Finite Group Databasebeta

← Group #326049

Character table — Group #326049

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444488888888224444448888888888888888444488884444
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-111111111-1-1-1-111111-11-111-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1111111-1-1-1-111111111-11-11-1-111-1-1-1-1
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
χ51111111111111111111111-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11-11-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-11
χ71111111111111111111111-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-1-1-111-1-11-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-111111-111-1
χ9111111111111111111-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-11-11
χ10111111111111111111-1-1-1-1111111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1111-11-1
χ11111111111111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-11-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-11-11111-11-11
χ13111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-111
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-11-1-1-111-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1
χ17222222222-22-22-22-2-2-2222200002200-2-20000-2-200000000000020-2000000000
χ18222222222-22-22-22-2-2-222220000-2-200220000-2-2000000000000-202000000000
χ19222222222-22-22-22-2-2-2-2-2-2-200002200-2-2000022000000000000-202000000000
χ20222222222-22-22-22-2-2-2-2-2-2-20000-2-2002200002200000000000020-2000000000
χ2122222222-22-22-22-22-2-200002222002200-2-2-2-200000000000000020-200000000
χ2222222222-22-22-22-22-2-20000222200-2-20022-2-2000000000000000-20200000000
χ2322222222-22-22-22-22-2-20000-2-2-2-2002200-2-222000000000000000-20200000000
χ2422222222-22-22-22-22-2-20000-2-2-2-200-2-200222200000000000000020-200000000
χ2522-2-22-2-2222-2-222-2-2-222i2i−2i−2i2i2i−2i−2i000000002i−2i2i−2i0000000022-2-2000000000000
χ2622-2-22-2-2222-2-222-2-2-222i2i−2i−2i−2i−2i2i2i00000000−2i2i2i−2i00000000-2-222000000000000
χ2722-2-22-2-2222-2-222-2-2-22−2i−2i2i2i2i2i−2i−2i000000002i−2i−2i2i00000000-2-222000000000000
χ2822-2-22-2-2222-2-222-2-2-22−2i−2i2i2i−2i−2i2i2i00000000−2i2i−2i2i0000000022-2-2000000000000
χ2922-2-22-2-222-2-222-2-222-22i2i−2i−2i00000000000000−2i2i22-2-20000000000002i−2i000000
χ3022-2-22-2-222-2-222-2-222-22i2i−2i−2i00000000000000−2i2i-2-222000000000000−2i2i000000
χ3122-2-22-2-222-2-222-2-222-2−2i−2i2i2i000000000000002i−2i22-2-2000000000000−2i2i000000
χ3222-2-22-2-222-2-222-2-222-2−2i−2i2i2i000000000000002i−2i-2-2220000000000002i−2i000000
χ3322-2-22-2-22-222-2-222-22-200002i2i−2i−2i00000000−2i2i00000022-2-200000000002i−2i0000
χ3422-2-22-2-22-222-2-222-22-200002i2i−2i−2i00000000−2i2i000000-2-2220000000000−2i2i0000
χ3522-2-22-2-22-222-2-222-22-20000−2i−2i2i2i000000002i−2i00000022-2-20000000000−2i2i0000
χ3622-2-22-2-22-222-2-222-22-20000−2i−2i2i2i000000002i−2i000000-2-22200000000002i−2i0000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ38444-4-44-4-440-40-4040000000000000000000000022−2222−2200000000000000000000
χ39444-4-44-4-440-40-40400000000000000000000000−2222−222200000000000000000000
χ40444-4-44-4-4-404040-4000000000004-40000000000000000000000000000000000
χ41444-4-44-4-4-404040-400000000000-440000000000000000000000000000000000
χ4244-44-4-44-44040-40-40000000000000000000000022−22−222200000000000000000000
χ4344-44-4-44-44040-40-400000000000000000000000−222222−2200000000000000000000
χ4444-44-4-44-4-40-404040000000000000004i−4i000000000000000000000000000000
χ4544-44-4-44-4-40-40404000000000000000−4i4i000000000000000000000000000000
χ4644-4-44-4-44-4-444-4-444-4400000000000000000000000000000000000000000000
χ474-4444-4-4-4000000000022−2222−2222−2222−22000000000000000000002-22-2000000000000
χ484-4444-4-4-4000000000022−2222−22−2222−222200000000000000000000-22-22000000000000
χ494-4444-4-4-40000000000−2222−222222−2222−2200000000000000000000-22-22000000000000
χ504-4444-4-4-40000000000−2222−2222−2222−2222000000000000000000002-22-2000000000000
χ514-44-4-4-444040-40-40400000000000000004-40000000000000000000000000000
χ524-44-4-4-444040-40-4040000000000000000-440000000000000000000000000000
χ534-44-4-4-4440-404040-40000000000000000000000000022−2222−220000000000000000
χ544-44-4-4-4440-404040-400000000000000000000000000−2222−22220000000000000000
χ554-4-44-44-4404040-40-40000000000004i−4i00000000000000000000000000000000
χ564-4-44-44-4404040-40-4000000000000−4i4i00000000000000000000000000000000
χ574-4-44-44-440-40-404040000000000000000000000000022−22−22220000000000000000
χ584-4-44-44-440-40-4040400000000000000000000000000−222222−220000000000000000
χ594-4-4-4444-400000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000002-2-22000000000000
χ604-4-4-4444-400000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000-222-2000000000000
χ614-4-4-4444-40000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000-222-2000000000000
χ624-4-4-4444-40000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000002-2-22000000000000

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