Finite Group Databasebeta

← Group #315535

Character table — Group #315535

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444488888888444444448888888888888888444488884444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-111-1-111-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11111-111-1
χ9111111111111111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-1
χ10111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ11111111111111111111-1-1-1-11111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1111-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-11
χ172222222222-2-22-2-22-2-20000222222-2-2000000-2-2000000000000-220000000000
χ182222222222-2-22-2-22-2-200002222-2-222000000-2-20000000000002-20000000000
χ192222222222-2-22-2-22-2-20000-2-2-2-222-2-2000000220000000000002-20000000000
χ202222222222-2-22-2-22-2-20000-2-2-2-2-2-22200000022000000000000-220000000000
χ2122222222-2-222-222-2-2-222220000000022-2-2-2-200000000000000002-200000000
χ2222222222-2-222-222-2-2-2222200000000-2-222-2-20000000000000000-2200000000
χ2322222222-2-222-222-2-2-2-2-2-2-20000000022-2-2220000000000000000-2200000000
χ2422222222-2-222-222-2-2-2-2-2-2-200000000-2-2222200000000000000002-200000000
χ2522-2-2-2-2222-2-2-2222-2-222i2i−2i−2i0000000000002i−2i00000022-2-200000000002i−2i0000
χ2622-2-2-2-2222-2-2-2222-2-222i2i−2i−2i0000000000002i−2i000000-2-2220000000000−2i2i0000
χ2722-2-2-2-2222-2-2-2222-2-22−2i−2i2i2i000000000000−2i2i00000022-2-20000000000−2i2i0000
χ2822-2-2-2-2222-2-2-2222-2-22−2i−2i2i2i000000000000−2i2i000000-2-22200000000002i−2i0000
χ2922-2-2-2-222-2222-2-2-22-22000022-2-200000000002-22i2i−2i−2i0000000000002i−2i000000
χ3022-2-2-2-222-2222-2-2-22-22000022-2-200000000002-2−2i−2i2i2i000000000000−2i2i000000
χ3122-2-2-2-222-2222-2-2-22-220000-2-2220000000000-222i2i−2i−2i000000000000−2i2i000000
χ3222-2-2-2-222-2222-2-2-22-220000-2-2220000000000-22−2i−2i2i2i0000000000002i−2i000000
χ3322-2-2-2-222-22-2-2-22222-22i2i−2i−2i22-2-200000000−2i2i-22000000002i2i−2i−2i000000000000
χ3422-2-2-2-222-22-2-2-22222-22i2i−2i−2i-2-22200000000−2i2i2-200000000−2i−2i2i2i000000000000
χ3522-2-2-2-222-22-2-2-22222-2−2i−2i2i2i22-2-2000000002i−2i-2200000000−2i−2i2i2i000000000000
χ3622-2-2-2-222-22-2-2-22222-2−2i−2i2i2i-2-222000000002i−2i2-2000000002i2i−2i−2i000000000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ384444-4-4-4-44-400-4004000000000000000000000022−2222−2200000000000000000000
χ394444-4-4-4-44-400-40040000000000000000000000−2222−222200000000000000000000
χ404444-4-4-4-4-4400400-400000000004-40000000000000000000000000000000000
χ414444-4-4-4-4-4400400-40000000000-440000000000000000000000000000000000
χ4244-4-444-4-44400-400-40000000000004-400000000000000000000000000000000
χ4344-4-444-4-44400-400-4000000000000-4400000000000000000000000000000000
χ4444-4-444-4-4-4-400400400000000000000000000002i2−2i2−2i22i200000000000000000000
χ4544-4-444-4-4-4-40040040000000000000000000000−2i22i22i2−2i200000000000000000000
χ4644-4-4-4-4444-4444-4-4-44-400000000000000000000000000000000000000000000
χ474-44-44-44-400000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000002-22-2000000000000
χ484-44-44-44-400000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000-22-22000000000000
χ494-44-44-44-40000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000-22-22000000000000
χ504-44-44-44-40000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000002-22-2000000000000
χ514-44-4-44-44004-404-40000000000000000000000000002i2−2i22i2−2i20000000000000000
χ524-44-4-44-44004-404-4000000000000000000000000000−2i22i2−2i22i20000000000000000
χ534-44-4-44-4400-440-440000000000000004i−4i000000000000000000000000000000
χ544-44-4-44-4400-440-44000000000000000−4i4i000000000000000000000000000000
χ554-4-444-4-44004-40-44000000000000000004i−4i0000000000000000000000000000
χ564-4-444-4-44004-40-4400000000000000000−4i4i0000000000000000000000000000
χ574-4-444-4-4400-4404-40000000000000000000000000002i2−2i2−2i22i20000000000000000
χ584-4-444-4-4400-4404-4000000000000000000000000000−2i22i22i2−2i20000000000000000
χ594-4-44-444-4000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i000000000000
χ604-4-44-444-4000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i000000000000
χ614-4-44-444-40000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i000000000000
χ624-4-44-444-40000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i000000000000

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