Finite Group Databasebeta

← Group #324124

Character table — Group #324124

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444444448888244444888888888888888888448888882444
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-11
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-11-1-11
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-111-1
χ91111111111111111-1-111-1-11111-1-11111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11-11-1
χ101111111111111111-1-111-1-11111-1-11111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-11-11
χ111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-11-11
χ121111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1111-11-1
χ131111111111111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111
χ141111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-111-1-1
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111111-1-111-1-1-1-111
χ17222222222-222-2-22-222-2-2-2-222222-20000-2-200000000-2-2220000000000000000
χ18222222222-222-2-22-222-2-2-2-2-2-2-2-22-20000220000000022-2-20000000000000000
χ19222222222-222-2-22-2-2-2-2-2222222-2200002200000000-2-2-2-20000000000000000
χ20222222222-222-2-22-2-2-2-2-222-2-2-2-2-220000-2-20000000022220000000000000000
χ2122222222-22-2-222-2222-2-2220000-2-222-2-20000000000000000002-20000000000
χ2222222222-22-2-222-2222-2-2220000-2-2-2-222000000000000000000-220000000000
χ2322222222-22-2-222-22-2-2-2-2-2-200002222-2-2000000000000000000-220000000000
χ2422222222-22-2-222-22-2-2-2-2-2-2000022-2-2220000000000000000002-20000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000-220000000000000000002i2i−2i−2i002i−2i00000000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000-22000000000000000000−2i−2i2i2i00−2i2i00000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200002-20000000000000000002i2i−2i−2i00−2i2i00000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200002-2000000000000000000−2i−2i2i2i002i−2i00000000
χ292-2-22-222-2222-2-2-2-22002-2002i2i−2i−2i000000002i2i−2i−2i00002i−2i00000000002-2000000
χ302-2-22-222-2222-2-2-2-22002-2002i2i−2i−2i00000000−2i−2i2i2i00002i−2i0000000000-22000000
χ312-2-22-222-2222-2-2-2-22002-200−2i−2i2i2i000000002i2i−2i−2i0000−2i2i0000000000-22000000
χ322-2-22-222-2222-2-2-2-22002-200−2i−2i2i2i00000000−2i−2i2i2i0000−2i2i00000000002-2000000
χ332-2-22-222-22-22-222-2-200-22002i2i−2i−2i00000000000022-2-2−2i2i0000000000002i−2i0000
χ342-2-22-222-22-22-222-2-200-22002i2i−2i−2i000000000000-2-222−2i2i000000000000−2i2i0000
χ352-2-22-222-22-22-222-2-200-2200−2i−2i2i2i00000000000022-2-22i−2i000000000000−2i2i0000
χ362-2-22-222-22-22-222-2-200-2200−2i−2i2i2i000000000000-2-2222i−2i0000000000002i−2i0000
χ374444-4-4-4-440-4-4004000000000000000000022−2222−22000000000000000000000000
χ384444-4-4-4-440-4-40040000000000000000000−2222−2222000000000000000000000000
χ394444-4-4-4-4-404400-40000000000000000000000022−2222−2200000000000000000000
χ404444-4-4-4-4-404400-400000000000000000000000−2222−222200000000000000000000
χ4144-4-444-4-404004-40-400000000000000000000000000000022−2222−22000000000000
χ4244-4-444-4-404004-40-4000000000000000000000000000000−2222−2222000000000000
χ4344-4-444-4-40-400-44040000000000000000000000000000002i2−2i2−2i22i2000000000000
χ4444-4-444-4-40-400-4404000000000000000000000000000000−2i22i22i2−2i2000000000000
χ4544-4-4-4-4440000000000004-422−2222−2200000022−220000000000000000000000000000
χ4644-4-4-4-4440000000000004-4−2222−2222000000−22220000000000000000000000000000
χ4744-4-4-4-444000000000000-4422−2222−22000000−22220000000000000000000000000000
χ4844-4-4-4-444000000000000-44−2222−222200000022−220000000000000000000000000000
χ494-44-44-44-4000000004i−4i00002i2−2i2−2i22i200000000000000000022−220000000000000000
χ504-44-44-44-4000000004i−4i0000−2i22i22i2−2i2000000000000000000−22220000000000000000
χ514-44-44-44-400000000−4i4i00002i2−2i2−2i22i2000000000000000000−22220000000000000000
χ524-44-44-44-400000000−4i4i0000−2i22i22i2−2i200000000000000000022−220000000000000000
χ534-44-4-44-440400-440-4000000000000004i−4i000000000000000000000000000000
χ544-44-4-44-440400-440-400000000000000−4i4i000000000000000000000000000000
χ554-44-4-44-440-4004-4040000000000004-400000000000000000000000000000000
χ564-44-4-44-440-4004-404000000000000-4400000000000000000000000000000000
χ574-4-444-4-4440-4400-400000000000000000002i2−2i2−2i22i2000000000000000000000000
χ584-4-444-4-4440-4400-40000000000000000000−2i22i22i2−2i2000000000000000000000000
χ594-4-444-4-44-404-40040000000000000000000000022−22−222200000000000000000000
χ604-4-444-4-44-404-400400000000000000000000000−222222−2200000000000000000000
χ614-4-44-444-4-44-44-4-44400-44000000000000000000000000000000000000000000
χ624-4-44-444-4-4-4-44444-4004-4000000000000000000000000000000000000000000

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