Finite Group Databasebeta

← Group #176155

Character table — Group #176155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222444444444444444422244444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-11-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111-1-11-1-1-11-111-1-11-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111111111-1-11-1-1-11-111-1-11-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111-1-11-1-1-1-11-1-11-1-11111111111-1-1-1-1-1-1-1-1
χ81111111111111111111-1-11-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-111111111
χ9111111111-1-11-1-11111-111-1-1-1-1111-111-1-1-111-1-111-1-111-1-111-1-1
χ10111111111-1-11-1-11111-111-1-1-1-1111-111-1-1-1-1-111-1-111-1-111-1-111
χ11111111111-1-11-1-11111-111-1-1-1-1-1-1-11-1111111-1-1-1-11111-1-1-1-111
χ12111111111-1-11-1-11111-111-1-1-1-1-1-1-11-11111-1-11111-1-1-1-11111-1-1
χ13111111111-1-11-1-11111-1-1-1-11111-11-1-1-1-11111-1-1-1-111-1-11111-1-1
χ14111111111-1-11-1-11111-1-1-1-11111-11-1-1-1-111-1-11111-1-111-1-1-1-111
χ15111111111-1-11-1-11111-1-1-1-1111-11-111-11-1-111-1-111-1-1-1-111-1-111
χ16111111111-1-11-1-11111-1-1-1-1111-11-111-11-1-1-1-111-1-11111-1-111-1-1
χ1722222222222-2-2-2-2-22-2222-2-2-2200000-20000000000000000000
χ1822222222222-2-2-2-2-22-22-2-2-222-20000020000000000000000000
χ19222222222-2-2-222-2-22-2-222222-200000-20000000000000000000
χ20222222222-2-2-222-2-22-2-2-2-22-2-220000020000000000000000000
χ2122222222-222222-2-2-22-200-200020-2-2002000000000000000000
χ2222222222-222222-2-2-22-200-2000-202200-2000000000000000000
χ2322222222-222-2-2-222-2-2-20020000200-2002-20000000000000000
χ2422222222-222-2-2-222-2-2-20020000-200200-220000000000000000
χ2522222222-2-2-22-2-2-2-2-22200200020-2200-2000000000000000000
χ2622222222-2-2-22-2-2-2-2-222002000-202-2002000000000000000000
χ2722222222-2-2-2-22222-2-2200-20000200-200-220000000000000000
χ2822222222-2-2-2-22222-2-2200-20000-2002002-20000000000000000
χ294444-4-4-4-440000000-4004-400000000000000000000000000000
χ304444-4-4-4-440000000-400-4400000000000000000000000000000
χ314444-4-4-4-4-400000004000004i−4i00000000000000000000000000
χ324444-4-4-4-4-40000000400000−4i4i00000000000000000000000000
χ3344-4-444-4-400004i−4i000000000000000000002-22i−2i000000000000
χ3444-4-444-4-400004i−4i00000000000000000000-22−2i2i000000000000
χ3544-4-444-4-40000−4i4i000000000000000000002-2−2i2i000000000000
χ3644-4-444-4-40000−4i4i00000000000000000000-222i−2i000000000000
χ374-44-44-44-40000004-40000000000000000000000000000002i2−2i200
χ384-44-44-44-40000004-4000000000000000000000000000000−2i22i200
χ394-44-44-44-4000000-44000000000000000000000000000000002i2−2i2
χ404-44-44-44-4000000-4400000000000000000000000000000000−2i22i2
χ414-4-444-4-4404i−4i0000000000000000000000000002i−2i2-200000000
χ424-4-444-4-4404i−4i000000000000000000000000000−2i2i-2200000000
χ434-4-444-4-440−4i4i0000000000000000000000000002i−2i-2200000000
χ444-4-444-4-440−4i4i000000000000000000000000000−2i2i2-200000000
χ454-4-44-444-4000400000-40000000000000000000000002i2−2i2000000
χ464-4-44-444-4000400000-4000000000000000000000000−2i22i2000000
χ474-4-44-444-4000-40000040000000000000000000000000022−220000
χ484-4-44-444-4000-400000400000000000000000000000000−22220000
χ4988-8-8-8-888000000000000000000000000000000000000000000
χ508-88-8-88-88000000000000000000000000000000000000000000

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