Finite Group Databasebeta

← Group #165779

Character table — Group #165779

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111111111111111144444444444488888888888888888888888888888888888816161616161616161616
order12222222444444442244444444442244444444448888888888888888888888882224444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-111
χ51111111111111111111111111111-1-11111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1
χ61111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1111
χ71111111111111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111
χ81111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-111-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-11-1-1-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111-1-11-11-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11-1-11111
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-11-11-111
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1111-11-11-1-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-111-11-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1111
χ17222222222222222222-2-2-2-22-2-2-2-22002222000000000000000000000000000000-2000000-200
χ18222222222222222222-2-2-2-22-2-2-2-2200-2-2-2-20000000000000000000000000000002000000200
χ192222222222222222-2-222-2-2-222-2-2-200000022220000000000000000000000000000000-2-2000
χ202222222222222222-2-222-2-2-222-2-2-2000000-2-2-2-2000000000000000000000000000000022000
χ212222222222222222-2-2-2-222-2-2-222-2220000000022000000000000000000000000000-2-200000
χ222222222222222222-2-2-2-222-2-2-222-2-2-200000000-2-20000000000000000000000000002200000
χ2322222222-2-2-2-2-2-2-2-22222-2-2-2-2-222-22200000000-2-2000000000000000000000000000-2200000
χ2422222222-2-2-2-2-2-2-2-22222-2-2-2-2-222-2-2-200000000220000000000000000000000000002-200000
χ2522222222-2-2-2-2-2-2-2-222-2-222-222-2-2-200000022-2-20000000000000000000000000000000-22000
χ2622222222-2-2-2-2-2-2-2-222-2-222-222-2-2-2000000-2-22200000000000000000000000000000002-2000
χ2722222222-2-2-2-2-2-2-2-2-2-222222-2-2-2-220022-2-2000000000000000000000000000000-2000000200
χ2822222222-2-2-2-2-2-2-2-2-2-222222-2-2-2-2200-2-2220000000000000000000000000000002000000-200
χ29222-2-2-2-222222-2-2-2-22-2000020000-2002i−2i2i−2i000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000000000
χ30222-2-2-2-222222-2-2-2-22-2000020000-2002i−2i2i−2i000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000000000
χ31222-2-2-2-222222-2-2-2-22-2000020000-200−2i2i−2i2i000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000000000
χ32222-2-2-2-222222-2-2-2-22-2000020000-200−2i2i−2i2i000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000000000
χ33222-2-2-2-22-2-2-2-22222-22000020000-2002i−2i−2i2i000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000000000
χ34222-2-2-2-22-2-2-2-22222-22000020000-2002i−2i−2i2i000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000000000
χ35222-2-2-2-22-2-2-2-22222-22000020000-200−2i2i2i−2i000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000000000
χ36222-2-2-2-22-2-2-2-22222-22000020000-200−2i2i2i−2i000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000000000
χ3722-222-2-2-22i2i−2i−2i2i2i−2i−2i00002i−2i0002-202-2000000002i−2i2−22−2i2−i2i2−i20000000022−2−2i2i2−i2−i20000000000
χ3822-222-2-2-22i2i−2i−2i2i2i−2i−2i00002i−2i0002-202-2000000002i−2i−22−22−i2i2−i2i200000000−2−222−i2−i2i2i20000000000
χ3922-222-2-2-22i2i−2i−2i2i2i−2i−2i00002i−2i0002-20-2200000000−2i2i2−22−2i2−i2i2−i200000000−2−222−i2−i2i2i20000000000
χ4022-222-2-2-22i2i−2i−2i2i2i−2i−2i00002i−2i0002-20-2200000000−2i2i−22−22−i2i2−i2i20000000022−2−2i2i2−i2−i20000000000
