Finite Group Databasebeta

← Group #317075

Character table — Group #317075

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222224444444448888888881616161616161616161616161616161632323232
order12222244444444488888888888888822244444888888884488
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-111-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111-1-1111-1-111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-11-11111-11-1-1-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1111111-1-1-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-111-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-11-11111-1-11111-1-1
χ9111111111111111-1-1-1-1-1-1-11111-1-1-1-11-111-11-1-111-1-1-1-1111-11-1
χ10111111111111111-1-1-1-1-1-1-11111-1-1-1-11-1-1-111-11-1-111-1-111-11-11
χ11111111111111111-1-1-1-1-1-1-11111-1-1-1-1-1111-1-11-111-1-111-1-1-11-11
χ12111111111111111-1-1-1-1-1-1-11111-1-1-1-1-11-1-11-111-1-11111-1-11-11-1
χ13111111111111111-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-111-1-1-1-11-1-11
χ14111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-111-1
χ15111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111-111-1
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1111-1-111111-1-11
χ1722222222-2-222-2-2-222-2-2-2-2200000000002-2200-2000000000000
χ1822222222-2-222-2-2-222-2-2-2-220000000000-22-2002000000000000
χ1922222222-2-222-2-2-2-2-22222-200000000002-2-2002000000000000
χ2022222222-2-222-2-2-2-2-22222-20000000000-22200-2000000000000
χ21222222-2-2-2-2-2-22-2200000002i2i−2i−2i000020000-2000000002i−2i0000
χ22222222-2-2-2-2-2-22-2200000002i2i−2i−2i0000-20000200000000−2i2i0000
χ23222222-2-2-2-2-2-22-220000000−2i−2i2i2i000020000-200000000−2i2i0000
χ24222222-2-2-2-2-2-22-220000000−2i−2i2i2i0000-200002000000002i−2i0000
χ252222-2-22-2-2-22-2-22200000002i−2i2i−2i0000020000-2000002i−2i000000
χ262222-2-22-2-2-22-2-22200000002i−2i2i−2i00000-20000200000−2i2i000000
χ272222-2-22-2-2-22-2-2220000000−2i2i−2i2i0000020000-200000−2i2i000000
χ282222-2-22-2-2-22-2-2220000000−2i2i−2i2i00000-200002000002i−2i000000
χ292222-2-2-2222-22-2-222222-2-2-22-2-2222-2-200000000000000000000
χ302222-2-2-2222-22-2-222222-2-2-2-222-2-2-22200000000000000000000
χ312222-2-2-2222-22-2-22-2-2-2-22222-2-22-2-22200000000000000000000
χ322222-2-2-2222-22-2-22-2-2-2-2222-222-222-2-200000000000000000000
χ332222-2-2-22-2-2-2222-222-2-222-200000000000000002i−2i2i−2i00000000
χ342222-2-2-22-2-2-2222-222-2-222-20000000000000000−2i2i−2i2i00000000
χ352222-2-2-22-2-2-2222-2-2-222-2-2200000000000000002i−2i−2i2i00000000
χ362222-2-2-22-2-2-2222-2-2-222-2-220000000000000000−2i2i2i−2i00000000
χ37444444-4-444-4-4-44-400000000000000000000000000000000000
χ384444-4-44-4444-44-4-400000000000000000000000000000000000
χ394-4-444-44400-4-40000000000000022−2222−2200000000000000000000
χ404-4-444-44400-4-400000000000000−2222−222200000000000000000000
χ414-4-444-4-4-40044000004-44-400000000000000000000000000000
χ424-4-444-4-4-4004400000-44-4400000000000000000000000000000
χ434-4-44-444-400-44000004-4-4400000000000000000000000000000
χ444-4-44-444-400-4400000-444-400000000000000000000000000000
χ454-4-44-44-44004-40000000000000022−22−222200000000000000000000
χ464-4-44-44-44004-400000000000000−222222−2200000000000000000000
χ4788-8-8000000000004i2−4i2000000000000000000000000000000000
χ4888-8-800000000000−4i24i2000000000000000000000000000000000
χ498-88-800008i−8i0000000000000000000000000000000000000000
χ508-88-80000−8i8i0000000000000000000000000000000000000000

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