Finite Group Databasebeta

← Group #314591

Character table — Group #314591

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222222224488888888888888888888161616161616161616161616161616163232
order12222222444444444422444444888888888888444444448888888844
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-1-1-11-111111-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-111-1-1-1-1-11111-1-1111-1-1-1-1-1-1-11
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1-111-1-1111-1
χ51111111111111111111111-1-111-1-111-1-111-1-1-1-111-1-1-1111-1-1-1-1-1-1111-1
χ61111111111111111111111-1-111-1-1-1-1-1-1-1-111111-1-1-1-111-11111-1-1-1-1-11
χ71111111111111111111111-1-1-1-1111111111111-11-1-1-1-1-11-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ9111111111111111111-1-1-1-111111111111111111-11-1-1-1-1-111-1-1-1-111-1-1
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1111-1-1-1-11-1-111-1-1-1-111
χ11111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11-1-111-1111111-1-11-1
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111-1-1111-1-1-1-11111-11
χ13111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-11-1-111-1-1-1-1-1111111-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-111-1-1111-1-111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-11111-1-1-1-1-1-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-11-1111111111-1-111-1-1
χ17222222222-22-22-22-2-2-200002222-2-20022000000-20-2000000000000000
χ18222222222-22-22-22-2-2-2000022-2-22200-2-200000020-2000000000000000
χ19222222222-22-22-22-2-2-20000-2-2222200-2-2000000-202000000000000000
χ20222222222-22-22-22-2-2-20000-2-2-2-2-2-20022000000202000000000000000
χ2122222222-22-22-22-22-2-222-2-20000002200-2-200000-20000020000000000
χ2222222222-22-22-22-22-2-222-2-2000000-2-2002200000200000-20000000000
χ2322222222-22-22-22-22-2-2-2-2220000002200-2-200000200000-20000000000
χ2422222222-22-22-22-22-2-2-2-222000000-2-2002200000-20000020000000000
χ252-2-2-2222-222-2-222-2-2-222-22-200002i−2i002i−2i0000000000000000002i−2i0000
χ262-2-2-2222-222-2-222-2-2-222-22-20000−2i2i00−2i2i000000000000000000−2i2i0000
χ272-2-2-2222-222-2-222-2-2-22-22-2200002i−2i002i−2i000000000000000000−2i2i0000
χ282-2-2-2222-222-2-222-2-2-22-22-220000−2i2i00−2i2i0000000000000000002i−2i0000
χ292-2-2-2222-22-2-222-2-222-2000000002i−2i00−2i2i0000000002-22i−2i00000000000
χ302-2-2-2222-22-2-222-2-222-2000000002i−2i00−2i2i000000000-22−2i2i00000000000
χ312-2-2-2222-22-2-222-2-222-200000000−2i2i002i−2i0000000002-2−2i2i00000000000
χ322-2-2-2222-22-2-222-2-222-200000000−2i2i002i−2i000000000-222i−2i00000000000
χ332-2-2-2222-2-222-2-222-22-22-2-220000000000002i2i−2i−2i00000000002i−2i000000
χ342-2-2-2222-2-222-2-222-22-22-2-22000000000000−2i−2i2i2i0000000000−2i2i000000
χ352-2-2-2222-2-222-2-222-22-2-222-20000000000002i2i−2i−2i0000000000−2i2i000000
χ362-2-2-2222-2-222-2-222-22-2-222-2000000000000−2i−2i2i2i00000000002i−2i000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000
χ3844-444-4-4-404040-40-400000000000000000022−2222−22000000000000000000
χ3944-444-4-4-404040-40-4000000000000000000−2222−2222000000000000000000
χ4044-444-4-4-40-40-404040000000000004i−4i00000000000000000000000000
χ4144-444-4-4-40-40-40404000000000000−4i4i00000000000000000000000000
χ4244-4-4-44-4440-40-40400000000000000000000000000000002i2−2i200000000
χ4344-4-4-44-4440-40-4040000000000000000000000000000000−2i22i200000000
χ4444-4-4-44-44-404040-400000004i−4i00000000000000000000000000000000
χ4544-4-4-44-44-404040-40000000−4i4i00000000000000000000000000000000
χ464-444-44-4-44040-40-4000000000000000000000000000000000000022−2200
χ474-444-44-4-44040-40-40000000000000000000000000000000000000−222200
χ484-444-44-4-4-40-404040000000004i−4i000000000000000000000000000000
χ494-444-44-4-4-40-40404000000000−4i4i000000000000000000000000000000
χ504-44-44-4-44040-40-4040000000000000000002i2−2i2−2i22i2000000000000000000
χ514-44-44-4-44040-40-404000000000000000000−2i22i22i2−2i2000000000000000000
χ524-44-44-4-440-404040-400000000000000004i−4i0000000000000000000000
χ534-44-44-4-440-404040-40000000000000000−4i4i0000000000000000000000
χ544-4-4-4444-4-4-444-4-444-4400000000000000000000000000000000000000
χ55888-8-8-88-8000000000000000000000000000000000000000000000000
χ568-8-88-8-888000000000000000000000000000000000000000000000000

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