Finite Group Databasebeta

← Group #317289

Character table — Group #317289

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444444444488888881616161616161616161616161616161632323232
order12224444244448888888888888888824444444888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111-1-1-1-11-1-1-1-1-1-11-11-1111111-1-1-1-1-1-111-1-1
χ61111111111111111111-1-1-1-11-1-1-1-1-1-11-11-1-1-1-1-111-1-11111-1-111
χ71111111111111111111-1-1-1-11-1-1-1-1-1-1-11-111111-1-111-1-1-1-1-1-111
χ81111111111111111111-1-1-1-11-1-1-1-1-1-1-11-11-1-1-1-1-1-111111111-1-1
χ91111111111111-1-1-1-1-1-11111-111-1-1-1-11-11-111-1-1-1-11111-1-11-11-1
χ101111111111111-1-1-1-1-1-11111-111-1-1-1-11-11-1-1-111-1-111-1-111-11-11
χ111111111111111-1-1-1-1-1-11111-111-1-1-1-1-11-1111-1-111-1-111-1-1-11-11
χ121111111111111-1-1-1-1-1-11111-111-1-1-1-1-11-11-1-11111-1-1-1-1111-11-1
χ131111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-11
χ141111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-1-111-1
χ151111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-111-1
χ161111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11-1-11
χ1722222222-2-22-2-22222-2-22222-2-2-222-2-200000000000000000000
χ1822222222-2-22-2-22222-2-2-2-2-2-2-222-2-22200000000000000000000
χ1922222222-2-22-2-2-2-2-2-22222222-2-2-2-22200000000000000000000
χ2022222222-2-22-2-2-2-2-2-222-2-2-2-222222-2-200000000000000000000
χ212222-2-22222-2-2-222-2-2220000-20000000000000000002i−2i2i−2i0000
χ222222-2-22222-2-2-222-2-2220000-2000000000000000000−2i2i−2i2i0000
χ232222-2-22222-2-2-2-2-222-2-2000020000000000000000002i−2i−2i2i0000
χ242222-2-22222-2-2-2-2-222-2-200002000000000000000000−2i2i2i−2i0000
χ252222-2-222-2-2-22222-2-2-2-20000200000000002-22-2000000000000
χ262222-2-222-2-2-22222-2-2-2-2000020000000000-22-22000000000000
χ272222-2-222-2-2-222-2-222220000-200000000002-2-22000000000000
χ282222-2-222-2-2-222-2-222220000-20000000000-222-2000000000000
χ292222-2-2-2-22-22-220000002i2i−2i−2i02i−2i0000020-200002i−2i0000000000
χ302222-2-2-2-22-22-220000002i2i−2i−2i02i−2i00000-2020000−2i2i0000000000
χ312222-2-2-2-22-22-22000000−2i−2i2i2i0−2i2i0000020-20000−2i2i0000000000
χ322222-2-2-2-22-22-22000000−2i−2i2i2i0−2i2i00000-20200002i−2i0000000000
χ332222-2-2-2-2-2222-20000002i2i−2i−2i0−2i2i000020-200000002i−2i00000000
χ342222-2-2-2-2-2222-20000002i2i−2i−2i0−2i2i0000-2020000000−2i2i00000000
χ352222-2-2-2-2-2222-2000000−2i−2i2i2i02i−2i000020-20000000−2i2i00000000
χ362222-2-2-2-2-2222-2000000−2i−2i2i2i02i−2i0000-20200000002i−2i00000000
χ37444444-4-44-4-44-40000000000000000000000000000000000000
χ38444444-4-4-44-4-440000000000000000000000000000000000000
χ394-44-4004-40000000004-42i2−2i22i2−2i2000002i2−2i200000000000000000000
χ404-44-4004-40000000004-4−2i22i2−2i22i200000−2i22i200000000000000000000
χ414-44-4004-4000000000-442i2−2i22i2−2i200000−2i22i200000000000000000000
χ424-44-4004-4000000000-44−2i22i2−2i22i2000002i2−2i200000000000000000000
χ434-44-400-44000004i−4i000022−22−22220002i2−2i20000000000000000000000
χ444-44-400-44000004i−4i0000−222222−22000−2i22i20000000000000000000000
χ454-44-400-4400000−4i4i000022−22−2222000−2i22i20000000000000000000000
χ464-44-400-4400000−4i4i0000−222222−220002i2−2i20000000000000000000000
χ4788-8-80000000000042−42000000000000000000000000000000000
χ4888-8-800000000000−4242000000000000000000000000000000000
χ498-8-888i−8i00000000000000000000000000000000000000000000
χ508-8-88−8i8i00000000000000000000000000000000000000000000

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