Finite Group Databasebeta

← Group #259019

Character table — Group #259019

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222444444444444444444448888888888888888224444444444244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-1-11-1-111111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-111-1-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111
χ91111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-111111-1-111-1-111-1-1
χ101111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-111-1-11111-1-1
χ111111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-111
χ121111111111-1-1-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-11111-1-1-1-111-1-111
χ131111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1111-1-111-1-111-1-111
χ141111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-111
χ151111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-111-1-1-1-11111-1-1
χ161111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11-11-111-1-11111-1-111-1-1
χ1722222222222222-2-2-222-222-2-2-2-2-2-20000000000000000220022000000-200-200000000000000
χ1822222222222222-2-2-222-222-2-2-2-2-2-20000000000000000-2-200-2-2000000200200000000000000
χ192222222222-2-2-2-2-2-2-222-2-2-22222-2-200000000000000002200-2-2000000200-200000000000000
χ202222222222-2-2-2-2-2-2-222-2-2-22222-2-20000000000000000-2-20022000000-200200000000000000
χ2122222222-2-22222222-2-22-2-222-2-2-2-200000000000000000022002200000-2-2000000000000000
χ2222222222-2-22222222-2-22-2-222-2-2-2-2000000000000000000-2-200-2-20000022000000000000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2-2-2222200000000000000000000000022-2-200002-2000000000000
χ2422222222-2-22222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000-2-2220000-22000000000000
χ2522222222-2-2-2-2-2-2222-2-2222-2-222-2-20000000000000000002200-2-200000-22000000000000000
χ2622222222-2-2-2-2-2-2222-2-2222-2-222-2-2000000000000000000-2-20022000002-2000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000000000000000000022-2-20000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-222000000000000000000000000-2-22200002-2000000000000
χ29222-2-2-2-222-22i2i−2i−2i0002-202i−2i0000002222−2−2−2−2i2i2i2i2−i2−i2−i2−i22-2002i−2i000000000000000000002−2i2−i2
χ30222-2-2-2-222-22i2i−2i−2i0002-202i−2i0000002222−2−2−2−2i2i2i2i2−i2−i2−i2−i2-2200−2i2i00000000000000000000−22−i2i2
χ31222-2-2-2-222-22i2i−2i−2i0002-202i−2i000000−2−2−2−22222−i2−i2−i2−i2i2i2i2i22-2002i−2i00000000000000000000−22−i2i2
χ32222-2-2-2-222-22i2i−2i−2i0002-202i−2i000000−2−2−2−22222−i2−i2−i2−i2i2i2i2i2-2200−2i2i000000000000000000002−2i2−i2
χ33222-2-2-2-222-2−2i−2i2i2i0002-20−2i2i0000002222−2−2−2−2−i2−i2−i2−i2i2i2i2i22-200−2i2i000000000000000000002−2−i2i2
χ34222-2-2-2-222-2−2i−2i2i2i0002-20−2i2i0000002222−2−2−2−2−i2−i2−i2−i2i2i2i2i2-22002i−2i00000000000000000000−22i2−i2
χ35222-2-2-2-222-2−2i−2i2i2i0002-20−2i2i000000−2−2−2−22222i2i2i2i2−i2−i2−i2−i22-200−2i2i00000000000000000000−22i2−i2
χ36222-2-2-2-222-2−2i−2i2i2i0002-20−2i2i000000−2−2−2−22222i2i2i2i2−i2−i2−i2−i2-22002i−2i000000000000000000002−2−i2i2
χ3722-2-2-222-22200002-2-2-2-220000002-222-2-222-2-200000000000000002i−2i2i−2i000000002i−2i00000000
χ3822-2-2-222-22200002-2-2-2-220000002-222-2-222-2-20000000000000000−2i2i−2i2i00000000−2i2i00000000
χ3922-2-2-222-22200002-2-2-2-220000002-2-2-222-2-22200000000000000002i−2i2i−2i00000000−2i2i00000000
χ4022-2-2-222-22200002-2-2-2-220000002-2-2-222-2-2220000000000000000−2i2i−2i2i000000002i−2i00000000
