Finite Group Databasebeta

← Group #289300

Character table — Group #289300

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111222222222244444444444488888888888888888881616161616161616161632323232
order12224444448888244488888888888888888888888888822244488884488
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-111111111111-1-11-1-111-1-1-1-1-1-1
χ311111111111111111111111111-1-11111111-1-11111-1-1-1-1-111-111-1-111-1-1-1-1
χ411111111111111111111111111-1-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ61111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-11111-111-111-1-1-1-111-1-1
χ71111111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-1111111-1-1
χ81111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111
χ91111111111-1-1-1-11111-1-1-1-1111111-11111-1-111-1-1-1-1-1-1-1-111-111-1-1-11-11-11-1
χ101111111111-1-1-1-11111-1-1-1-1111111-111-1-11111-1-1-1-1-1-1-1-11-111-11-1-1-11-11-11
χ111111111111-1-1-1-11111-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-11111-11-1-11-1111-1-11-11
χ121111111111-1-1-1-11111-1-1-1-11111-1-1-111-1-111-1-1-1-1-1-11111-1-11-1-1111-111-11-1
χ131111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-111-1-1111111-1-1-1-1-1-11-1-11111-1-111-1
χ141111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-1-11-1-11-111-111-1-11
χ151111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-111-11-1-11-11-1-11
χ161111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-111-1-1-1-11-111-1
χ172222222-2-222222-2-22-222-2-2000000-200000000000000000220-2-200000000
χ182222222-2-222222-2-22-222-2-2000000-200000000000000000-2-202200000000
χ192222222-2-22-2-2-2-2-2-22-2-2-2220000002000000000000000002-20-2200000000
χ202222222-2-22-2-2-2-2-2-22-2-2-222000000200000000000000000-2202-200000000
χ2122222-2222-22222-2-2-22-2-222000000-2002222000000000000000000-2-20000
χ2222222-2222-22222-2-2-22-2-222000000-200-2-2-2-2000000000000000000220000
χ2322222-2222-2-2-2-2-2-2-2-2222-2-200000020022-2-2000000000000000000-220000
χ2422222-2222-2-2-2-2-2-2-2-2222-2-2000000200-2-2220000000000000000002-20000
χ2522222-22-2-2-2222222-2-2-2-2-2-22i2i−2i−2i0022i−2i0000002i2i−2i−2i000000000000000000
χ2622222-22-2-2-2222222-2-2-2-2-2-2−2i−2i2i2i002−2i2i000000−2i−2i2i2i000000000000000000
χ2722222-22-2-2-2-2-2-2-222-2-222222i2i−2i−2i00-22i−2i000000−2i−2i2i2i000000000000000000
χ2822222-22-2-2-2-2-2-2-222-2-22222−2i−2i2i2i00-2−2i2i0000002i2i−2i−2i000000000000000000
χ292222-22-22220000-22-2-200002222220-2-20000-2-200000000-20020000000000
χ302222-22-22220000-22-2-200002222-2-20-2-200002200000000200-20000000000
χ312222-22-22220000-22-2-20000-2-2-2-2220220000-2-200000000200-20000000000
χ322222-22-22220000-22-2-20000-2-2-2-2-2-202200002200000000-20020000000000
χ332222-2-2-2-2-2-20000-222200002i2i−2i−2i000−2i2i000000000022-2-20000002i−2i000000
χ342222-2-2-2-2-2-20000-222200002i2i−2i−2i000−2i2i0000000000-2-222000000−2i2i000000
χ352222-2-2-2-2-2-20000-22220000−2i−2i2i2i0002i−2i000000000022-2-2000000−2i2i000000
χ362222-2-2-2-2-2-20000-22220000−2i−2i2i2i0002i−2i0000000000-2-2220000002i−2i000000
χ374444-44-4-4-4400004-4-4400000000000000000000000000000000000000000
χ384444-4-4-444-400004-44-400000000000000000000000000000000000000000
χ3944-4-4-40400044-4-4000000000000000002i2−2i22i2−2i2000000000000000000000000
χ4044-4-4-40400044-4-400000000000000000−2i22i2−2i22i2000000000000000000000000
χ4144-4-4-404000-4-444000000000000000002i2−2i2−2i22i2000000000000000000000000
χ4244-4-4-404000-4-44400000000000000000−2i22i22i2−2i2000000000000000000000000
χ434-44-40004-4022−2222−2200000022−2200002i2−2i200000000000002i−2i2i−2i00000000000000
χ444-44-40004-4022−2222−2200000022−220000−2i22i20000000000000−2i2i−2i2i00000000000000
χ454-44-40004-40−2222−2222000000−222200002i2−2i20000000000000−2i2i−2i2i00000000000000
χ464-44-40004-40−2222−2222000000−22220000−2i22i200000000000002i−2i2i−2i00000000000000
χ474-44-4000-44022−2222−22000000−222200000000000002i2−2i200002i−2i−2i2i00000000000000
χ484-44-4000-44022−2222−22000000−22220000000000000−2i22i20000−2i2i2i−2i00000000000000
χ494-44-4000-440−2222−222200000022−2200000000000002i2−2i20000−2i2i2i−2i00000000000000
χ504-44-4000-440−2222−222200000022−220000000000000−2i22i200002i−2i−2i2i00000000000000
χ514-4-4404000-422−22−2222000022−22002i2−2i22i2−2i2000000000002i−2i2i−2i000000000000000000
χ524-4-4404000-422−22−2222000022−2200−2i22i2−2i22i200000000000−2i2i−2i2i000000000000000000
χ534-4-4404000-4−222222−220000−2222002i2−2i22i2−2i200000000000−2i2i−2i2i000000000000000000
χ544-4-4404000-4−222222−220000−222200−2i22i2−2i22i2000000000002i−2i2i−2i000000000000000000
χ554-4-440-4000422−22−22220000−22220022−22−2222000000000002-2-22000000000000000000
χ564-4-440-4000422−22−22220000−222200−222222−2200000000000-222-2000000000000000000
χ574-4-440-40004−222222−22000022−220022−22−222200000000000-222-2000000000000000000
χ584-4-440-40004−222222−22000022−2200−222222−22000000000002-2-22000000000000000000
χ5988-8-880-80000000000000000000000000000000000000000000000000000

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