Finite Group Databasebeta

← Group #246421

Character table — Group #246421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444888888888888161616161616161616161616161616161616
order12222222444444444444224444448888888888888888224444444444222244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-11-111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-11-11111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111
χ9111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-111-1-1-111-1-111-1-1
χ10111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-111
χ11111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-11111-1-1
χ12111111111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111-1-11-1-1-1-111-1-111
χ13111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-1-111-111-1-111-1-111
χ14111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1
χ15111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-11111-1-1-1-111-1-1-1-111
χ16111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111-1-11-1-111111-1-111-1-1
χ172222222222-2-2222222-2-2-2-2-2-222-2-200000000000000002222000000000000-20-200000000000
χ182222222222-2-2222222-2-2-2-2-2-222-2-20000000000000000-2-2-2-200000000000020200000000000
χ192222222222-2-2-2-2-2-222-2-22222-2-2-2-2000000000000000022-2-200000000000020-200000000000
χ202222222222-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000-2-222000000000000-20200000000000
χ2122222222-2-2222222-2-222-2-222-2-2-2-2000000000000000000002222000000000-20-20000000000
χ2222222222-2-2222222-2-222-2-222-2-2-2-200000000000000000000-2-2-2-20000000002020000000000
χ2322222222-2-222-2-2-2-2-2-22222-2-222-2-20000000000000000000022-2-2000000000-2020000000000
χ2422222222-2-222-2-2-2-2-2-22222-2-222-2-200000000000000000000-2-22200000000020-20000000000
χ2522222222-2-2-2-22222-2-2-2-222-2-2-2-22200000000000000000000000022-2-22-20000000000000000
χ2622222222-2-2-2-22222-2-2-2-222-2-2-2-222000000000000000000000000-2-222-220000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222222200000000000000000000000022-2-2-220000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000-2-2222-20000000000000000
χ29222-2-2-22-2002-22i2i−2i−2i002-2002i−2i00002222−2−2−2−2i2i2i2i2−i2−i2−i2−i200002-22i−2i0000000000000000002−2i2−i2
χ30222-2-2-22-2002-22i2i−2i−2i002-2002i−2i00002222−2−2−2−2i2i2i2i2−i2−i2−i2−i20000-22−2i2i000000000000000000−22−i2i2
χ31222-2-2-22-2002-22i2i−2i−2i002-2002i−2i0000−2−2−2−22222−i2−i2−i2−i2i2i2i2i200002-22i−2i000000000000000000−22−i2i2
χ32222-2-2-22-2002-22i2i−2i−2i002-2002i−2i0000−2−2−2−22222−i2−i2−i2−i2i2i2i2i20000-22−2i2i0000000000000000002−2i2−i2
χ33222-2-2-22-2002-2−2i−2i2i2i002-200−2i2i00002222−2−2−2−2−i2−i2−i2−i2i2i2i2i200002-2−2i2i0000000000000000002−2−i2i2
χ34222-2-2-22-2002-2−2i−2i2i2i002-200−2i2i00002222−2−2−2−2−i2−i2−i2−i2i2i2i2i20000-222i−2i000000000000000000−22i2−i2
χ35222-2-2-22-2002-2−2i−2i2i2i002-200−2i2i0000−2−2−2−22222i2i2i2i2−i2−i2−i2−i200002-2−2i2i000000000000000000−22i2−i2
χ36222-2-2-22-2002-2−2i−2i2i2i002-200−2i2i0000−2−2−2−22222i2i2i2i2−i2−i2−i2−i20000-222i−2i0000000000000000002−2−i2i2
χ372-222-22-2-22-2002i−2i2i−2i2-20000002i−2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i22-22i−2i0000000000000000002−2i2−i20000
χ382-222-22-2-22-2002i−2i2i−2i2-20000002i−2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i2-22−2i2i000000000000000000−22−i2i20000
