Finite Group Databasebeta

← Group #257385

Character table — Group #257385

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222222244444444444444444422444444444888888888888888844444444448888
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
χ3111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ7111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ911111111-1-1-1-111111111-1-1-1-111111111-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-11111-1-111-1-1
χ1011111111-1-1-1-111111111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-111-1-111-1-111
χ1111111111-1-1-1-111111111-1-1-1-1111111-1-111-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1111-1-111-1-1-1-111
χ1211111111-1-1-1-111111111-1-1-1-1111111-1-111-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-1-1-11111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-111-1-1-1-111-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-111-1-111-1-111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-111111111-1-1-1-1-1-1-1-11111-11-1-111-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-111
χ1722222222222222-2-2-222-222-2-20000-2-22222-20000000000000000000000-2-2000000000000
χ1822222222222222-2-2-222-222-2-20000-2-2-2-2-2-2-2000000000000000000000022000000000000
χ19222222222222-2-2222-2-22-2-2222222-2-20000-2-2-2-2-222000000000000000000000000000000
χ20222222222222-2-2222-2-22-2-222-2-2-2-2-2-20000-22222-2-2000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-2000022000020000000000000000000000002-22-200000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-200002200002000000000000000000000000-22-2200000000
χ2322222222-2-2-2-222-2-2-222-2-2-2220000-2-222-2-220000000000000000000000-22000000000000
χ2422222222-2-2-2-222-2-2-222-2-2-2220000-2-2-2-222200000000000000000000002-2000000000000
χ2522222222-2-2-2-2-2-2222-2-2222-2-22222-2-200002-2-222-2-2000000000000000000000000000000
χ2622222222-2-2-2-2-2-2222-2-2222-2-2-2-2-2-2-2-20000222-2-222000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-20000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-2000000000000000000000000-222-200000000
χ29222-2-2-22-222-2-2-2-20002202-2000000002-22-20000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000
χ30222-2-2-22-222-2-2-2-20002202-2000000002-22-20000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000
χ31222-2-2-22-222-2-2-2-20002202-200000000-22-220000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000
χ32222-2-2-22-222-2-2-2-20002202-200000000-22-220000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000
χ33222-2-2-22-2-2-222-2-2000220-22000000002-2-220000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ34222-2-2-22-2-2-222-2-2000220-22000000002-2-220000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ35222-2-2-22-2-2-222-2-2000220-2200000000-222-20000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ36222-2-2-22-2-2-222-2-2000220-2200000000-222-20000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ3722-222-2-2-200002-22-2-22-2200002i2i−2i−2i2-2000002i−2i000000002-22-200000000000000002i−2i0000
χ3822-222-2-2-200002-22-2-22-2200002i2i−2i−2i2-2000002i−2i00000000-22-220000000000000000−2i2i0000
χ3922-222-2-2-200002-22-2-22-220000−2i−2i2i2i2-200000−2i2i000000002-22-20000000000000000−2i2i0000
χ4022-222-2-2-200002-22-2-22-220000−2i−2i2i2i2-200000−2i2i00000000-22-2200000000000000002i−2i0000
χ4122-222-2-2-20000-222-2-2-22200002i2i−2i−2i-2200000−2i2i00002-22-20000000000000000002i−2i000000
χ4222-222-2-2-20000-222-2-2-22200002i2i−2i−2i-2200000−2i2i0000-22-22000000000000000000−2i2i000000
χ4322-222-2-2-20000-222-2-2-2220000−2i−2i2i2i-22000002i−2i00002-22-2000000000000000000−2i2i000000
χ4422-222-2-2-20000-222-2-2-2220000−2i−2i2i2i-22000002i−2i0000-22-220000000000000000002i−2i000000
χ452-222-22-2-22-22-200-22-2002002-22i−2i2i−2i000000000002i−2i000000002−22−22−22−20000000000i2−i2i2−i2
χ462-222-22-2-22-22-200-22-2002002-22i−2i2i−2i000000000002i−2i00000000−22−22−22−220000000000−i2i2−i2i2
χ472-222-22-2-22-22-200-22-2002002-2−2i2i−2i2i00000000000−2i2i000000002−22−22−22−20000000000−i2i2−i2i2
χ482-222-22-2-22-22-200-22-2002002-2−2i2i−2i2i00000000000−2i2i00000000−22−22−22−220000000000i2−i2i2−i2
χ492-222-22-2-2-22-2200-22-200200-222i−2i2i−2i00000000000−2i2i000000002−22−2−22−220000000000i2−i2−i2i2
χ502-222-22-2-2-22-2200-22-200200-222i−2i2i−2i00000000000−2i2i00000000−22−222−22−20000000000−i2i2i2−i2
χ512-222-22-2-2-22-2200-22-200200-22−2i2i−2i2i000000000002i−2i000000002−22−2−22−220000000000−i2i2i2−i2
χ522-222-22-2-2-22-2200-22-200200-22−2i2i−2i2i000000000002i−2i00000000−22−222−22−20000000000i2−i2−i2i2
χ53444-4-4-44-444-4-444000-4-40-440000000000000000000000000000000000000000000000000
χ54444-4-4-44-4-4-44444000-4-404-40000000000000000000000000000000000000000000000000
χ5544-444-4-4-400004-4-4444-4-400000000-4400000000000000000000000000000000000000000
χ5644-444-4-4-40000-44-444-44-4000000004-400000000000000000000000000000000000000000
χ5744-4-4-44-4400004-4000-4400000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ5844-4-4-44-4400004-4000-440000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ5944-4-4-44-440000-440004-4000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ6044-4-4-44-440000-440004-400000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ614-444-44-4-44-44-4004-4400-400-4400000000000000000000000000000000000000000000000
χ624-444-44-4-4-44-44004-4400-4004-400000000000000000000000000000000000000000000000
χ634-44-44-4-444-4-4400000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ644-44-44-4-444-4-440000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ654-44-44-4-44-444-400000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ664-44-44-4-44-444-40000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ674-4-44-4-44400000044-400-4000000000000000004i−4i00000000000000000000000000000000
χ684-4-44-4-44400000044-400-400000000000000000−4i4i00000000000000000000000000000000
χ694-4-44-4-444000000-4-4400400004-4-440000000000000000000000000000000000000000000
χ704-4-44-4-444000000-4-440040000-444-40000000000000000000000000000000000000000000
χ718-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000

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