Finite Group Databasebeta

← Group #252710

Character table — Group #252710

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444444444444444444444444888888888888888824444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-11111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111-1-111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ71111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ911111111-1-1-1-111111111-1-11111-1-111-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-111-1-1
χ1011111111-1-1-1-111111111-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-111-1-111
χ1111111111-1-1-1-111111111-1-11111-1-111-1-1-1-111-1-111-11111-1-1-1-1-1-1-1-11111-11-1-11111-1-1-1-111
χ1211111111-1-1-1-111111111-1-11111-1-111-1-1-1-111-1-111-1-1-1-1-111111111-1-1-1-1-11-1-111-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-11111-1-1-1-11111-1-1-1-11-1-1-111-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11111-1-1-1-1-1-1-1-11111-1111-1-1-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111111111-1-1-1-1-1111-1-111-1-1-1-111
χ17222222222222222-2-2-2-22222222-2-2-2-22200-2-2-2-200-2000000000000000000000000000000
χ18222222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-200222200-2000000000000000000000000000000
χ19222222222222-2-2-22222-2-2-2000022-2-20022000022-20000000000000000-2-2000000000000
χ20222222222222-2-2-22222-2-2-2000022-2-200-2-20000-2-2-2000000000000000022000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-20000-2-222000000000020000000000000000002-22-200000000
χ22222222222222-2-2-2-2-2-2-2-2-2-20000-2-22200000000002000000000000000000-22-2200000000
χ2322222222-2-2-2-2222-2-2-2-22-2-2222222-2-2-2-200-2-222002000000000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-22-2-2-2-2-2-222-2-2220022-2-2002000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-2220000-2-2-2-200220000-2-220000000000000000-22000000000000
χ2622222222-2-2-2-2-2-2-22222-2220000-2-2-2-200-2-2000022200000000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222000022220000000000-20000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222000022220000000000-2000000000000000000-222-200000000
χ29222-2-22-2-222-2-2000-2-22200000002-200002i−2i00002i−2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000000000
χ30222-2-22-2-222-2-2000-2-22200000002-200002i−2i00002i−2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000000000
χ31222-2-22-2-222-2-2000-2-22200000002-20000−2i2i0000−2i2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000000000
χ32222-2-22-2-222-2-2000-2-22200000002-20000−2i2i0000−2i2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000000000
χ33222-2-22-2-2-2-222000-2-2220000000-2200002i−2i0000−2i2i022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000000000
χ34222-2-22-2-2-2-222000-2-2220000000-2200002i−2i0000−2i2i0−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000000000
χ35222-2-22-2-2-2-222000-2-2220000000-220000−2i2i00002i−2i022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000000000
χ36222-2-22-2-2-2-222000-2-2220000000-220000−2i2i00002i−2i0−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000000000
χ3722-22-2-22-22-22-22-2-2000022-22i2i−2i−2i00002i−2i000000000000000002−22−22−22−20000000000i2−i2i2−i2
χ3822-22-2-22-22-22-22-2-2000022-22i2i−2i−2i00002i−2i00000000000000000−22−22−22−220000000000−i2i2−i2i2
χ3922-22-2-22-22-22-22-2-2000022-2−2i−2i2i2i0000−2i2i000000000000000002−22−22−22−20000000000−i2i2−i2i2
χ4022-22-2-22-22-22-22-2-2000022-2−2i−2i2i2i0000−2i2i00000000000000000−22−22−22−220000000000i2−i2i2−i2
χ4122-22-2-22-2-22-222-2-200002-222i2i−2i−2i0000−2i2i000000000000000002−22−2−22−220000000000i2−i2−i2i2
χ4222-22-2-22-2-22-222-2-200002-222i2i−2i−2i0000−2i2i00000000000000000−22−222−22−20000000000−i2i2i2−i2
χ4322-22-2-22-2-22-222-2-200002-22−2i−2i2i2i00002i−2i000000000000000002−22−2−22−220000000000−i2i2i2−i2
χ4422-22-2-22-2-22-222-2-200002-22−2i−2i2i2i00002i−2i00000000000000000−22−222−22−20000000000i2−i2−i2i2
χ452-2-22-22-22000022-22-22-2-2002i−2i2i−2i002-200002i−2i0000000002i−2i2i−2i00000000000000002-20000
χ462-2-22-22-22000022-22-22-2-2002i−2i2i−2i002-200002i−2i000000000−2i2i−2i2i0000000000000000-220000
χ472-2-22-22-22000022-22-22-2-200−2i2i−2i2i002-20000−2i2i0000000002i−2i2i−2i0000000000000000-220000
χ482-2-22-22-22000022-22-22-2-200−2i2i−2i2i002-20000−2i2i000000000−2i2i−2i2i00000000000000002-20000
χ492-2-22-22-22000022-2-22-22-2002i−2i2i−2i00-220000−2i2i000002i−2i2i−2i0000000000000000002-2000000
χ502-2-22-22-22000022-2-22-22-2002i−2i2i−2i00-220000−2i2i00000−2i2i−2i2i000000000000000000-22000000
χ512-2-22-22-22000022-2-22-22-200−2i2i−2i2i00-2200002i−2i000002i−2i2i−2i000000000000000000-22000000
χ522-2-22-22-22000022-2-22-22-200−2i2i−2i2i00-2200002i−2i00000−2i2i−2i2i0000000000000000002-2000000
χ53444-4-44-4-444-4-400044-4-40000000-440000000000000000000000000000000000000000000
χ54444-4-44-4-4-4-44400044-4-400000004-40000000000000000000000000000000000000000000
χ5544-44-4-44-44-44-4-4440000-4-440000000000000000000000000000000000000000000000000
χ5644-44-4-44-4-44-44-4440000-44-40000000000000000000000000000000000000000000000000
χ5744-4-44-4-444-4-4400000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ5844-4-44-4-444-4-440000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ5944-4-44-4-44-444-400000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ6044-4-44-4-44-444-40000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ614-4444-4-4-400004-440000-4004-4-44000000000000000000000000000000000000000000000
χ624-4444-4-4-400004-440000-400-444-4000000000000000000000000000000000000000000000
χ634-4444-4-4-40000-44-40000400000000000000004i−4i000000000000000000000000000000000
χ644-4444-4-4-40000-44-4000040000000000000000−4i4i000000000000000000000000000000000
χ654-4-44-44-440000-4-444-44-4400000000-4400000000000000000000000000000000000000000
χ664-4-44-44-440000-4-44-44-444000000004-400000000000000000000000000000000000000000
χ674-4-4-4444-400000004-4-4400000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ684-4-4-4444-400000004-4-440000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ694-4-4-4444-40000000-444-4000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ704-4-4-4444-40000000-444-400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ718-88-8-8-888000000000000000000000000000000000000000000000000000000000000000

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