Finite Group Databasebeta

← Group #309124

Character table — Group #309124

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-11-111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-11-1-1-1-1-1111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-11-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-1-11-1-11111-1-1-1-111-11
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-11111-1-11-1
χ911111111111111111-1-1-1-111111-1-111111111-1-1-1-11111111-1-1-1-1-11-1-1-11111-1-1
χ1011111111111111111-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-111-1-11111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-111-11-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-11-111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1111-1-111-1-111-1-1-11
χ17222222222-2-222-22-2-20000-22222002222-2-2000000000000-200000-2000000000
χ18222222222-2-222-22-2-20000-2222200-2-2-2-2-2-20000000000002000002000000000
χ19222222222-2-222-22-2-20000-2-2-2-2-20022-2-222000000000000-2000002000000000
χ20222222222-2-222-22-2-20000-2-2-2-2-200-2-22222000000000000200000-2000000000
χ2122222222-222-2-22-22-22222-20000-2-2000000220000-2-200000200000-200000000
χ2222222222-222-2-22-22-22222-20000-2-2000000-2-200002200000-200000200000000
χ2322222222-222-2-22-22-2-2-2-2-2-2000022000000220000-2-200000-200000200000000
χ2422222222-222-2-22-22-2-2-2-2-2-2000022000000-2-200002200000200000-200000000
χ2522-2-222-2-22-2-2-2-222222i2i−2i−2i-200002i−2i000000000000002i2i−2i−2i000000002-2000000
χ2622-2-222-2-22-2-2-2-222222i2i−2i−2i-200002i−2i00000000000000−2i−2i2i2i00000000-22000000
χ2722-2-222-2-22-2-2-2-22222−2i−2i2i2i-20000−2i2i000000000000002i2i−2i−2i00000000-22000000
χ2822-2-222-2-22-2-2-2-22222−2i−2i2i2i-20000−2i2i00000000000000−2i−2i2i2i000000002-2000000
χ2922-2-222-2-2-22222-2-2-220000-222-2-20000002-2000000000000002-22-20000000000
χ3022-2-222-2-2-22222-2-2-220000-222-2-20000002-200000000000000-22-220000000000
χ3122-2-222-2-2-22222-2-2-220000-2-2-222000000-22000000000000002-2-220000000000
χ3222-2-222-2-2-22222-2-2-220000-2-2-222000000-2200000000000000-222-20000000000
χ3322-2-222-2-2-2-2-2222-22-22i2i−2i−2i222-2-2−2i2i0000-22002i2i−2i−2i0000000000000000000000
χ3422-2-222-2-2-2-2-2222-22-22i2i−2i−2i2-2-222−2i2i00002-200−2i−2i2i2i0000000000000000000000
χ3522-2-222-2-2-2-2-2222-22-2−2i−2i2i2i222-2-22i−2i0000-2200−2i−2i2i2i0000000000000000000000
χ3622-2-222-2-2-2-2-2222-22-2−2i−2i2i2i2-2-2222i−2i00002-2002i2i−2i−2i0000000000000000000000
χ3744444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ38444-4-4-44-44004-40-4000000000000000000000000000000000000000000022−2200
χ39444-4-4-44-44004-40-40000000000000000000000000000000000000000000−222200
χ40444-4-4-44-4-400-44040000000000000004i−4i000000000000000000000000000000
χ41444-4-4-44-4-400-4404000000000000000−4i4i000000000000000000000000000000
χ4244-44-4-4-44400-440-400000000000004-400000000000000000000000000000000
χ4344-44-4-4-44400-440-40000000000000-4400000000000000000000000000000000
χ4444-44-4-4-44-4004-404000000000000000000000000000000000000000002i2−2i20000
χ4544-44-4-4-44-4004-40400000000000000000000000000000000000000000−2i22i20000
χ4644-4-444-4-4444-4-4-44-4-4000040000000000000000000000000000000000000000
χ474-4444-4-4-404-40040-40000000000000000000022−2222−220000000000000000000000
χ484-4444-4-4-404-40040-400000000000000000000−2222−22220000000000000000000000
χ494-4444-4-4-40-4400-40404i−4i4i−4i00000000000000000000000000000000000000000
χ504-4444-4-4-40-4400-4040−4i4i−4i4i00000000000000000000000000000000000000000
χ514-44-4-44-44000000000000002i2−2i22i2−2i20000000022−220000002i−2i2i−2i0000000000000000
χ524-44-4-44-44000000000000002i2−2i22i2−2i200000000−2222000000−2i2i−2i2i0000000000000000
χ534-44-4-44-4400000000000000−2i22i2−2i22i20000000022−22000000−2i2i−2i2i0000000000000000
χ544-44-4-44-4400000000000000−2i22i2−2i22i200000000−22220000002i−2i2i−2i0000000000000000
χ554-4-44-444-4000000000000002i2−2i2−2i22i2000000000000002i2−2i22-2-220000000000000000
χ564-4-44-444-4000000000000002i2−2i2−2i22i200000000000000−2i22i2-222-20000000000000000
χ574-4-44-444-400000000000000−2i22i22i2−2i2000000000000002i2−2i2-222-20000000000000000
χ584-4-44-444-400000000000000−2i22i22i2−2i200000000000000−2i22i22-2-220000000000000000
χ594-4-4-44-44404-400-40404-4-4400000000000000000000000000000000000000000
χ604-4-4-44-44404-400-4040-444-400000000000000000000000000000000000000000
χ614-4-4-44-4440-440040-4000000000000000000002i2−2i2−2i22i20000000000000000000000
χ624-4-4-44-4440-440040-400000000000000000000−2i22i22i2−2i20000000000000000000000

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