Finite Group Databasebeta

← Group #313708

Character table — Group #313708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888224444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111111-111-1-1-1-1-111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-11111-1-11-1-111-1-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1111-1-1111-1
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1111-1-111-1-1-1-1-1111-1
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-11111-1-1-11
χ911111111111111111-1-1-1-1111111111-1-11111-1-1-1-11111111-1-1-1-1-1-11-1-11111-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-11111111-1-11-1
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-111-1-1111-1-1-1-111-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1111111-1-1-1-11-1-111-1-1-111-1-111-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111111-1-1-1-1-111-1-11-1
χ17222222222-22-22-22-2-20000-2222222220000-2-20000000000-2000000-200000000
χ18222222222-22-22-22-2-20000-22222-2-2-2-20000-2-200000000002000000200000000
χ19222222222-22-22-22-2-20000-2-2-2-2-222-2-200002200000000002000000-200000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-2220000220000000000-2000000200000000
χ2122222222-22-22-22-22-22222-200000000-2-222000000-2-200000-220000000000000
χ2222222222-22-22-22-22-22222-200000000-2-2-2-200000022000002-20000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000000002222000000-2-2000002-20000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000000022-2-20000002200000-220000000000000
χ25222-2-2-22-2-20-2020200000002i2i−2i−2i2-22i−2i002−20000002−2i2i2−i2−i200000000002−2i2−i200
χ26222-2-2-22-2-20-2020200000002i2i−2i−2i2-22i−2i00−22000000−22−i2−i2i2i20000000000−22−i2i200
χ27222-2-2-22-2-20-2020200000002i2i−2i−2i-22−2i2i002−20000002−2i2i2−i2−i20000000000−22−i2i200
χ28222-2-2-22-2-20-2020200000002i2i−2i−2i-22−2i2i00−22000000−22−i2−i2i2i200000000002−2i2−i200
χ29222-2-2-22-2-20-202020000000−2i−2i2i2i2-2−2i2i002−20000002−2−i2−i2i2i200000000002−2−i2i200
χ30222-2-2-22-2-20-202020000000−2i−2i2i2i2-2−2i2i00−22000000−22i2i2−i2−i20000000000−22i2−i200
χ31222-2-2-22-2-20-202020000000−2i−2i2i2i-222i−2i002−20000002−2−i2−i2i2i20000000000−22i2−i200
χ32222-2-2-22-2-20-202020000000−2i−2i2i2i-222i−2i00−22000000−22i2i2−i2−i200000000002−2−i2i200
χ3322-2-2-22-2222-2-222-2-2-222-2-222i−2i2i−2i00002-2002i−2i2i2i−2i−2i0000000000000000000000
χ3422-2-2-22-2222-2-222-2-2-222-2-22−2i2i−2i2i00002-200−2i2i−2i−2i2i2i0000000000000000000000
χ3522-2-2-22-2222-2-222-2-2-2-2-22222i−2i2i−2i0000-22002i−2i−2i−2i2i2i0000000000000000000000
χ3622-2-2-22-2222-2-222-2-2-2-2-2222−2i2i−2i2i0000-2200−2i2i2i2i−2i−2i0000000000000000000000
χ3722-2-2-22-222-2-222-2-2220000-22i−2i2i−2i00000000−2i2i00000000000002-22i−2i000000000
χ3822-2-2-22-222-2-222-2-2220000-22i−2i2i−2i00000000−2i2i0000000000000-22−2i2i000000000
χ3922-2-2-22-222-2-222-2-2220000-2−2i2i−2i2i000000002i−2i00000000000002-2−2i2i000000000
χ4022-2-2-22-222-2-222-2-2220000-2−2i2i−2i2i000000002i−2i0000000000000-222i−2i000000000
χ4122-2-2-22-22-222-2-222-2222-2-2-200000000-2200000000002i−2i2i−2i000000002i−2i000000
χ4222-2-2-22-22-222-2-222-2222-2-2-200000000-220000000000−2i2i−2i2i00000000−2i2i000000
χ4322-2-2-22-22-222-2-222-22-2-222-2000000002-200000000002i−2i2i−2i00000000−2i2i000000
χ4422-2-2-22-22-222-2-222-22-2-222-2000000002-20000000000−2i2i−2i2i000000002i−2i000000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ46444-4-4-44-44040-40-40000000000000000022−22000000−222200000000000000000000
χ47444-4-4-44-44040-40-400000000000000000−222200000022−2200000000000000000000
χ4844-444-4-4-440-40-40400000000000000000000000000022−22−22220000000000000000
χ4944-444-4-4-440-40-404000000000000000000000000000−222222−220000000000000000
χ5044-444-4-4-4-404040-400000004-4-44000000000000000000000000000000000000
χ5144-444-4-4-4-404040-40000000-444-4000000000000000000000000000000000000
χ5244-4-4-44-44-4-444-4-444-4000040000000000000000000000000000000000000000
χ534-44-44-4-44040-40-40404i−4i4i−4i00000000000000000000000000000000000000000
χ544-44-44-4-44040-40-4040−4i4i−4i4i00000000000000000000000000000000000000000
χ554-44-44-4-440-404040-4000000000000000000002i2−2i22i2−2i20000000000000000000000
χ564-44-44-4-440-404040-400000000000000000000−2i22i2−2i22i20000000000000000000000
χ574-4-44-4-44404040-40-404i−4i−4i4i00000000000000000000000000000000000000000
χ584-4-44-4-44404040-40-40−4i4i4i−4i00000000000000000000000000000000000000000
χ594-4-44-4-4440-40-404040000000000000000000022−22−22220000000000000000000000
χ604-4-44-4-4440-40-4040400000000000000000000−222222−220000000000000000000000
χ618-888-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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