Finite Group Databasebeta

← Group #7054972

Character table — Group #7054972

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83
size111111112222222244444444444444444444444444444444888888888888888888888888816161616161616161616
order12222222444444442222222244444444888888888888888822444444444444444888888882244444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-111-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111-1-111-1-11
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-111-1-1-11111-1-11-111-1-111-1-11-1-11-1-1-1-111
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-111-1-111-1-1-111-11111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-11-1-1-111-1-111-1111-111-11-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-11111-1-1111-1-1-111-1-1111-1-1-11-1-11-11
χ9111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-111-1-1-1-1-111111-1-111-11-1-111-111-1
χ10111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-111111-1-1111-111-1-11-1-11
χ11111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11-11-11-11111
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-11-111-111111111-11-1-1-1-111-1-1-11-11-11-1-1-1-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1111111-111111111-1-111-1-111-1-1-1-1-1-1-1-11-1-1-11-11-1
χ14111111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-11-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1111-11-11
χ15111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11-1-1111-1-1-1-111-1-1-1-111111111-1-1-11-1-111
χ16111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1111111-1-1111-111-1-1
χ17111111111-1-1-1-1111-1-111-1-111-1-111-1-1111111-1-1-1-11111111111-1111-111-1-1-1-1-1-1-11-1-1-1-1-1-111-11-11-1-111-11
χ18111111111-1-1-1-1111-1-111-1-111-1-111-1-1111111-1-1-1-111111111-1-1-11-1-1-1-1-1111111-11-1-1-1-1-1-1111-11-111-1-11-1
χ19111111111-1-1-1-1111-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-11-1-1-11111-1-1-1-1-11111111-1-11-111-11-11-1-1
χ20111111111-1-1-1-1111-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-11111-11111111-1-1-11-1-11-11-111
χ21111111111-1-1-1-1111-1-111-1-1-1-111-1-11111111111111111-1-1-1-1111-1111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-11
χ22111111111-1-1-1-1111-1-111-1-1-1-111-1-11111111111111111-1-1-1-1-1-11-1-1-11111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1111-1
χ23111111111-1-1-1-1111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-11-1-111-1-111-1-111-1-1111111-111-11-1-1-1
χ24111111111-1-1-1-1111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-111111-1-111-1-1-1-111-1-11111-1-11-1-11-1111
χ25111111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-11111111-1-1-1-11-1-1
χ26111111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-11111-1-1-11111-111
χ27111111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1111-11
χ28111111111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-1-1111111-1-1-1-111111-1-1-11-1
χ29111111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-111-1-111-1-11-1-1-11111-1-11-1-1-1111-1-1-1
χ30111111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-1111-1-1-11111-1-1-1111-1-1-1111
χ31111111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1111111-1-11-111-1-1-1-111-111-11-1-1-1-11
χ32111111111-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1111-111-1-1-1-1111-1-11-11111-1
χ3322222222-22222-2-2-2-2-222-2-22222-2-2-2-2-2-2000000000000000000-22002000000002-2000000000000000000
χ3422222222-22222-2-2-2-2-222-2-2-2-2-2-22222-2-20000000000000000002-200-20000000022000000000000000000
χ3522222222-22222-2-2-2-2-2-2-2222222222222000000000000000000-2-200-200000000-2-2000000000000000000
χ3622222222-22222-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2220000000000000000002200200000000-22000000000000000000
χ3722222222-2-2-2-2-2-2-2-222222222-2-2-2-222-2-20000000000000000002200-200000000-2-2000000000000000000
χ3822222222-2-2-2-2-2-2-2-2222222-2-22222-2-2-2-2000000000000000000-2-200200000000-22000000000000000000
χ3922222222-2-2-2-2-2-2-2-222-2-2-2-222-2-222-2-2220000000000000000002-2002000000002-2000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-2-2-2-2-222-2-22222000000000000000000-2200-20000000022000000000000000000
χ41222-2-2-22-202i2i−2i−2i00000002-22-22i−2i2i−2i2-22i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000i2−i2i2−i22−22−20000000000
χ42222-2-2-22-202i2i−2i−2i00000002-22-22i−2i2i−2i2-22i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000000−i2i2−i2i2−22−220000000000
χ43222-2-2-22-202i2i−2i−2i00000002-2-22−2i2i−2i2i-222i−2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000000i2−i2−i2i22−2−220000000000
