Finite Group Databasebeta

← Group #285389

Character table — Group #285389

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444448888888888888881616161616161616161616161616323232
order12224444442444448888888824488888888888824444488888888288
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-111-111-1-1-1-1-1-1111-1-1-1-1-1
χ311111111111111111111-1-1-1-1111-1-111-1-1-1-111-1-11-1-111111111-1-1-1-1-1-1
χ411111111111111111111-1-1-1-1111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111
χ51111111111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1111-1-1111-11-1
χ61111111111111111-1-1-1-11111111-1-1-1-111-1-1-1-1111-1-1111-1-1-1-1-11-1-11-11
χ71111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-111-1-1-1111-1-1-1-1-11-11
χ81111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-11-1
χ9111111111111-1-11111111111-1-1-11111-1-11111111-1-11-1-11-1-1-1-1-111-1-11
χ10111111111111-1-11111111111-1-1-11111-1-111-1-111-1-1-1-111-111-1-1-1-1-111-1
χ11111111111111-1-1111111-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-11-1-1-1-11-1-111-1
χ12111111111111-1-1111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-111-111-111-1-1111-1-11
χ13111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-111-1111-1-111-1111-1-1
χ14111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-111
χ15111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1111-1-1111-1-1-111
χ16111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-1-11-1-1-111111111-1-1
χ17222222-2-222-2-2222-2000022222-2-20000220000-2-200000000000-200000
χ18222222-2-222-2-2222-20000-2-2-2-22-2-20000-2-200002200000000000200000
χ19222222-2-222-2-2-2-22-200002222-2220000-2-20000-2-200000000000200000
χ20222222-2-222-2-2-2-22-20000-2-2-2-2-22200002200002200000000000-200000
χ2122222-2222-2-2-222-2200000000-2-22220000-2-2000002-200000000000000
χ2222222-2222-2-2-222-2200000000-2-22-2-200002200000-2200000000000000
χ2322222-2222-2-2-2-2-2-220000000022-2220000-2-200000-2200000000000000
χ2422222-2222-2-2-2-2-2-220000000022-2-2-2000022000002-200000000000000
χ2522222-2-2-22-22222-2-22i2i−2i−2i0000-22-2002i−2i000000000000000002i−2i000000
χ2622222-2-2-22-22222-2-2−2i−2i2i2i0000-22-200−2i2i00000000000000000−2i2i000000
χ2722222-2-2-22-222-2-2-2-22i2i−2i−2i00002-22002i−2i00000000000000000−2i2i000000
χ2822222-2-2-22-222-2-2-2-2−2i−2i2i2i00002-2200−2i2i000000000000000002i−2i000000
χ292222-2222-22-2200-2-22222000000000-2-200002200200-200-20000000000
χ302222-2222-22-2200-2-22222000000000-2-20000-2-200-20020020000000000
χ312222-2222-22-2200-2-2-2-2-2-20000000002200002200-200200-20000000000
χ322222-2222-22-2200-2-2-2-2-2-2000000000220000-2-200200-20020000000000
χ332222-2-2-2-2-2-2-2200222i2i−2i−2i000000000−2i2i0000000000002-202i−2i00000000
χ342222-2-2-2-2-2-2-2200222i2i−2i−2i000000000−2i2i000000000000-220−2i2i00000000
χ352222-2-2-2-2-2-2-220022−2i−2i2i2i0000000002i−2i0000000000002-20−2i2i00000000
χ362222-2-2-2-2-2-2-220022−2i−2i2i2i0000000002i−2i000000000000-2202i−2i00000000
χ374444-44-4-4-444-400-440000000000000000000000000000000000000000
χ384444-4-444-4-44-4004-40000000000000000000000000000000000000000
χ3944-4-4004-4000000002i2−2i22i2−2i22i2i−2i−2i00000000022−22002i−2i00000000000000000
χ4044-4-4004-4000000002i2−2i22i2−2i2−2i−2i2i2i000000000−222200−2i2i00000000000000000
χ4144-4-4004-400000000−2i22i2−2i22i22i2i−2i−2i000000000−2222002i−2i00000000000000000
χ4244-4-4004-400000000−2i22i2−2i22i2−2i−2i2i2i00000000022−2200−2i2i00000000000000000
χ4344-4-400-440000000022−22−22222i2i−2i−2i0002i2−2i200000000−2i2i00000000000000000
χ4444-4-400-440000000022−22−2222−2i−2i2i2i000−2i22i2000000002i−2i00000000000000000
χ4544-4-400-4400000000−222222−222i2i−2i−2i000−2i22i200000000−2i2i00000000000000000
χ4644-4-400-4400000000−222222−22−2i−2i2i2i0002i2−2i2000000002i−2i00000000000000000
χ474-44-404000-4000000000022−2222−22000000000002i2−2i2000000000000002i−2i000
χ484-44-404000-4000000000022−2222−2200000000000−2i22i200000000000000−2i2i000
χ494-44-404000-40000000000−2222−2222000000000002i2−2i200000000000000−2i2i000
χ504-44-404000-40000000000−2222−222200000000000−2i22i2000000000000002i−2i000
χ514-4-444000-40004i−4i0000002i2−2i2−2i22i2000000022−2200000000000000000000000
χ524-4-444000-40004i−4i000000−2i22i22i2−2i20000000−222200000000000000000000000
χ534-4-444000-4000−4i4i0000002i2−2i2−2i22i20000000−222200000000000000000000000
χ544-4-444000-4000−4i4i000000−2i22i22i2−2i2000000022−2200000000000000000000000
χ558-88-80-800080000000000000000000000000000000000000000000000
χ568-8-88-8000800000000000000000000000000000000000000000000000

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