Finite Group Databasebeta

← Group #256373

Character table — Group #256373

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222244444444444422444444244444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1111111-1-1-1-1-1-111-11-1-11-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1111111-1-1-1-1-1-111-11-1-11-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-111-111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-111-11-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-1111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-111-111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-111-1-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1111-1-11-1-111-1-1-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1111-1-11-1-1-1-11111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-11111-1-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-111-1-11111-1-111-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-222-2-2-2-2000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ19222222222222-2-2-2-22222-2-2-2-222-2-222-2-2000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222000000000000000000000000
χ2122222222-2-2-2-222-2-2000022-2-22-200000000202-20-20000000000000000
χ2222222222-2-2-2-222-2-2000022-2-22-200000000-20-22020000000000000000
χ2322222222-2-2-2-222-2-20000-2-222-220000002-20200-200000000000000000
χ2422222222-2-2-2-222-2-20000-2-222-22000000-220-200200000000000000000
χ2522222222-2-2-2-2-2-222000022-2-2-220000000020-2-2020000000000000000
χ2622222222-2-2-2-2-2-222000022-2-2-2200000000-20220-20000000000000000
χ2722222222-2-2-2-2-2-2220000-2-2222-20000002-20-200200000000000000000
χ2822222222-2-2-2-2-2-2220000-2-2222-2000000-220200-200000000000000000
χ29222-2-22-2-2-2-22200002i2i−2i−2i2-22-20000002i−2i00000000002i−2i002-200000000
χ30222-2-22-2-2-2-22200002i2i−2i−2i2-22-20000002i−2i0000000000−2i2i00-2200000000
χ31222-2-22-2-2-2-22200002i2i−2i−2i-22-22000000−2i2i000000002i−2i002-20000000000
χ32222-2-22-2-2-2-22200002i2i−2i−2i-22-22000000−2i2i00000000−2i2i00-220000000000
χ33222-2-22-2-2-2-2220000−2i−2i2i2i2-22-2000000−2i2i00000000002i−2i00-2200000000
χ34222-2-22-2-2-2-2220000−2i−2i2i2i2-22-2000000−2i2i0000000000−2i2i002-200000000
χ35222-2-22-2-2-2-2220000−2i−2i2i2i-22-220000002i−2i000000002i−2i00-220000000000
χ36222-2-22-2-2-2-2220000−2i−2i2i2i-22-220000002i−2i00000000−2i2i002-20000000000
χ3722-22-2-22-22-22-22i−2i2i−2i2-22-20000002i−2i000000000000000000002−2i2−i22−2i2−i2
χ3822-22-2-22-22-22-22i−2i2i−2i2-22-20000002i−2i00000000000000000000−22−i2i2−22−i2i2
χ3922-22-2-22-22-22-22i−2i2i−2i-22-22000000−2i2i000000000000000000002−2i2−i2−22−i2i2
χ4022-22-2-22-22-22-22i−2i2i−2i-22-22000000−2i2i00000000000000000000−22−i2i22−2i2−i2
χ4122-22-2-22-22-22-2−2i2i−2i2i2-22-2000000−2i2i000000000000000000002−2−i2i22−2−i2i2
χ4222-22-2-22-22-22-2−2i2i−2i2i2-22-2000000−2i2i00000000000000000000−22i2−i2−22i2−i2
χ4322-22-2-22-22-22-2−2i2i−2i2i-22-220000002i−2i000000000000000000002−2−i2i2−22i2−i2
χ4422-22-2-22-22-22-2−2i2i−2i2i-22-220000002i−2i00000000000000000000−22i2−i22−2−i2i2
χ45444-4-44-4-444-4-4000000004-4-4400000000000000000000000000000000
χ46444-4-44-4-444-4-400000000-444-400000000000000000000000000000000
χ4744-44-4-44-4-44-444i−4i−4i4i0000000000000000000000000000000000000000
χ4844-44-4-44-4-44-44−4i4i4i−4i0000000000000000000000000000000000000000
χ4944-4-44-4-444-4-4400000000000000004i−4i00000000000000000000000000
χ5044-4-44-4-444-4-440000000000000000−4i4i00000000000000000000000000
χ5144-4-44-4-44-444-400004i−4i−4i4i000000000000000000000000000000000000
χ5244-4-44-4-44-444-40000−4i4i4i−4i000000000000000000000000000000000000
χ538-8888-8-8-8000000000000000000000000000000000000000000000000
χ548-88-8-8-888000000000000000000000000000000000000000000000000
χ558-8-88-88-88000000000000000000000000000000000000000000000000
χ568-8-8-8888-8000000000000000000000000000000000000000000000000

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