Finite Group Databasebeta

← Group #455646

Character table — Group #455646

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111111111112222222244448888888888888888888888888888888888161616161616161616161616
order12222222222222224444444444442222224444444444448888888888888888224444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ51111111111111111111111111111-1-1-1-11111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ71111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ81111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1
χ9111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ10111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ11111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ12111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111
χ13111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ14111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1
χ172222222222222222-2-2-2-2-2-2-2-22222000022-2-222-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222220000-2-2-2-2-2-2222200000000000000000000000000000000
χ192222222222222222-2-2-2-2-2-2-2-2-2-2-2-200002222-2-222-2-200000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-2-22222-2-22200000000000000000000000000000000
χ2122222-2-2-2-2-2222-2-2-222-2-222-2-22i2i−2i−2i0000002i−2i00000000000000000000000000002-22i−2i000000
χ2222222-2-2-2-2-2222-2-2-222-2-222-2-22i2i−2i−2i0000002i−2i0000000000000000000000000000-22−2i2i000000
χ2322222-2-2-2-2-2222-2-2-222-2-222-2-2−2i−2i2i2i000000−2i2i00000000000000000000000000002-2−2i2i000000
χ2422222-2-2-2-2-2222-2-2-222-2-222-2-2−2i−2i2i2i000000−2i2i0000000000000000000000000000-222i−2i000000
χ2522222-2-2-2-2-2222-2-2-2-2-222-2-2222i2i−2i−2i22-2-200−2i2i0000002i2i−2i−2i0000000000000000000000000000
χ2622222-2-2-2-2-2222-2-2-2-2-222-2-2222i2i−2i−2i-2-22200−2i2i000000−2i−2i2i2i0000000000000000000000000000
χ2722222-2-2-2-2-2222-2-2-2-2-222-2-222−2i−2i2i2i22-2-2002i−2i000000−2i−2i2i2i0000000000000000000000000000
χ2822222-2-2-2-2-2222-2-2-2-2-222-2-222−2i−2i2i2i-2-222002i−2i0000002i2i−2i−2i0000000000000000000000000000
χ29222-2-22-222-22-2-2-2-222-2222-2-2-20000000000000000002i−2i2i−2i0000000000002i2i−2i−2i00000000002-2
χ30222-2-22-222-22-2-2-2-222-2222-2-2-20000000000000000002i−2i2i−2i000000000000−2i−2i2i2i0000000000-22
χ31222-2-22-222-22-2-2-2-222-2222-2-2-2000000000000000000−2i2i−2i2i0000000000002i2i−2i−2i0000000000-22
χ32222-2-22-222-22-2-2-2-222-2222-2-2-2000000000000000000−2i2i−2i2i000000000000−2i−2i2i2i00000000002-2
χ33222-2-2-22-2-222-2-222-2-2222-22-2-20000000000000000002-2-22000000002i2i−2i−2i00000000002i−2i0000
χ34222-2-2-22-2-222-2-222-2-2222-22-2-20000000000000000002-2-2200000000−2i−2i2i2i0000000000−2i2i0000
χ35222-2-2-22-2-222-2-222-2-2222-22-2-2000000000000000000-222-2000000002i2i−2i−2i0000000000−2i2i0000
χ36222-2-2-22-2-222-2-222-2-2222-22-2-2000000000000000000-222-200000000−2i−2i2i2i00000000002i−2i0000
χ3722-2-2-2-2-22-2-2-222222000000002-22-200002-2002-20000000022−2−222−2−22−22−22−22−2000000000000
χ3822-2-2-2-2-22-2-2-222222000000002-22-200002-2002-200000000−2−222−2−222−22−22−22−22000000000000
χ3922-2-2-2-2-22-2-2-222222000000002-22-20000-2200-220000000022−2−222−2−2−22−22−22−22000000000000
χ4022-2-2-2-2-22-2-2-222222000000002-22-20000-2200-2200000000−2−222−2−2222−22−22−22−2000000000000
χ4122-2-2-2-2-22-2-2-22222200000000-22-2200002-200-220000000022−2−2−2−2222−22−2−22−22000000000000
χ4222-2-2-2-2-22-2-2-22222200000000-22-2200002-200-2200000000−2−22222−2−2−22−222−22−2000000000000
χ4322-2-2-2-2-22-2-2-22222200000000-22-220000-22002-20000000022−2−2−2−222−22−222−22−2000000000000
χ4422-2-2-2-2-22-2-2-22222200000000-22-220000-22002-200000000−2−22222−2−22−22−2−22−22000000000000
χ452-2-22-22-2-2-2222-2-222-2-22-2222-200002-22-2000000000000002-22-20000000000002-20000000000
χ462-2-22-22-2-2-2222-2-222-2-22-2222-200002-22-200000000000000-22-22000000000000-220000000000
χ472-2-22-22-2-2-2222-2-222-2-22-2222-20000-22-22000000000000002-22-2000000000000-220000000000
χ482-2-22-22-2-2-2222-2-222-2-22-2222-20000-22-2200000000000000-22-220000000000002-20000000000
χ492-2-22-2-2222-222-22-2-2222-2-2-22-200002-2-220000000000000000002i−2i2i−2i00000000000000002i−2i00
χ502-2-22-2-2222-222-22-2-2222-2-2-22-200002-2-22000000000000000000−2i2i−2i2i0000000000000000−2i2i00
χ512-2-22-2-2222-222-22-2-2222-2-2-22-20000-222-20000000000000000002i−2i2i−2i0000000000000000−2i2i00
χ522-2-22-2-2222-222-22-2-2222-2-2-22-20000-222-2000000000000000000−2i2i−2i2i00000000000000002i−2i00
χ53444-4-44-444-44-4-4-4-44-44-4-4-444400000000000000000000000000000000000000000000000000
χ54444-4-4-44-4-444-4-444-44-4-4-44-44400000000000000000000000000000000000000000000000000
χ5544-4444-4-44-4-4-4-444-4000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ5644-4444-4-44-4-4-4-444-400000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ5744-444-444-44-4-4-4-4-440000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ5844-444-444-44-4-4-4-4-44000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ5944-4-4-444-444-444-4-4-4000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ6044-4-4-444-444-444-4-4-400000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ614-444-4444-4-4-4-44-44-40000000000000000000000004i−4i00000000000000000000000000000000
χ624-444-4444-4-4-4-44-44-4000000000000000000000000−4i4i00000000000000000000000000000000
χ634-444-4-4-4-444-4-444-4400000000000000000000004-40000000000000000000000000000000000
χ644-444-4-4-4-444-4-444-440000000000000000000000-440000000000000000000000000000000000
χ654-44-444-44-44-44-44-4-400000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ664-44-444-44-44-44-44-4-40000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ674-44-44-44-44-4-44-4-44400000000000000000000000000000022−22−2222000000000000000000000000
χ684-44-44-44-44-4-44-4-444000000000000000000000000000000−222222−22000000000000000000000000
χ694-4-44-44-4-4-4444-4-44444-44-4-4-4400000000000000000000000000000000000000000000000000
χ704-4-44-4-4444-444-44-4-4-4-4-4444-4400000000000000000000000000000000000000000000000000
χ714-4-4-4444-4-4-44-444-444-4-44-444-400000000000000000000000000000000000000000000000000
χ724-4-4-4444-4-4-44-444-44-444-44-4-4400000000000000000000000000000000000000000000000000
χ734-4-4-44-4-44444-44-44-44-44-4-44-4400000000000000000000000000000000000000000000000000
χ744-4-4-44-4-44444-44-44-4-44-444-44-400000000000000000000000000000000000000000000000000

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