Finite Group Databasebeta

← Group #169124

Character table — Group #169124

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111111114444444444888888888816161616161616161616161616161616161616163232
order12222222444444444444444444442244444488888888888844
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-11-1-11-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-11-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ61111111111111111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ71111111111111111111-1-11-1-1-1-1-1-1-1-1-111-1111111-1-1-1-11111-1-1
χ81111111111111111111-1-11-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-111
χ911111111-1-111-1-11111-111-1-1-111-1-11-111-1-11-111-1-111-1-111-1-11-1
χ1011111111-1-111-1-11111-111-1-1-111-1-11-111-1-11-1-1-111-1-111-1-111-11
χ1111111111-1-111-1-11111-111-1-1-1-1-111-111-11-1-1111-1-111-1-1-1-111-11
χ1211111111-1-111-1-11111-111-1-1-1-1-111-111-11-1-11-1-111-1-11111-1-11-1
χ1311111111-1-111-1-11111-1-1-1-11111-1-11-1-1-111-1111-1-1-1-111-1-1111-1
χ1411111111-1-111-1-11111-1-1-1-11111-1-11-1-1-111-11-1-11111-1-111-1-1-11
χ1511111111-1-111-1-11111-1-1-1-111-1-111-11-11-111-111-1-1-1-11111-1-1-11
χ1611111111-1-111-1-11111-1-1-1-111-1-111-11-11-111-1-1-11111-1-1-1-1111-1
χ1722222222222-222-2-22-2-222-222000000-200-20000000000000000
χ1822222222222-222-2-22-2-2-2-2-2-2-200000020020000000000000000
χ192222222222-22-2-2-2-2-22200-2000000000220-2-200000000000000
χ202222222222-22-2-2-2-2-22200-2000000000-2-202200000000000000
χ212222222222-2-2-2-222-2-2-2002002222-2-200000000000000000000
χ222222222222-2-2-2-222-2-2-200200-2-2-2-22200000000000000000000
χ2322222222-2-22-2-2-2-2-22-22222-2-2000000-20020000000000000000
χ2422222222-2-22-2-2-2-2-22-22-2-2222000000200-20000000000000000
χ2522222222-2-2-2222-2-2-22-20020000000002-20-2200000000000000
χ2622222222-2-2-2222-2-2-22-2002000000000-2202-200000000000000
χ2722222222-2-2-2-22222-2-2200-20022-2-2-2200000000000000000000
χ2822222222-2-2-2-22222-2-2200-200-2-2222-200000000000000000000
χ29222-2-22-2-22-2-202-2002002i−2i02i−2i000000000000i2−i2i2−i22−22−2000000
χ30222-2-22-2-22-2-202-2002002i−2i02i−2i000000000000−i2i2−i2i2−22−22000000
χ31222-2-22-2-22-2-202-200200−2i2i0−2i2i000000000000i2−i2i2−i2−22−22000000
χ32222-2-22-2-22-2-202-200200−2i2i0−2i2i000000000000−i2i2−i2i22−22−2000000
χ33222-2-22-2-2-22-20-22002002i−2i0−2i2i000000000000i2−i2−i2i22−2−22000000
χ34222-2-22-2-2-22-20-22002002i−2i0−2i2i000000000000−i2i2i2−i2−222−2000000
χ35222-2-22-2-2-22-20-2200200−2i2i02i−2i000000000000i2−i2−i2i2−222−2000000
χ36222-2-22-2-2-22-20-2200200−2i2i02i−2i000000000000−i2i2i2−i22−2−22000000
χ37444-4-44-4-44-440-4400-4000000000000000000000000000000000
χ38444-4-44-4-4-44404-400-4000000000000000000000000000000000
χ3944-4-44-4-440000004-400000000004i−4i0000000000000000000000
χ4044-4-44-4-440000004-40000000000−4i4i0000000000000000000000
χ4144-4-44-4-44000000-44000000004i−4i000000000000000000000000
χ4244-4-44-4-44000000-4400000000−4i4i000000000000000000000000
χ434-4-4-4444-4000400000-4000000000000000000000000002i2−2i20000
χ444-4-4-4444-4000400000-400000000000000000000000000−2i22i20000
χ454-4-4-4444-4000-4000004000000000000000000000000000022−2200
χ464-4-4-4444-4000-40000040000000000000000000000000000−222200
χ4788-88-8-88-8000000000000000000000000000000000000000000
χ488-8888-8-8-8000000000000000000000000000000000000000000
χ498-88-8-8-888000000000000000000000000000000000000000000
χ508-8-88-88-88000000000000000000000000000000000000000000

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