Finite Group Databasebeta

← Group #176109

Character table — Group #176109

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222444444444422444422244444444444888888888888
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111
χ5111111111111111111-1-111-1-1-11-111-11-1-111-111-1-1-1-1-1-1-1-11111
χ6111111111111111111-1-111-1-1-11-111-11-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111-1-111-1-1-1-11-1-11-11111-1111111-1-1-1-1-1-1-1-1
χ8111111111111111111-1-111-1-1-1-11-1-11-111-1-1-1-1-1-1-1-1-111111111
χ91111111111-1-1-1-1111111-1-1-1-1-1111-11-1-1-1111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-1111111-1-1-1-1-1111-11-1-1-1-1-1111-1-111-1-111-1-111
χ111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1111111-1-1-1-11111-1-1-1-111
χ121111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1111-1-111111-1-1-1-11111-1-1
χ131111111111-1-1-1-11111-1-1-1-11111-11-1-1-11111-1-1-1-1-111-1-11111-1-1
χ141111111111-1-1-1-11111-1-1-1-11111-11-1-1-111-1-1-11111-1-111-1-1-1-111
χ151111111111-1-1-1-11111-1-1-1-1111-11-1111-1-111-1-1-111-1-1-1-111-1-111
χ161111111111-1-1-1-11111-1-1-1-1111-11-1111-1-1-1-1-111-1-11111-1-111-1-1
χ17222222222-222-2-2-2-22-2222-2-2-220000000000-200000000000000
χ18222222222-222-2-2-2-22-2-2-22-222-20000000000200000000000000
χ19222222222-2-2-222-2-22-222-2222-20000000000-200000000000000
χ20222222222-2-2-222-2-22-2-2-2-22-2-220000000000200000000000000
χ2122222222-2222-2-2-2-2-2200-2200020-220-20000000000000000000
χ2222222222-2222-2-2-2-2-2200-22000-202-2020000000000000000000
χ2322222222-22-2-222-2-2-22002-200020-2-2020000000000000000000
χ2422222222-22-2-222-2-2-22002-2000-20220-20000000000000000000
χ2522222222-2-2222222-2-200-2-20000200-202-200000000000000000
χ2622222222-2-2222222-2-200-2-20000-20020-2200000000000000000
χ2722222222-2-2-2-2-2-222-2-200220000200-20-2200000000000000000
χ2822222222-2-2-2-2-2-222-2-200220000-200202-200000000000000000
χ294444-4-4-4-440000000-404-4000000000000000000000000000000
χ304444-4-4-4-440000000-40-44000000000000000000000000000000
χ314444-4-4-4-4-400000004000004i−4i00000000000000000000000000
χ324444-4-4-4-4-40000000400000−4i4i00000000000000000000000000
χ3344-4-44-44-400004i−4i00000000000000000002-202i−2i000000000000
χ3444-4-44-44-400004i−4i0000000000000000000-220−2i2i000000000000
χ3544-4-44-44-40000−4i4i00000000000000000002-20−2i2i000000000000
χ3644-4-44-44-40000−4i4i0000000000000000000-2202i−2i000000000000
χ374-44-444-4-4004-400000000000000000000000000000000002i−2i2i−2i
χ384-44-444-4-4004-40000000000000000000000000000000000−2i2i−2i2i
χ394-44-444-4-400-4400000000000000000000000000000000002i−2i−2i2i
χ404-44-444-4-400-440000000000000000000000000000000000−2i2i2i−2i
χ414-44-4-4-4440000004-40000000000000000000000000022−22000000
χ424-44-4-4-4440000004-400000000000000000000000000−2222000000
χ434-44-4-4-444000000-44000000000000000000000000000022−220000
χ444-44-4-4-444000000-440000000000000000000000000000−22220000
χ454-4-444-4-44040000000-4000000000000000000002i2−2i20000000000
χ464-4-444-4-44040000000-400000000000000000000−2i22i20000000000
χ474-4-444-4-440-400000004000000000000000000000022−2200000000
χ484-4-444-4-440-4000000040000000000000000000000−222200000000
χ4988-8-8-88-88000000000000000000000000000000000000000000
χ508-8-88-888-8000000000000000000000000000000000000000000

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