Finite Group Databasebeta

← Group #285415

Character table — Group #285415

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444448888888888888881616161616161616161616161616323232
order12224444442224448888888844488888888888844444488888888488
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1111-11-1-1-1-1-1-1111-1-1-1-1-1
χ311111111111111111111-1-1-1-1111-1-111-1-1-1-111-1-1-11-111111111-1-1-1-1-1-1
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
χ61111111111111111-1-1-1-11111111-1-1-1-111-1-1-1-111-11-1111-1-1-1-1-11-1-11-11
χ71111111111111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-11-11-1-1-1111-1-1-1-1-11-11
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
χ911111111111-1-111111111111-1-1-11111-1-1111111-11-11-1-11-1-1-1-1-111-1-11
χ1011111111111-1-111111111111-1-1-11111-1-111-1-111-1-1-1-111-111-1-1-1-1-111-1
χ1111111111111-1-11111111-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-11-1-1-1-11-1-111-1
χ1211111111111-1-11111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-111-111-1-1111-1-11
χ1311111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111111-11-1111-1-111-1111-1-1
χ1411111111111-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-111
χ1511111111111-1-1111-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1111-1-1111-1-1-111
χ1611111111111-1-1111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-11-1-1-111111111-1-1
χ172222222-2-22-222-2-2200002222-22-20000220000-2-200000000000-200000
χ182222222-2-22-222-2-220000-2-2-2-2-22-20000-2-200002200000000000200000
χ192222222-2-22-2-2-2-2-22000022222-220000-2-20000-2-200000000000200000
χ202222222-2-22-2-2-2-2-220000-2-2-2-22-2200002200002200000000000-200000
χ2122222-2222-2-222-22-200000000-2-22220000-2-2000020-200000000000000
χ2222222-2222-2-222-22-200000000-2-22-2-20000220000-20200000000000000
χ2322222-2222-2-2-2-2-22-20000000022-2220000-2-20000-20200000000000000
χ2422222-2222-2-2-2-2-22-20000000022-2-2-2000022000020-200000000000000
χ2522222-22-2-2-22222-2-22i2i−2i−2i00002-2-2002i−2i000000000000000002i−2i000000
χ2622222-22-2-2-22222-2-2−2i−2i2i2i00002-2-200−2i2i00000000000000000−2i2i000000
χ2722222-22-2-2-22-2-22-2-22i2i−2i−2i0000-222002i−2i00000000000000000−2i2i000000
χ2822222-22-2-2-22-2-22-2-2−2i−2i2i2i0000-22200−2i2i000000000000000002i−2i000000
χ292222-22-2222-2002-2-22222000000000-2-2000022000-20200-20000000000
χ302222-22-2222-2002-2-22222000000000-2-20000-2-200020-20020000000000
χ312222-22-2222-2002-2-2-2-2-2-20000000002200002200020-200-20000000000
χ322222-22-2222-2002-2-2-2-2-2-2000000000220000-2-2000-2020020000000000
χ332222-2-2-2-2-2-2-2002222i2i−2i−2i000000000−2i2i0000000000002-202i−2i00000000
χ342222-2-2-2-2-2-2-2002222i2i−2i−2i000000000−2i2i000000000000-220−2i2i00000000
χ352222-2-2-2-2-2-2-200222−2i−2i2i2i0000000002i−2i0000000000002-20−2i2i00000000
χ362222-2-2-2-2-2-2-200222−2i−2i2i2i0000000002i−2i000000000000-2202i−2i00000000
χ374444-44-4-4-44400-44-40000000000000000000000000000000000000000
χ384444-4-4-444-4400-4-440000000000000000000000000000000000000000
χ3944-4-440-400004-400000002222−22−22000000022−2200000000000000000000000
χ4044-4-440-400004-40000000−22−2222220000000−222200000000000000000000000
χ4144-4-440-40000-4400000002222−22−220000000−222200000000000000000000000
χ4244-4-440-40000-440000000−22−222222000000022−2200000000000000000000000
χ434-44-40-4000400000000002i2−2i22i2−2i2000000000002i2−2i2000000000000002-2000
χ444-44-40-4000400000000002i2−2i22i2−2i200000000000−2i22i200000000000000-22000
χ454-44-40-400040000000000−2i22i2−2i22i2000000000002i2−2i200000000000000-22000
χ464-44-40-400040000000000−2i22i2−2i22i200000000000−2i22i2000000000000002-2000
χ474-4-440004-400000002i2−2i22i2−2i22i−2i−2i2i00000000022−22002i−2i00000000000000000
χ484-4-440004-400000002i2−2i22i2−2i2−2i2i2i−2i000000000−222200−2i2i00000000000000000
χ494-4-440004-40000000−2i22i2−2i22i22i−2i−2i2i000000000−2222002i−2i00000000000000000
χ504-4-440004-40000000−2i22i2−2i22i2−2i2i2i−2i00000000022−2200−2i2i00000000000000000
χ514-4-44000-44000000022−22−22222i−2i−2i2i0002i2−2i200000000−2i2i00000000000000000
χ524-4-44000-44000000022−22−2222−2i2i2i−2i000−2i22i2000000002i−2i00000000000000000
χ534-4-44000-440000000−222222−222i−2i−2i2i000−2i22i200000000−2i2i00000000000000000
χ544-4-44000-440000000−222222−22−2i2i2i−2i0002i2−2i2000000002i−2i00000000000000000
χ5588-8-8-8080000000000000000000000000000000000000000000000000
χ568-88-808000-80000000000000000000000000000000000000000000000

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