Finite Group Databasebeta

← Group #309010

Character table — Group #309010

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-111111-11-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-11-1111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-111-1-111-11-1-111-1-11-1
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111-1111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-11111-1-11-1
χ911111111111111111-1-1-1-1111111111-1-11111-1-1-1-1111111-1-1-1-11-11-1-1-11111-1-1
χ1011111111111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-11111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-11111-11-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11-111-1-1111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-1-1111-1-111-1-1-11
χ17222222222-2-222-22-2-20000-22222222200-2-20000000000000000-20-2000000000
χ18222222222-2-222-22-2-20000-22222-2-2-2-200-2-20000000000000000202000000000
χ19222222222-2-222-22-2-20000-2-2-2-2-222-2-200220000000000000000-202000000000
χ20222222222-2-222-22-2-20000-2-2-2-2-2-2-2220022000000000000000020-2000000000
χ2122222222-222-2-22-22-22222-200000000-2-200220000-2-200000000020-200000000
χ2222222222-222-2-22-22-22222-200000000-2-200-2-2000022000000000-20200000000
χ2322222222-222-2-22-22-2-2-2-2-2-2000000002200220000-2-2000000000-20200000000
χ2422222222-222-2-22-22-2-2-2-2-2-2000000002200-2-200002200000000020-200000000
χ252222-2-2-2-22002-20-2000000022-2-22-22-200002−200002−222−2−200000000002−22−200
χ262222-2-2-2-22002-20-2000000022-2-22-22-20000−220000−22−2−2220000000000−22−2200
χ272222-2-2-2-22002-20-2000000022-2-2-22-2200002−200002−222−2−20000000000−22−2200
χ282222-2-2-2-22002-20-2000000022-2-2-22-220000−220000−22−2−22200000000002−22−200
χ292222-2-2-2-22002-20-20000000-2-2222-2-2200002−200002−2−2−22200000000002−2−2200
χ302222-2-2-2-22002-20-20000000-2-2222-2-220000−220000−2222−2−20000000000−222−200
χ312222-2-2-2-22002-20-20000000-2-222-222-200002−200002−2−2−2220000000000−222−200
χ322222-2-2-2-22002-20-20000000-2-222-222-20000−220000−2222−2−200000000002−2−2200
χ3322-2-222-2-22-2-2-2-222222i2i−2i−2i-2000000002i−2i00000000002i−2i2i−2i000000002-2000000
χ3422-2-222-2-22-2-2-2-222222i2i−2i−2i-2000000002i−2i0000000000−2i2i−2i2i00000000-22000000
χ3522-2-222-2-22-2-2-2-22222−2i−2i2i2i-200000000−2i2i00000000002i−2i2i−2i00000000-22000000
χ3622-2-222-2-22-2-2-2-22222−2i−2i2i2i-200000000−2i2i0000000000−2i2i−2i2i000000002-2000000
χ3722-2-222-2-2-22222-2-2-220000-22-22-20000002-20000000000002-22-2000000000000
χ3822-2-222-2-2-22222-2-2-220000-22-22-20000002-2000000000000-22-22000000000000
χ3922-2-222-2-2-22222-2-2-220000-2-22-22000000-220000000000002-2-22000000000000
χ4022-2-222-2-2-22222-2-2-220000-2-22-22000000-22000000000000-222-2000000000000
χ4122-2-222-2-2-2-2-2222-22-22i2i−2i−2i22-22-20000−2i2i-22002i2i−2i−2i0000000000000000000000
χ4222-2-222-2-2-2-2-2222-22-22i2i−2i−2i2-22-220000−2i2i2-200−2i−2i2i2i0000000000000000000000
χ4322-2-222-2-2-2-2-2222-22-2−2i−2i2i2i22-22-200002i−2i-2200−2i−2i2i2i0000000000000000000000
χ4422-2-222-2-2-2-2-2222-22-2−2i−2i2i2i2-22-2200002i−2i2-2002i2i−2i−2i0000000000000000000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ464444-4-4-4-4-400-4404000000000000000000022−220000−222200000000000000000000
χ474444-4-4-4-4-400-44040000000000000000000−2222000022−2200000000000000000000
χ4844-4-444-4-4444-4-4-44-4-4000040000000000000000000000000000000000000000
χ4944-4-4-4-444400-440-40000000000000000000000000002i2−2i2−2i22i20000000000000000
χ5044-4-4-4-444400-440-4000000000000000000000000000−2i22i22i2−2i20000000000000000
χ5144-4-4-4-444-4004-40400000004-4-44000000000000000000000000000000000000
χ5244-4-4-4-444-4004-4040000000-444-4000000000000000000000000000000000000
χ534-44-44-44-404-40040-404-44-400000000000000000000000000000000000000000
χ544-44-44-44-404-40040-40-44-4400000000000000000000000000000000000000000
χ554-44-44-44-40-4400-404000000000000000000002i2−2i22i2−2i20000000000000000000000
χ564-44-44-44-40-4400-40400000000000000000000−2i22i2−2i22i20000000000000000000000
χ574-4-444-4-4404-400-4040000000000000000000022−22−22220000000000000000000000
χ584-4-444-4-4404-400-40400000000000000000000−222222−220000000000000000000000
χ594-4-444-4-440-440040-404i−4i−4i4i00000000000000000000000000000000000000000
χ604-4-444-4-440-440040-40−4i4i4i−4i00000000000000000000000000000000000000000
χ618-88-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-88-888-8000000000000000000000000000000000000000000000000000000

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