Finite Group Databasebeta

← Group #268708

Character table — Group #268708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444448888888888888888888161616161616161616161616161616163232
order12224444442444442224444444488888888444444888888888848
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ511111111111111111-1-111-1-1111111-1-111-1-11-1-1-11-11-1111-1-1-111-1-1
χ611111111111111111-1-111-1-11111-1-111-1-111-11-1-1-11-11-1-1-111111-1-1
χ711111111111111111-1-111-1-1-1-1-1-111-1-1-1-111-11-1-1-11-11111-1-1-1-1-111
χ811111111111111111-1-111-1-1-1-1-1-1-1-11111-1-11-1-1-11-11-1-1-1-1111-1-111
χ91111111111111-1-11-111-1-111111111111111-1-1-1-1-1-1111-1-11-1-1-1-1-11
χ101111111111111-1-11-111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-111-111-1-1-11
χ111111111111111-1-11-111-1-111-1-1-1-11111-1-1-1-111-1-111-1-11-1-11-1-1111-1
χ121111111111111-1-11-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111-111111-1
χ131111111111111-1-11-1-1-1-1-1-1-1111111-1-111-1-1-1111-111-11-1-1-111-1-11-1
χ141111111111111-1-11-1-1-1-1-1-1-11111-1-111-1-1111-1111-1-11-1111-1-1-1-11-1
χ151111111111111-1-11-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1111-1-111-1-1-11111-11
χ161111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1111-111-1-1111-1-111-11
χ17222222-222-2-2-2-200202200-2-200002222000000000000-200-2000000
χ18222222-222-2-2-2-200202200-2-20000-2-2-2-20000000000002002000000
χ19222222-222-2-2-2-20020-2-20022000022-2-2000000000000-2002000000
χ20222222-222-2-2-2-20020-2-200220000-2-222000000000000200-2000000
χ2122222-222-22-22-222-2-2002-2000000000000220-200020-20000000000
χ2222222-222-22-22-222-2-2002-2000000000000-2-202000-2020000000000
χ2322222-222-22-22-2-2-2-2200-220000000000002202000-20-20000000000
χ2422222-222-22-22-2-2-2-2200-22000000000000-2-20-20002020000000000
χ252222-222-222-2-2222-2-200-2200000000002200-200020-200000000000
χ262222-222-222-2-2222-2-200-220000000000-2-2002000-20200000000000
χ272222-222-222-2-22-2-2-22002-2000000000022002000-20-200000000000
χ282222-222-222-2-22-2-2-22002-20000000000-2-200-200020200000000000
χ292222-2-22-2-222-2-222222-2-2-22-2000000000000002-200000000000000
χ302222-2-22-2-222-2-22222-22-2-2-2200000000000000-2200000000000000
χ312222-2-22-2-222-2-2-2-22-22-2222-200000000000000-2200000000000000
χ322222-2-22-2-222-2-2-2-22-2-2222-22000000000000002-200000000000000
χ332222-2-2-2-2-2-2-22200202-200-220000000000000000000002i−2i02i−2i0000
χ342222-2-2-2-2-2-2-22200202-200-22000000000000000000000−2i2i0−2i2i0000
χ352222-2-2-2-2-2-2-2220020-22002-20000000000000000000002i−2i0−2i2i0000
χ362222-2-2-2-2-2-2-2220020-22002-2000000000000000000000−2i2i02i−2i0000
χ3744444-4-44-4-44-4400-40000000000000000000000000000000000000
χ384444-44-4-44-444-400-40000000000000000000000000000000000000
χ3944-4-40400-40000000000000022-2-222−220022−2200000000000000000000
χ4044-4-40400-40000000000000022-2-2−222200−222200000000000000000000
χ4144-4-40400-400000000000000-2-22222−2200−222200000000000000000000
χ4244-4-40400-400000000000000-2-222−22220022−2200000000000000000000
χ434-44-4400-40000000000000002-22-20022−220022−22000000000000000000
χ444-44-4400-40000000000000002-22-200−222200−2222000000000000000000
χ454-44-4400-4000000000000000-22-220022−2200−2222000000000000000000
χ464-44-4400-4000000000000000-22-2200−22220022−22000000000000000000
χ474-4-4400-40040004-4000000002-2-2200000000000000000000002-200
χ484-4-4400-40040004-400000000-222-20000000000000000000000-2200
χ494-4-4400-4004000-44000000002-2-220000000000000000000000-2200
χ504-4-4400-4004000-4400000000-222-200000000000000000000002-200
χ5188-8-80-800800000000000000000000000000000000000000000000
χ528-88-8-8008000000000000000000000000000000000000000000000
χ538-8-8800800-80000000000000000000000000000000000000000000

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