Finite Group Databasebeta

← Group #345395

Character table — Group #345395

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222222224488888888888888888888161616161616161616161616161616163232
order12222222444444444422444444888888888888444444448888888844
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-1-11111-1-1-1-1-1-1-1-111111-1-1-111-1-1-1-1-1-11-1
χ31111111111111111111111-1-111-1-1-1-11111-1-1-1-111-1-1-1111-1-1-1-111-1-11-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111
χ511111111111111111111-1-11111-1-1-1-11111-1-1-1-1-11111-1-11-1-1-1-1-1-111-11
χ611111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1111111-1-1-11111-1-1-1-1
χ711111111111111111111-1-1-1-111111111111111-11-1-1-1-1-111111-1-1-1-1-1-1
χ811111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-111-111-1-11111-11
χ9111111111111111111-1-11111111111-1-1-1-1-1-1-1-11-11-1-1111-1-111-1-1-1-1-11
χ10111111111111111111-1-11111-1-11111111111111-11-1-1-1-1-1-1-1-1-11111-1-1
χ11111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111-1-11111111-1-1-1-111-1-1
χ12111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-111-1-1-1111111-1-1-11
χ13111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1-1-1-1111-1-111-1-111
χ14111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-111-11111-1-1111-1
χ15111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11111111-1
χ16111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-11111-1-1-1-1-1-1-1-1-111
χ17222222222-2-222-22-2-2-20022220022-2-200000000-20-2000000000000000
χ18222222222-2-222-22-2-2-20022-2-200-2-22200000000-202000000000000000
χ19222222222-2-222-22-2-2-200-2-22200-2-2220000000020-2000000000000000
χ20222222222-2-222-22-2-2-200-2-2-2-20022-2-200000000202000000000000000
χ2122222222-222-2-22-22-2-222000022000022-2-200000-200000-20000000000
χ2222222222-222-2-22-22-2-2220000-2-20000-2-22200000-20000020000000000
χ2322222222-222-2-22-22-2-2-2-20000220000-2-22200000200000-20000000000
χ2422222222-222-2-22-22-2-2-2-20000-2-2000022-2-20000020000020000000000
χ252-2-22-2-222222-2-2-22-2-22000000000000000022-2-20002i−2i2i−2i00000000000
χ262-2-22-2-222222-2-2-22-2-22000000000000000022-2-2000−2i2i−2i2i00000000000
χ272-2-22-2-222222-2-2-22-2-220000000000000000-2-2220002i−2i−2i2i00000000000
χ282-2-22-2-222222-2-2-22-2-220000000000000000-2-222000−2i2i2i−2i00000000000
χ2944444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000
χ30444-4-4-44-404-40040-40000000000000000000000000000000022−22000000
χ31444-4-4-44-404-40040-400000000000000000000000000000000−2222000000
χ32444-4-4-44-40-4400-404000000004i−4i000000000000000000000000000000
χ33444-4-4-44-40-4400-40400000000−4i4i000000000000000000000000000000
χ3444-444-4-4-44004-40-400000004-400000000000000000000000000000000
χ3544-444-4-4-44004-40-40000000-4400000000000000000000000000000000
χ3644-444-4-4-4-400-440400000000000000000000000000000000000002i2−2i200
χ3744-444-4-4-4-400-44040000000000000000000000000000000000000−2i22i200
χ3844-4-4-44-440000000000000000002i2−2i20022−22002i−2i2i−2i000000000000000000
χ3944-4-4-44-440000000000000000002i2−2i200−222200−2i2i−2i2i000000000000000000
χ4044-4-4-44-44000000000000000000−2i22i20022−2200−2i2i−2i2i000000000000000000
χ4144-4-4-44-44000000000000000000−2i22i200−2222002i−2i2i−2i000000000000000000
χ424-444-44-4-4400-440-40000000000000000000000000000000000022−220000
χ434-444-44-4-4400-440-400000000000000000000000000000000000−22220000
χ444-444-44-4-4-4004-404000004i−4i0000000000000000000000000000000000
χ454-444-44-4-4-4004-40400000−4i4i0000000000000000000000000000000000
χ464-44-44-4-440000000000000000000022−22002i2−2i22i−2i−2i2i000000000000000000
χ474-44-44-4-440000000000000000000022−2200−2i22i2−2i2i2i−2i000000000000000000
χ484-44-44-4-4400000000000000000000−2222002i2−2i2−2i2i2i−2i000000000000000000
χ494-44-44-4-4400000000000000000000−222200−2i22i22i−2i−2i2i000000000000000000
χ504-4-44-4-4444-4-4-4-44444-400000000000000000000000000000000000000
χ514-4-44-4-444-44444-4-4-44-400000000000000000000000000000000000000
χ524-4-44-4-444-4-4-4444-44-4400000000000000000000000000000000000000
χ534-4-4-4444-404-400-404004-4000000000000000000000000000000000000
χ544-4-4-4444-404-400-40400-44000000000000000000000000000000000000
χ554-4-4-4444-40-440040-40000000000000000000000000000002i2−2i200000000
χ564-4-4-4444-40-440040-4000000000000000000000000000000−2i22i200000000

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