

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