Finite Group Databasebeta

← Group #296397

Character table — Group #296397

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222222244444444444444888888884444444444444444448888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1111111-1-1-1-1
χ511111111111111111111-1-11-1-1111111111-111-1-1-1-1-1-111-1-1-11111-1-1-1-1
χ611111111111111111111-1-11-1-1111111111-1-1-111111-1-1-1111-1-1-1-1-1-1-1-1
χ711111111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-111-1-1-111-111-111-1-1-1-11111
χ811111111111111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-111111111
χ9111111111111-1-1-1-1111111-111-11111-1-1-1-1-11-11-1-111-11-11-1-111-1-111-1-1
χ10111111111111-1-1-1-1111111-111-11111-1-1-1-1-1-11-111-1-1-1-11-111-1-11111-1-1
χ11111111111111-1-1-1-1111111-111-1-1-1-1-11111-11-11-1-1-1-1-11-1111-1-111-1-111
χ12111111111111-1-1-1-1111111-111-1-1-1-1-11111-1-11-11111-1-11-1-1-111-1-1-1-111
χ13111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11-111-1-1111-111-1-1-1-111-1-111
χ15111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-11111-1-1
χ16111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-11-1111111-1-111-1-1
χ1722222222222222-2-2-2-2-2-2222-2-2-20000000020000000-20000000000000
χ1822222222222222-2-2-2-2-2-2-2-2222-200000000-2000000020000000000000
χ19222222222222-2-222-2-2-2-222-2-2-2200000000-2000000020000000000000
χ20222222222222-2-222-2-2-2-2-2-2-22220000000020000000-20000000000000
χ2122222222-2-2-2-2222222-2-200-200-20000000000022-200000-20000000000
χ2222222222-2-2-2-2222222-2-200-200-200000000000-2-220000020000000000
χ2322222222-2-2-2-222-2-2-2-22200-20020000000002-2000000-2200000000000
χ2422222222-2-2-2-222-2-2-2-22200-2002000000000-220000002-200000000000
χ2522222222-2-2-2-2-2-222-2-22200200-200000000022000000-2-200000000000
χ2622222222-2-2-2-2-2-222-2-22200200-2000000000-2-20000002200000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2002002000000000002-2200000-20000000000
χ2822222222-2-2-2-2-2-2-2-222-2-200200200000000000-22-20000020000000000
χ29222-2-2-22-22-2-2200002-22-22i−2i02i−2i0000022-2-2000000000000000000002i−2i
χ30222-2-2-22-22-2-2200002-22-22i−2i02i−2i00000-2-22200000000000000000000−2i2i
χ31222-2-2-22-22-2-2200002-22-2−2i2i0−2i2i0000022-2-200000000000000000000−2i2i
χ32222-2-2-22-22-2-2200002-22-2−2i2i0−2i2i00000-2-222000000000000000000002i−2i
χ33222-2-2-22-22-2-220000-22-222i−2i0−2i2i022-2-200000000000000000000002i−2i00
χ34222-2-2-22-22-2-220000-22-222i−2i0−2i2i0-2-2220000000000000000000000−2i2i00
χ35222-2-2-22-22-2-220000-22-22−2i2i02i−2i022-2-20000000000000000000000−2i2i00
χ36222-2-2-22-22-2-220000-22-22−2i2i02i−2i0-2-22200000000000000000000002i−2i00
χ37444-4-4-44-4-444-400004-4-44000000000000000000000000000000000000
χ38444-4-4-44-4-444-40000-444-4000000000000000000000000000000000000
χ3944-44-4-4-4444-4-400000000000000000022−2222−220000000000000000000000
χ4044-44-4-4-4444-4-4000000000000000000−2222−22220000000000000000000000
χ4144-44-4-4-44-4-444000000000000002i2−2i22i2−2i200000000000000000000000000
χ4244-44-4-4-44-4-44400000000000000−2i22i2−2i22i200000000000000000000000000
χ4344-4-444-4-44-44-400000000000000000022−22−22220000000000000000000000
χ4444-4-444-4-44-44-4000000000000000000−222222−220000000000000000000000
χ4544-4-444-4-4-44-44000000000000002i2−2i2−2i22i200000000000000000000000000
χ4644-4-444-4-4-44-4400000000000000−2i22i22i2−2i200000000000000000000000000
χ474-44-44-4-440000004-4000000000000000000000000000000002i−2i2i−2i0000
χ484-44-44-4-440000004-400000000000000000000000000000000−2i2i−2i2i0000
χ494-44-44-4-44000000-44000000000000000000000000000000002i−2i−2i2i0000
χ504-44-44-4-44000000-4400000000000000000000000000000000−2i2i2i−2i0000
χ514-4-444-44-400004i−4i000000000000000000000000002-200002i−2i00000000
χ524-4-444-44-400004i−4i00000000000000000000000000-220000−2i2i00000000
χ534-4-444-44-40000−4i4i000000000000000000000000002-20000−2i2i00000000
χ544-4-444-44-40000−4i4i00000000000000000000000000-2200002i−2i00000000
χ558-888-88-8-8000000000000000000000000000000000000000000000000
χ568-8-8-8-8888000000000000000000000000000000000000000000000000

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