Finite Group Databasebeta

← Group #306309

Character table — Group #306309

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222222224488888888888888888888161616161616161616161616161616163232
order12222222444444444422444444888888888888444444448888888844
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-1-1-1111-1-1111-1-111-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-111-1-1-1-111-1111-1-1-1-1-1-111-1-11-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1-111-1-1-1-111-11
χ51111111111111111111111-1-111-1-111-1-111-1-1-1-1-1-1111-111-1-1-1-1-1-111-11
χ61111111111111111111111-1-111-1-1-1-1-1-1-1-11111-1-11-1-1-11111-1-111-1-11-1
χ71111111111111111111111-1-1-1-1111111111111-1-1-111-1-1-11111-1-1-1-1-1-1
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ9111111111111111111-1-1-1-11111111111111111-1-11-1-11-1-1-1-1-1-11111-1-1
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111
χ11111111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1111111111-1-1-11
χ12111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-111-1-1111-1
χ13111111111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1111-1-1-1-1-11111-1-1111-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-1-1-11111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-111-11111-1-11111-1-1
χ172222222222-22-2-2-22-2-222-2-20000002200-2-200000002-20000000000000
χ182222222222-22-2-2-22-2-222-2-2000000-2-200220000000-220000000000000
χ192222222222-22-2-2-22-2-2-2-2220000002200-2-20000000-220000000000000
χ202222222222-22-2-2-22-2-2-2-222000000-2-2002200000002-20000000000000
χ2122222222-2-22-2222-2-2-200002222-2-2002200000000-200-2000000000000
χ2222222222-2-22-2222-2-2-2000022-2-22200-2-200000000200-2000000000000
χ2322222222-2-22-2222-2-2-20000-2-2222200-2-200000000-2002000000000000
χ2422222222-2-22-2222-2-2-20000-2-2-2-2-2-20022000000002002000000000000
χ252222-2-2-2-2222-2-22-2-2-222-22-200000000000022-2-2000000002-200000000
χ262222-2-2-2-2222-2-22-2-2-222-22-2000000000000-2-22200000000-2200000000
χ272222-2-2-2-2222-2-22-2-2-22-22-2200000000000022-2-200000000-2200000000
χ282222-2-2-2-2222-2-22-2-2-22-22-22000000000000-2-222000000002-200000000
χ292222-2-2-2-222-2-22-22-22-22-2-2200002-2002-200000000000000002-2000000
χ302222-2-2-2-222-2-22-22-22-22-2-220000-2200-220000000000000000-22000000
χ312222-2-2-2-222-2-22-22-22-2-222-200002-2002-20000000000000000-22000000
χ322222-2-2-2-222-2-22-22-22-2-222-20000-2200-2200000000000000002-2000000
χ332222-2-2-2-2-2-2-222-222-22000000002-200-220000002i−2i00002i−2i0000000000
χ342222-2-2-2-2-2-2-222-222-22000000002-200-22000000−2i2i0000−2i2i0000000000
χ352222-2-2-2-2-2-2-222-222-2200000000-22002-20000002i−2i0000−2i2i0000000000
χ362222-2-2-2-2-2-2-222-222-2200000000-22002-2000000−2i2i00002i−2i0000000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000
χ384444-4-4-4-4-4-444-44-444-400000000000000000000000000000000000000
χ3944-4-444-4-44-404000-40000000000004-400000000000000000000000000
χ4044-4-444-4-44-404000-4000000000000-4400000000000000000000000000
χ4144-4-444-4-4-440-400040000000000000000002i2−2i22i2−2i2000000000000000000
χ4244-4-444-4-4-440-40004000000000000000000−2i22i2−2i22i2000000000000000000
χ4344-4-4-4-4444-40-4000400000000000000004-40000000000000000000000
χ4444-4-4-4-4444-40-400040000000000000000-440000000000000000000000
χ4544-4-4-4-444-4404000-40000000000000000002i2−2i2−2i22i2000000000000000000
χ4644-4-4-4-444-4404000-4000000000000000000−2i22i22i2−2i2000000000000000000
χ474-4-444-4-4400404-4-400000004i−4i00000000000000000000000000000000
χ484-4-444-4-4400404-4-40000000−4i4i00000000000000000000000000000000
χ494-4-444-4-4400-40-4440000000000000000000000000000000000022−220000
χ504-4-444-4-4400-40-44400000000000000000000000000000000000−22220000
χ514-4-44-444-40040-4-4400000000000000000000000000000000000002i2−2i200
χ524-4-44-444-40040-4-440000000000000000000000000000000000000−2i22i200
χ534-4-44-444-400-4044-40000000004i−4i000000000000000000000000000000
χ544-4-44-444-400-4044-4000000000−4i4i000000000000000000000000000000
χ558-88-88-88-8000000000000000000000000000000000000000000000000
χ568-88-8-88-88000000000000000000000000000000000000000000000000

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