χ44222-2-2-22-202i2i−2i−2i00000002-2-22−2i2i−2i2i-222i−2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000−i2i2i2−i2−222−20000000000
χ45222-2-2-22-202i2i−2i−2i0000000-222-22i−2i−2i2i-22−2i2i22−2−2−2−222−i2−i2i2i2−i2−i2i2i200000000000000000i2−i2i2−i2−222−20000000000
χ46222-2-2-22-202i2i−2i−2i0000000-222-22i−2i−2i2i-22−2i2i−2−22222−2−2i2i2−i2−i2i2i2−i2−i200000000000000000−i2i2−i2i22−2−220000000000
χ47222-2-2-22-202i2i−2i−2i0000000-22-22−2i2i2i−2i2-2−2i2i22−2−222−2−2−i2−i2i2i2i2i2−i2−i200000000000000000i2−i2−i2i2−22−220000000000
χ48222-2-2-22-202i2i−2i−2i0000000-22-22−2i2i2i−2i2-2−2i2i−2−222−2−222i2i2−i2−i2−i2−i2i2i200000000000000000−i2i2i2−i22−22−20000000000
χ49222-2-2-22-20−2i−2i2i2i00000002-22-2−2i2i−2i2i2-2−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000000−i2i2−i2i22−22−20000000000
χ50222-2-2-22-20−2i−2i2i2i00000002-22-2−2i2i−2i2i2-2−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000000i2−i2i2−i2−22−220000000000
χ51222-2-2-22-20−2i−2i2i2i00000002-2-222i−2i2i−2i-22−2i2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000000−i2i2i2−i22−2−220000000000
χ52222-2-2-22-20−2i−2i2i2i00000002-2-222i−2i2i−2i-22−2i2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000i2−i2−i2i2−222−20000000000
χ53222-2-2-22-20−2i−2i2i2i0000000-222-2−2i2i2i−2i-222i−2i22−2−2−2−222i2i2−i2−i2i2i2−i2−i200000000000000000−i2i2−i2i2−222−20000000000
χ54222-2-2-22-20−2i−2i2i2i0000000-222-2−2i2i2i−2i-222i−2i−2−22222−2−2−i2−i2i2i2−i2−i2i2i200000000000000000i2−i2i2−i22−2−220000000000
χ55222-2-2-22-20−2i−2i2i2i0000000-22-222i−2i−2i2i2-22i−2i22−2−222−2−2i2i2−i2−i2−i2−i2i2i200000000000000000−i2i2i2−i2−22−220000000000
χ56222-2-2-22-20−2i−2i2i2i0000000-22-222i−2i−2i2i2-22i−2i−2−222−2−222−i2−i2i2i2i2i2−i2−i200000000000000000i2−i2−i2i22−22−20000000000
χ5722-22-2-2-2222-22-22-2-22-20000000000000000002i−2i2i−2i00002i−2i2i−2i00002-202i−2i2-2002i−2i00000000000000000000
χ5822-22-2-2-2222-22-22-2-22-20000000000000000002i−2i2i−2i00002i−2i2i−2i0000-220−2i2i-2200−2i2i00000000000000000000
χ5922-22-2-2-2222-22-22-2-22-2000000000000000000−2i2i−2i2i0000−2i2i−2i2i00002-20−2i2i2-200−2i2i00000000000000000000
χ6022-22-2-2-2222-22-22-2-22-2000000000000000000−2i2i−2i2i0000−2i2i−2i2i0000-2202i−2i-22002i−2i00000000000000000000
χ6122-22-2-2-222-22-222-2-2-220000000000000000002i−2i2i−2i0000−2i2i−2i2i00002-20−2i2i-22002i−2i00000000000000000000
χ6222-22-2-2-222-22-222-2-2-220000000000000000002i−2i2i−2i0000−2i2i−2i2i0000-2202i−2i2-200−2i2i00000000000000000000
χ6322-22-2-2-222-22-222-2-2-22000000000000000000−2i2i−2i2i00002i−2i2i−2i00002-202i−2i-2200−2i2i00000000000000000000
χ6422-22-2-2-222-22-222-2-2-22000000000000000000−2i2i−2i2i00002i−2i2i−2i0000-220−2i2i2-2002i−2i00000000000000000000
χ6544-44-4-4-44-44-44-4-444-4400000000000000000000000000000000000000000000000000000000000000000
χ6644-44-4-4-44-4-44-44-4444-400000000000000000000000000000000000000000000000000000000000000000
χ6744-4-444-4-404i−4i−4i4i000000000000000000000002i2−2i2−2i22i20000−222222−2200000000000000000000000000000000000
χ6844-4-444-4-404i−4i−4i4i00000000000000000000000−2i22i22i2−2i2000022−22−222200000000000000000000000000000000000
χ6944-4-444-4-40−4i4i4i−4i000000000000000000000002i2−2i2−2i22i2000022−22−222200000000000000000000000000000000000
χ7044-4-444-4-40−4i4i4i−4i00000000000000000000000−2i22i22i2−2i20000−222222−2200000000000000000000000000000000000
χ714-4444-4-4-400000000004-40000000000002i2−2i22i2−2i200002i2−2i22i2−2i2000000000000000000000000000000000000000
χ724-4444-4-4-400000000004-4000000000000−2i22i2−2i22i20000−2i22i2−2i22i2000000000000000000000000000000000000000
χ734-4444-4-4-40000000000-440000000000002i2−2i22i2−2i20000−2i22i2−2i22i2000000000000000000000000000000000000000
χ744-4444-4-4-40000000000-44000000000000−2i22i2−2i22i200002i2−2i22i2−2i2000000000000000000000000000000000000000
χ754-44-4-44-4440000-44-400000000000000004i−4i−4i4i00000000000000000000000000000000000000000000000
χ764-44-4-44-4440000-44-40000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000
χ774-44-4-44-44-400004-440000000000000000000000004-4-44000000000000000000000000000000000000000
χ784-44-4-44-44-400004-44000000000000000000000000-444-4000000000000000000000000000000000000000
χ794-4-4-44-44440000-4-44000000000000000000000000000000004-4000000000000000000000000000000000
χ804-4-4-44-44440000-4-4400000000000000000000000000000000-44000000000000000000000000000000000
χ814-4-4-44-444-4000044-400000000000000000000000000000000000000000004-40000000000000000000000
χ824-4-4-44-444-4000044-40000000000000000000000000000000000000000000-440000000000000000000000
χ838-8-88-888-8000000000000000000000000000000000000000000000000000000000000000000000000000

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