Finite Group Databasebeta

← Group #272384

Character table — Group #272384

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size111122222222444448888888888888888816161616161616161616161616161616163232
order12222244444444444244444444888888882222488888888888848
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-11-1-11111111-1-1-11-1-1-1-1-1111-1-111-1-1
χ411111111111111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-1-1-111-1-111
χ511111111111111111-111-11-111-1-1-1111111-1111-111-1-1-11-1-1-1-1-1-11-1
χ611111111111111111-111-11-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111111-11
χ711111111111111111-111-11-1-1-1-111111111-1-1-1-1-1-1-11111-1-111-1-1-11
χ811111111111111111-111-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111-111-1-1111-1
χ91111111111111-1-1111-1-11-111111111-1-1-1-1-11-1-1-1-1-11-1-1111-1-1-1-111
χ101111111111111-1-1111-1-11-1111111-1-11111-11-1-1-1111-1-1-1-1-11111-1-1
χ111111111111111-1-1111-1-11-11-1-11-1-111-1-1-1-1-1-111-111-11111111-1-1-1-1
χ121111111111111-1-1111-1-11-11-1-11-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-11111
χ131111111111111-1-111-1-1-1-1-1-111-1-1-111-1-1-1-111-1-11-1-1-1111-1-111111-1
χ141111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1111111-1-1111-111-111-1-1-1-1-11
χ151111111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11-1111111-1-11-1-1-1-111-11
χ161111111111111-1-111-1-1-1-1-1-1-1-1-111-1-111111-1111-1-11-1-1-11111-1-11-1
χ172222222-22-2-2-2222-2-20-2-202000000000000000000000002i−2i002i−2i00
χ182222222-22-2-2-2222-2-20-2-20200000000000000000000000−2i2i00−2i2i00
χ192222222-22-2-2-22-2-2-2-20220-2000000000000000000000002i−2i00−2i2i00
χ202222222-22-2-2-22-2-2-2-20220-200000000000000000000000−2i2i002i−2i00
χ21222222-22-2222-200-2-2200-20-2222-2-20000000-200000200000000000
χ22222222-22-2222-200-2-2200-20-2-2-22220000000200000-200000000000
χ23222222-22-2222-200-2-2-20020222-2220000000-200000-200000000000
χ24222222-22-2222-200-2-2-200202-2-2-2-2-20000000200000200000000000
χ252222-2-2222-2-22-222-2202-20-20000002222-2-20000000000-200000000
χ262222-2-2222-2-22-222-2202-20-2000000-2-2-2-2220000000000200000000
χ272222-2-2222-2-22-2-2-2-220-220200000022-2-2220000000000-200000000
χ282222-2-2222-2-22-2-2-2-220-2202000000-2-222-2-20000000000200000000
χ292222-2-22-2222-2-2222-22-22-2-2200-2000000002000-200000000000000
χ302222-2-22-2222-2-2222-2-2-222-2-200200000000-2000200000000000000
χ312222-2-22-2222-2-2-2-22-222-2-22200-200000000-2000200000000000000
χ322222-2-22-2222-2-2-2-22-2-22-222-2002000000002000-200000000000000
χ332222-2-2-2-2-222-2200-2220020-200-200000000002-200002-2000000000
χ342222-2-2-2-2-222-2200-2220020-200-20000000000-220000-22000000000
χ352222-2-2-2-2-222-2200-22-200-20200200000000002-20000-22000000000
χ362222-2-2-2-2-222-2200-22-200-2020020000000000-2200002-2000000000
χ37444444-4-4-4-4-4-4-40044000000000000000000000000000000000000
χ384444-4-4-44-4-4-444004-4000000000000000000000000000000000000
χ394-44-40040-400004-400000000000002i2−2i22i2−2i2000000000000000000000
χ404-44-40040-400004-40000000000000−2i22i2−2i22i2000000000000000000000
χ414-44-40040-40000-4400000000000002i2−2i2−2i22i2000000000000000000000
χ424-44-40040-40000-440000000000000−2i22i22i2−2i2000000000000000000000
χ434-4-444-40404-4-40000000000000000000000000002i2−2i2000000000000
χ444-4-444-40404-4-4000000000000000000000000000−2i22i2000000000000
χ454-4-444-40-40-444000000000000004-40000000000000000000000000
χ464-4-444-40-40-44400000000000000-440000000000000000000000000
χ474-4-44-44040-44-4000000000004i−4i0000000000000000000000000000
χ484-4-44-44040-44-400000000000−4i4i0000000000000000000000000000
χ494-4-44-440-404-440000000000000000000000000000000000022−220000
χ504-4-44-440-404-4400000000000000000000000000000000000−22220000
χ5188-8-800000000000000000000000000004i−4i0000000000000000000
χ5288-8-80000000000000000000000000000−4i4i0000000000000000000
χ538-88-800-80800000000000000000000000000000000000000000000

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