Finite Group Databasebeta

← Group #268671

Character table — Group #268671

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444448888888888888888888161616161616161616161616161616163232
order12224444442444442444444444488888888224444888888888828
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11-1-1-1-1
χ5111111111111111111-1-11-1-1111111-1-111-1-11-11-1-1-1-1111-1-1-1111-1-1
χ6111111111111111111-1-11-1-11111-1-111-1-111-11-1-1-111-1-1-1111-111-1-1
χ7111111111111111111-1-11-1-1-1-1-1-111-1-1-1-111-11-1-1-111111-1-1-1-1-1-111
χ8111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-11-11-1-1-1-1-1-1-11111-1-111
χ911111111111-1-1111-1-111-111111111111111-1-1-1-1-1-111-1-11-1-11-1-1-11
χ1011111111111-1-1111-1-111-1111111-1-1-1-1-1-1-1-1111-1-11-1-111-111-1-1-1-11
χ1111111111111-1-1111-1-111-111-1-1-1-11111-1-1-1-1111-1-11-11-1-11-1-1-1111-1
χ1211111111111-1-1111-1-111-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-111-1111111-1
χ1311111111111-1-1111-1-1-1-1-1-1-1111111-1-111-1-1-11-1111-11-1-1-1111-1-11-1
χ1411111111111-1-1111-1-1-1-1-1-1-11111-1-111-1-1111-1111-11-1111-1-1-1-1-11-1
χ1511111111111-1-1111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1111-111-1-1-111-111-11
χ1611111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11-1111-1-1111-1-1111-11
χ17222222-222-2-200-2-2200220-2-20000222200000000000-200-20000000
χ18222222-222-2-200-2-2200220-2-20000-2-2-2-20000000000020020000000
χ19222222-222-2-200-2-2200-2-2022000022-2-200000000000-20020000000
χ20222222-222-2-200-2-2200-2-20220000-2-22200000000000200-20000000
χ2122222-222-22-222-22-2-2-20020000000000002202000-2-200000000000
χ2222222-222-22-222-22-2-2-2002000000000000-2-20-20002200000000000
χ2322222-222-22-2-2-2-22-22200-2000000000000220-20002-200000000000
χ2422222-222-22-2-2-2-22-22200-2000000000000-2-202000-2200000000000
χ252222-222-222-2222-2-2-2200-200000000002200-2020000000000-20000
χ262222-222-222-2222-2-2-2200-20000000000-2-20020-2000000000020000
χ272222-222-222-2-2-22-2-22-20020000000000220020-20000000000-20000
χ282222-222-222-2-2-22-2-22-20020000000000-2-200-202000000000020000
χ292222-2-22-2-22222-2-222-22-2-22-20000000000000002-20000000000000
χ302222-2-22-2-22222-2-222-2-22-2-22000000000000000-220000000000000
χ312222-2-22-2-222-2-2-2-22-222-222-2000000000000000-220000000000000
χ322222-2-22-2-222-2-2-2-22-22-222-220000000000000002-20000000000000
χ332222-2-2-2-2-2-2-200222002-20-22000000000000000000002i−2i02i−2i00000
χ342222-2-2-2-2-2-2-200222002-20-2200000000000000000000−2i2i0−2i2i00000
χ352222-2-2-2-2-2-2-20022200-2202-2000000000000000000002i−2i0−2i2i00000
χ362222-2-2-2-2-2-2-20022200-2202-200000000000000000000−2i2i02i−2i00000
χ3744444-4-44-4-44004-4-40000000000000000000000000000000000000
χ384444-44-4-44-4400-44-40000000000000000000000000000000000000
χ3944-4-400-400404-400000000002i2i−2i−2i00000000000000000000002i−2i00
χ4044-4-400-400404-40000000000−2i−2i2i2i0000000000000000000000−2i2i00
χ4144-4-400-40040-4400000000002i2i−2i−2i0000000000000000000000−2i2i00
χ4244-4-400-40040-440000000000−2i−2i2i2i00000000000000000000002i−2i00
χ434-44-4400-40000000000000002i−2i2i−2i0022−22002i2−2i2000000000000000000
χ444-44-4400-40000000000000002i−2i2i−2i00−222200−2i22i2000000000000000000
χ454-44-4400-4000000000000000−2i2i−2i2i0022−2200−2i22i2000000000000000000
χ464-44-4400-4000000000000000−2i2i−2i2i00−2222002i2−2i2000000000000000000
χ474-4-440-4004000000000000002-2-2222−220022−2200000000000000000000
χ484-4-440-4004000000000000002-2-22−222200−222200000000000000000000
χ494-4-440-400400000000000000-222-222−2200−222200000000000000000000
χ504-4-440-400400000000000000-222-2−22220022−2200000000000000000000
χ5188-8-800800-80000000000000000000000000000000000000000000
χ528-88-8-8008000000000000000000000000000000000000000000000
χ538-8-880800-800000000000000000000000000000000000000000000

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