Finite Group Databasebeta

← Group #268755

Character table — Group #268755

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11112222224444448888888888888888888161616161616161616161616161616163232
order12224444442444442224444444488888888444444888888888848
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11-1-111111-1-1-1-1
χ411111111111111111111111-1-1-1-1-1-1-1-11111111111-111-1-1-1-1-1-1-1-1-1
χ511111111111111111-1-111-1-1111111-1-111-1-1-1-111-1-1-11-1111-1-111-1-1
χ611111111111111111-1-111-1-11111-1-111-1-111-1-1-1-1111-11-1-1-11111-1-1
χ711111111111111111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111
χ811111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111
χ91111111111111-1-11-111-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-11
χ101111111111111-1-11-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-11
χ111111111111111-1-11-111-1-111-1-1-1-11111-1-1-1-1-1-111111-1-11-1-1-1-1111-1
χ121111111111111-1-11-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-11111111-1
χ131111111111111-1-11-1-1-1-1-1-1-1111111-1-111-1-111-1-111-11-11-1-111-1-11-1
χ141111111111111-1-11-1-1-1-1-1-1-11111-1-111-1-1111111-1-11-11-111-1-1-1-11-1
χ151111111111111-1-11-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-11111-11
χ161111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-111-11
χ17222222-222-2-2-2-200202200-2-2000022-2-20000000000200-200000000
χ18222222-222-2-2-2-200202200-2-20000-2-2220000000000-200200000000
χ19222222-222-2-2-2-20020-2-20022000022220000000000-200-200000000
χ20222222-222-2-2-2-20020-2-200220000-2-2-2-20000000000200200000000
χ2122222-222-22-22-222-2200-2-200000000002200002-2000-20000000000
χ2222222-222-22-22-222-2200-2-20000000000-2-20000-2200020000000000
χ2322222-222-22-22-2-2-2-2-200220000000000220000-22000-20000000000
χ2422222-222-22-22-2-2-2-2-200220000000000-2-200002-200020000000000
χ252222-222-222-2-2222-2-2002-20000000000002200002-200-2000000000
χ262222-222-222-2-2222-2-2002-2000000000000-2-20000-22002000000000
χ272222-222-222-2-22-2-2-2200-22000000000000220000-2200-2000000000
χ282222-222-222-2-22-2-2-2200-22000000000000-2-200002-2002000000000
χ292222-2-22-2-222-2-2222-22-2-222-20000000000002-20000000000000000
χ302222-2-22-2-222-2-2222-2-22-22-22000000000000-220000000000000000
χ312222-2-22-2-222-2-2-2-2222-22-22-2000000000000-220000000000000000
χ322222-2-22-2-222-2-2-2-222-222-2-220000000000002-20000000000000000
χ332222-2-2-2-2-2-2-22200202-200-2200000000000000000000002i−2i2i−2i0000
χ342222-2-2-2-2-2-2-22200202-200-220000000000000000000000−2i2i−2i2i0000
χ352222-2-2-2-2-2-2-2220020-22002-200000000000000000000002i−2i−2i2i0000
χ362222-2-2-2-2-2-2-2220020-22002-20000000000000000000000−2i2i2i−2i0000
χ3744444-4-44-4-44-4400-40000000000000000000000000000000000000
χ384444-44-4-44-444-400-40000000000000000000000000000000000000
χ3944-4-400-40040004i−4i0000000022-2-200000000000000000000002i−2i00
χ4044-4-400-40040004i−4i00000000-2-2220000000000000000000000−2i2i00
χ4144-4-400-4004000−4i4i0000000022-2-20000000000000000000000−2i2i00
χ4244-4-400-4004000−4i4i00000000-2-22200000000000000000000002i−2i00
χ434-44-40-4004000000000000002i−2i2i−2i0022−22002i2−2i2000000000000000000
χ444-44-40-4004000000000000002i−2i2i−2i00−222200−2i22i2000000000000000000
χ454-44-40-400400000000000000−2i2i−2i2i0022−2200−2i22i2000000000000000000
χ464-44-40-400400000000000000−2i2i−2i2i00−2222002i2−2i2000000000000000000
χ474-4-44-40040000000000000002i−2i−2i2i2i2−2i20022−2200000000000000000000
χ484-4-44-40040000000000000002i−2i−2i2i−2i22i200−222200000000000000000000
χ494-4-44-4004000000000000000−2i2i2i−2i2i2−2i200−222200000000000000000000
χ504-4-44-4004000000000000000−2i2i2i−2i−2i22i20022−2200000000000000000000
χ5188-8-800800-80000000000000000000000000000000000000000000
χ528-88-80800-800000000000000000000000000000000000000000000
χ538-8-88800-8000000000000000000000000000000000000000000000

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