Finite Group Databasebeta

← Group #239495

Character table — Group #239495

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222222224444444422444422224444444444448888888888888888244444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111
χ91111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-1-11-111-1-1
χ101111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1111-1-1
χ111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1111-11-1-111
χ121111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111-1-1-11-1-1-111
χ131111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-11-1-1-11-1-111
χ141111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1111-1-1-111
χ151111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-1111-111-1-1
χ161111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-11-1-1-1111-1-1
χ172222222222222222-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ192222222222-2-2-2-22222222222-2-2-2-2-2-222-2-2-2-222000000000000000000000000000000000000
χ202222222222-2-2-2-22222222222-2-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000
χ2122222222-2-22222-2-22222-2-2-2-2-2-22-22-2000000000000000000000000000000002-2002-2000000
χ2222222222-2-22222-2-22222-2-2-2-2-2-22-22-200000000000000000000000000000000-2200-22000000
χ2322222222-2-22222-2-2-2-2-2-22222-2-2-22-2200000000000000000000000000000000002200-2-20000
χ2422222222-2-22222-2-2-2-2-2-22222-2-2-22-220000000000000000000000000000000000-2-200220000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-222-22-2200000000000000000000000000000000002-200-220000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-222-22-220000000000000000000000000000000000-22002-20000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222222-22-2000000000000000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222222-22-200000000000000000000000000000000-22002-2000000
χ29222-22-2-2-22-200002-22i2i−2i−2i2i2i−2i−2i000000002-22i−2i000000000022−2−2i2i2−i2−i2i2i2−i2−i222−2−2000000000000
χ30222-22-2-2-22-200002-22i2i−2i−2i2i2i−2i−2i000000002-22i−2i0000000000−2−222−i2−i2i2i2−i2−i2i2i2−2−222000000000000
χ31222-22-2-2-22-200002-22i2i−2i−2i2i2i−2i−2i00000000-22−2i2i000000000022−2−2i2i2−i2−i2−i2−i2i2i2−2−222000000000000
χ32222-22-2-2-22-200002-22i2i−2i−2i2i2i−2i−2i00000000-22−2i2i0000000000−2−222−i2−i2i2i2i2i2−i2−i222−2−2000000000000
χ33222-22-2-2-22-200002-2−2i−2i2i2i−2i−2i2i2i000000002-2−2i2i000000000022−2−2−i2−i2i2i2−i2−i2i2i222−2−2000000000000
χ34222-22-2-2-22-200002-2−2i−2i2i2i−2i−2i2i2i000000002-2−2i2i0000000000−2−222i2i2−i2−i2i2i2−i2−i2−2−222000000000000
χ35222-22-2-2-22-200002-2−2i−2i2i2i−2i−2i2i2i00000000-222i−2i000000000022−2−2−i2−i2i2i2i2i2−i2−i2−2−222000000000000
χ36222-22-2-2-22-200002-2−2i−2i2i2i−2i−2i2i2i00000000-222i−2i0000000000−2−222i2i2−i2−i2−i2−i2i2i222−2−2000000000000
χ3722-22-22-2-2-2200002-22i−2i2i−2i2i−2i2i−2i0000002-200002i−2i00000000i2−i2i2−i22−22−2i2−i2i2−i22−22−2000000000000
χ3822-22-22-2-2-2200002-22i−2i2i−2i2i−2i2i−2i0000002-200002i−2i00000000−i2i2−i2i2−22−22−i2i2−i2i2−22−22000000000000
χ3922-22-22-2-2-2200002-22i−2i2i−2i2i−2i2i−2i000000-220000−2i2i00000000i2−i2i2−i22−22−2−i2i2−i2i2−22−22000000000000
χ4022-22-22-2-2-2200002-22i−2i2i−2i2i−2i2i−2i000000-220000−2i2i00000000−i2i2−i2i2−22−22i2−i2i2−i22−22−2000000000000
χ4122-22-22-2-2-2200002-2−2i2i−2i2i−2i2i−2i2i0000002-20000−2i2i00000000i2−i2i2−i2−22−22i2−i2i2−i2−22−22000000000000
χ4222-22-22-2-2-2200002-2−2i2i−2i2i−2i2i−2i2i0000002-20000−2i2i00000000−i2i2−i2i22−22−2−i2i2−i2i22−22−2000000000000
χ4322-22-22-2-2-2200002-2−2i2i−2i2i−2i2i−2i2i000000-2200002i−2i00000000i2−i2i2−i2−22−22−i2i2−i2i22−22−2000000000000
χ4422-22-22-2-2-2200002-2−2i2i−2i2i−2i2i−2i2i000000-2200002i−2i00000000−i2i2−i2i22−22−2i2−i2i2−i2−22−22000000000000
χ4522-2-2-2-2222222-2-2-2-22-2-22-222-22-22-2-22000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ4622-2-2-2-2222222-2-2-2-22-2-22-222-22-22-2-2200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ4722-2-2-2-2222222-2-2-2-2-222-22-2-222-2-222-200000000000000000000000000000000000000002i−2i2i−2i
χ4822-2-2-2-2222222-2-2-2-2-222-22-2-222-2-222-20000000000000000000000000000000000000000−2i2i−2i2i
χ4922-2-2-2-22222-2-222-2-22-2-22-222-2-22-222-200000000000000000000000000000000000000002i−2i−2i2i
χ5022-2-2-2-22222-2-222-2-22-2-22-222-2-22-222-20000000000000000000000000000000000000000−2i2i2i−2i
χ5122-2-2-2-22222-2-222-2-2-222-22-2-22-222-2-22000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ5222-2-2-2-22222-2-222-2-2-222-22-2-22-222-2-2200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ5322-2-2-2-222-2-222-2-2222-2-222-2-22-2222-2-200000000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000
χ5422-2-2-2-222-2-222-2-2222-2-222-2-22-2222-2-20000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000
χ5522-2-2-2-222-2-222-2-222-222-2-222-2-22-2-2220000000000000000000000002-2-22-222-2000000000000
χ5622-2-2-2-222-2-222-2-222-222-2-222-2-22-2-222000000000000000000000000-222-22-2-22000000000000
χ5722-2-2-2-222-2-2-2-222222-2-222-2-222-2-2-2220000000000000000000000002-2-222-2-22000000000000
χ5822-2-2-2-222-2-2-2-222222-2-222-2-222-2-2-222000000000000000000000000-222-2-222-2000000000000
χ5922-2-2-2-222-2-2-2-22222-222-2-222-22-222-2-200000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ6022-2-2-2-222-2-2-2-22222-222-2-222-22-222-2-20000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ61444-44-4-4-4-440000-444i4i−4i−4i−4i−4i4i4i00000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-440000-44−4i−4i4i4i4i4i−4i−4i00000000000000000000000000000000000000000000000000
χ6344-44-44-4-44-40000-444i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ6444-44-44-4-44-40000-44−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000
χ654-444-4-44-4004-44-40000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ664-444-4-44-4004-44-4000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ674-444-4-44-400-44-440000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ684-444-4-44-400-44-44000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ694-4-4-4444-4004-4-440000000000000000000000002-2-222-2-220000000000000000000000000000
χ704-4-4-4444-4004-4-44000000000000000000000000-222-2-222-20000000000000000000000000000
χ714-4-4-4444-400-444-40000000000000000000000002-2-22-222-20000000000000000000000000000
χ724-4-4-4444-400-444-4000000000000000000000000-222-22-2-220000000000000000000000000000
χ738-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000

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