χ4122-2-2-222-2-2-20000-22222-20000002-2000000002i2i−2i−2i2i2i−2i−2i000000002i−2i−2i2i0000002-20000000000
χ4222-2-2-222-2-2-20000-22222-20000002-2000000002i2i−2i−2i2i2i−2i−2i00000000−2i2i2i−2i000000-220000000000
χ4322-2-2-222-2-2-20000-22222-20000002-200000000−2i−2i2i2i−2i−2i2i2i000000002i−2i−2i2i000000-220000000000
χ4422-2-2-222-2-2-20000-22222-20000002-200000000−2i−2i2i2i−2i−2i2i2i00000000−2i2i2i−2i0000002-20000000000
χ452-222-22-2-2002-22-2-22-2002002-200002−22−22−22−22−22−22−22−2002i−2i002i−2i00000000000000i2−i2i2−i20000
χ462-222-22-2-2002-22-2-22-2002002-200002−22−22−22−22−22−22−22−200−2i2i00−2i2i00000000000000−i2i2−i2i20000
χ472-222-22-2-2002-22-2-22-2002002-20000−22−22−22−22−22−22−22−22002i−2i002i−2i00000000000000−i2i2−i2i20000
χ482-222-22-2-2002-22-2-22-2002002-20000−22−22−22−22−22−22−22−2200−2i2i00−2i2i00000000000000i2−i2i2−i20000
χ492-222-22-2-200-22-22-22-200200-2200002−22−22−22−2−22−22−22−22002i−2i00−2i2i00000000000000i2−i2−i2i20000
χ502-222-22-2-200-22-22-22-200200-2200002−22−22−22−2−22−22−22−2200−2i2i002i−2i00000000000000−i2i2i2−i20000
χ512-222-22-2-200-22-22-22-200200-220000−22−22−22−222−22−22−22−2002i−2i00−2i2i00000000000000−i2i2i2−i20000
χ522-222-22-2-200-22-22-22-200200-220000−22−22−22−222−22−22−22−200−2i2i002i−2i00000000000000i2−i2−i2i20000
χ53444-4-4-4-44-444i4i−4i−4i000-440−4i4i0000000000000000000000000000000000000000000000000000
χ54444-4-4-4-44-44−4i−4i4i4i000-4404i−4i0000000000000000000000000000000000000000000000000000
χ5544-444-4-4-44-40000000-440000000002222−22−22−22−22222200000000000000000000000000000000000000
χ5644-444-4-4-44-40000000-44000000000−22−2222222222−22−2200000000000000000000000000000000000000
χ5744-444-4-4-4-4400000004-4000000000000000002222−22−22−22−222222000000000000000000000000000000
χ5844-444-4-4-4-4400000004-400000000000000000−22−2222222222−22−22000000000000000000000000000000
χ5944-4-4-444-4440000-444-4-4-4000000-440000000000000000000000000000000000000000000000
χ6044-4-4-444-4-4-400004-4-4444000000-440000000000000000000000000000000000000000000000
χ614-444-44-4-4004-44-44-4400-400-4400000000000000000000000000000000000000000000000000
χ624-444-44-4-400-44-444-4400-4004-400000000000000000000000000000000000000000000000000
χ634-44-44-44-4004i−4i−4i4i000000000000002-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ644-44-44-44-4004i−4i−4i4i00000000000000-22-222-22-2−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ654-44-44-44-400−4i4i4i−4i000000000000002-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000
χ664-44-44-44-400−4i4i4i−4i00000000000000-22-222-22-22i−2i2i−2i−2i2i−2i2i000000000000000000000000000000
χ674-4-44-4-44400000000000000004-4002-2-22-222-22-2-22-222-2000000000000000000000000000000
χ684-4-44-4-44400000000000000004-400-222-22-2-22-222-22-2-22000000000000000000000000000000
χ694-4-44-4-4440000000000000000-44002-2-22-222-2-222-22-2-22000000000000000000000000000000
χ704-4-44-4-4440000000000000000-4400-222-22-2-222-2-22-222-2000000000000000000000000000000
χ714-4-4-444-4400000044-400-400000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ724-4-4-444-4400000044-400-40000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ734-4-4-444-44000000-4-440040000000022−22−222222−22−222200000000000000000000000000000000000000
χ744-4-4-444-44000000-4-4400400000000−222222−22−222222−2200000000000000000000000000000000000000

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