Finite Group Databasebeta

← Group #296524

Character table — Group #296524

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11111111222244444488888888888161616161616161616161616161616161616161616161616
order12222222222244444444444444444444444444444444488888888
χ111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-1-1111-1-111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1
χ511111111111111111111-1-11-1-11111-111-1-111-1-1-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-11-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111-1-11-1-1-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-1-1-1
χ811111111111111111111-1-11-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-1-1-1-11111
χ9111111111111-1-11111-1-111-11111-1-1-11-11-111-11-1-1-111-1-111-1-111-1-1
χ10111111111111-1-11111-1-111-11111-1-1-11-11-1-1-1-11-111-1-111-1-111-1-111
χ11111111111111-1-11111-1-111-111-1-111-1-11-1111-1-11-1-1-1-111-1-11111-1-1
χ12111111111111-1-11111-1-111-111-1-111-1-11-11-1-1-1-111111-1-111-1-1-1-111
χ13111111111111-1-11111-1-1-1-1-1-1-111-1-111-1-11111-11-1-111-1-1-1-111-1-111
χ14111111111111-1-11111-1-1-1-1-1-1-111-1-111-1-11-1-11-1111-1-11111-1-111-1-1
χ15111111111111-1-11111-1-1-1-1-1-1-1-1-1111-111-11111-1-1-1-1-11111-1-1-1-111
χ16111111111111-1-11111-1-1-1-1-1-1-1-1-1111-111-1-1-111-11111-1-1-1-11111-1-1
χ1722222222222222-2-2-2-2-2-20020022220-2-2000000000000000000000
χ1822222222222222-2-2-2-2-2-200200-2-2-2-2022000000000000000000000
χ19222222222222-2-2-2-2-2-22200-20022-2-20-22000000000000000000000
χ20222222222222-2-2-2-2-2-22200-200-2-22202-2000000000000000000000
χ2122222222-2-2-2-2222-2-222-222-2-2-20000-200000020000000000000000
χ2222222222-2-2-2-2222-2-222-2-2-2-22200002000000-20000000000000000
χ2322222222-2-2-2-222-222-2-2200-200000000022000-2-200000000000000
χ2422222222-2-2-2-222-222-2-2200-2000000000-2-20002200000000000000
χ2522222222-2-2-2-2-2-22-2-22-22222-2-200002000000-20000000000000000
χ2622222222-2-2-2-2-2-22-2-22-22-2-22220000-200000020000000000000000
χ2722222222-2-2-2-2-2-2-222-22-20020000000002-2000-2200000000000000
χ2822222222-2-2-2-2-2-2-222-22-2002000000000-220002-200000000000000
χ29222-2-2-22-22-22-200-22-22002i−2i02i−2i0000000000000000002i−2i002-20000
χ30222-2-2-22-22-22-200-22-22002i−2i02i−2i000000000000000000−2i2i00-220000
χ31222-2-2-22-22-22-200-22-2200−2i2i0−2i2i0000000000000000002i−2i00-220000
χ32222-2-2-22-22-22-200-22-2200−2i2i0−2i2i000000000000000000−2i2i002-20000
χ33222-2-2-22-2-22-2200-2-222002i−2i0−2i2i00000000000000002i−2i002-2000000
χ34222-2-2-22-2-22-2200-2-222002i−2i0−2i2i0000000000000000−2i2i00-22000000
χ35222-2-2-22-2-22-2200-2-22200−2i2i02i−2i00000000000000002i−2i00-22000000
χ36222-2-2-22-2-22-2200-2-22200−2i2i02i−2i0000000000000000−2i2i002-2000000
χ37444-4-4-44-44-44-4004-44-400000000000000000000000000000000000
χ38444-4-4-44-4-44-440044-4-400000000000000000000000000000000000
χ394-4444-4-4-444-4-4000000000000000000000000000000000000022−2200
χ404-4444-4-4-444-4-40000000000000000000000000000000000000−222200
χ414-4444-4-4-4-4-4440000000000000000000000000000000000000002i2−2i2
χ424-4444-4-4-4-4-444000000000000000000000000000000000000000−2i22i2
χ434-44-4-44-444-4-440000000000000004i−4i000000000000000000000000
χ444-44-4-44-444-4-44000000000000000−4i4i000000000000000000000000
χ454-44-4-44-44-444-400000000000004i−4i00000000000000000000000000
χ464-44-4-44-44-444-40000000000000−4i4i00000000000000000000000000
χ474-4-44-444-400004-4000000000000000000002i−2i0002i−2i000000000000
χ484-4-44-444-400004-400000000000000000000−2i2i000−2i2i000000000000
χ494-4-44-444-40000-44000000000000000000002i−2i000−2i2i000000000000
χ504-4-44-444-40000-4400000000000000000000−2i2i0002i−2i000000000000
χ5188-88-8-8-88000000000000000000000000000000000000000000000
χ5288-8-888-8-8000000000000000000000000000000000000000000000
χ538-8-8-88-888000000000000000000000000000000000000000000000

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