χ4122-222-2-2-2−2i−2i2i2i−2i−2i2i2i0000−2i2i0002-202-200000000−2i2i2−22−2−i2i2−i2i20000000022−2−2−i2−i2i2i20000000000
χ4222-222-2-2-2−2i−2i2i2i−2i−2i2i2i0000−2i2i0002-202-200000000−2i2i−22−22i2−i2i2−i200000000−2−222i2i2−i2−i20000000000
χ4322-222-2-2-2−2i−2i2i2i−2i−2i2i2i0000−2i2i0002-20-22000000002i−2i2−22−2−i2i2−i2i200000000−2−222i2i2−i2−i20000000000
χ4422-222-2-2-2−2i−2i2i2i−2i−2i2i2i0000−2i2i0002-20-22000000002i−2i−22−22i2−i2i2−i20000000022−2−2−i2−i2i2i20000000000
χ452-222-22-2-22i−2i2i−2i2i−2i2i−2i002i−2i0002-20000000002-22i−2i00000000002−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000000
χ462-222-22-2-22i−2i2i−2i2i−2i2i−2i002i−2i0002-20000000002-22i−2i0000000000−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000000
χ472-222-22-2-22i−2i2i−2i2i−2i2i−2i002i−2i0002-2000000000-22−2i2i00000000002−22−2i2−i2i2−i2−22−22−i2i2−i2i20000000000
χ482-222-22-2-22i−2i2i−2i2i−2i2i−2i002i−2i0002-2000000000-22−2i2i0000000000−22−22−i2i2−i2i22−22−2i2−i2i2−i20000000000
χ492-222-22-2-2−2i2i−2i2i−2i2i−2i2i00−2i2i0002-20000000002-2−2i2i00000000002−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000000
χ502-222-22-2-2−2i2i−2i2i−2i2i−2i2i00−2i2i0002-20000000002-2−2i2i0000000000−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000000
χ512-222-22-2-2−2i2i−2i2i−2i2i−2i2i00−2i2i0002-2000000000-222i−2i00000000002−22−2−i2i2−i2i2−22−22i2−i2i2−i20000000000
χ522-222-22-2-2−2i2i−2i2i−2i2i−2i2i00−2i2i0002-2000000000-222i−2i0000000000−22−22i2−i2i2−i22−22−2−i2i2−i2i20000000000
χ53444-4-4-4-444444-4-4-4-4-440000-4000040000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4-4-4-444444-40000-4000040000000000000000000000000000000000000000000000
χ5544-444-4-4-44i4i−4i−4i4i4i−4i−4i0000−4i4i000-4400000000000000000000000000000000000000000000000
χ5644-444-4-4-4−4i−4i4i4i−4i−4i4i4i00004i−4i000-4400000000000000000000000000000000000000000000000
χ5744-4-4-444-44i4i−4i−4i−4i−4i4i4i0000000000000000000000002i−2i−2i2i-222-200000000000000000000000000
χ5844-4-4-444-44i4i−4i−4i−4i−4i4i4i000000000000000000000000−2i2i2i−2i2-2-2200000000000000000000000000
χ5944-4-4-444-4−4i−4i4i4i4i4i−4i−4i0000000000000000000000002i−2i−2i2i2-2-2200000000000000000000000000
χ6044-4-4-444-4−4i−4i4i4i4i4i−4i−4i000000000000000000000000−2i2i2i−2i-222-200000000000000000000000000
χ614-444-44-4-44i−4i4i−4i4i−4i4i−4i00−4i4i000-440000000000000000000000000000000000000000000000000
χ624-444-44-4-4−4i4i−4i4i−4i4i−4i4i004i−4i000-440000000000000000000000000000000000000000000000000
χ634-44-44-44-44i−4i4i−4i−4i4i−4i4i000000000000000000000000000000002-2-222i−2i−2i2i000000000000000000
χ644-44-44-44-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000-222-2−2i2i2i−2i000000000000000000
χ654-44-44-44-4−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000002-2-22−2i2i2i−2i000000000000000000
χ664-44-44-44-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000-222-22i−2i−2i2i000000000000000000
χ674-4-44-4-4444-4-444-4-4400000000000000000000000000000000000000002-2-222-2-220000000000
χ684-4-44-4-4444-4-444-4-440000000000000000000000000000000000000000-222-2-222-20000000000
χ694-4-44-4-444-444-4-444-400000000000000000000000000000000000000002-2-22-222-20000000000
χ704-4-44-4-444-444-4-444-40000000000000000000000000000000000000000-222-22-2-220000000000
χ714-4-4-444-444-4-44-444-400000000000000000000000000000000000000000000000002-2000002-2
χ724-4-4-444-444-4-44-444-40000000000000000000000000000000000000000000000000-2200000-22
χ734-4-4-444-44-444-44-4-4400000000000000000000000000000000000000000000000002-200000-22
χ744-4-4-444-44-444-44-4-440000000000000000000000000000000000000000000000000-22000002-2

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