χ392-222-22-2-22-2002i−2i2i−2i2-20000002i−2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i22-22i−2i000000000000000000−22−i2i20000
χ402-222-22-2-22-2002i−2i2i−2i2-20000002i−2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i2-22−2i2i0000000000000000002−2i2−i20000
χ412-222-22-2-22-200−2i2i−2i2i2-2000000−2i2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i22-2−2i2i0000000000000000002−2−i2i20000
χ422-222-22-2-22-200−2i2i−2i2i2-2000000−2i2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i2-222i−2i000000000000000000−22i2−i20000
χ432-222-22-2-22-200−2i2i−2i2i2-2000000−2i2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i22-2−2i2i000000000000000000−22i2−i20000
χ442-222-22-2-22-200−2i2i−2i2i2-2000000−2i2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i2-222i−2i0000000000000000002−2−i2i20000
χ452-2-22-2-2222-2-220000-222-2000000-222-22-22-22-200000000000000002-22-2000000002-200000000
χ462-2-22-2-2222-2-220000-222-2000000-222-22-22-22-20000000000000000-22-2200000000-2200000000
χ472-2-22-2-2222-2-220000-222-2000000-22-22-22-22-2200000000000000002-22-200000000-2200000000
χ482-2-22-2-2222-2-220000-222-2000000-22-22-22-22-220000000000000000-22-22000000002-200000000
χ492-2-22-2-222-222-200002-2-22000000-22000000002-22-22-22-2000000002-2-22002-200000000000000
χ502-2-22-2-222-222-200002-2-22000000-22000000002-22-22-22-200000000-222-200-2200000000000000
χ512-2-22-2-222-222-200002-2-22000000-2200000000-22-22-22-22000000002-2-2200-2200000000000000
χ522-2-22-2-222-222-200002-2-22000000-2200000000-22-22-22-2200000000-222-2002-200000000000000
χ53444-4-4-44-400-444i4i−4i−4i00-4400−4i4i00000000000000000000000000000000000000000000000000
χ54444-4-4-44-400-44−4i−4i4i4i00-44004i−4i00000000000000000000000000000000000000000000000000
χ5544-444-4-4-444000000-4-4000000000022−22−222222−22−222200000000000000000000000000000000000000
χ5644-444-4-4-444000000-4-40000000000−222222−22−222222−2200000000000000000000000000000000000000
χ5744-444-4-4-4-4-4000000440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ5844-444-4-4-4-4-400000044000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ5944-4-4-44-440000000000004-40000002-2-22-222-22-2-22-222-2000000000000000000000000000000
χ6044-4-4-44-440000000000004-4000000-222-22-2-22-222-22-2-22000000000000000000000000000000
χ6144-4-4-44-44000000000000-440000002-2-22-222-2-222-22-2-22000000000000000000000000000000
χ6244-4-4-44-44000000000000-44000000-222-22-2-222-2-22-222-2000000000000000000000000000000
χ634-444-44-4-4-44004i−4i4i−4i-44000000−4i4i000000000000000000000000000000000000000000000000
χ644-444-44-4-4-4400−4i4i−4i4i-440000004i−4i000000000000000000000000000000000000000000000000
χ654-44-44-4-4400004-4-4400000000000022-2-2-2-22222-2-2-2-222000000000000000000000000000000
χ664-44-44-4-4400004-4-44000000000000-2-22222-2-2-2-22222-2-2000000000000000000000000000000
χ674-44-44-4-440000-444-400000000000022-2-2-2-222-2-22222-2-2000000000000000000000000000000
χ684-44-44-4-440000-444-4000000000000-2-22222-2-222-2-2-2-222000000000000000000000000000000
χ694-4-44-4-4444-44-40000-44-440000004-40000000000000000000000000000000000000000000000
χ704-4-44-4-444-44-4400004-44-40000004-40000000000000000000000000000000000000000000000
χ714-4-4-4444-40044000000-4-400000000000000002i2−2i22i2−2i2−2i22i2−2i22i2000000000000000000000000000000
χ724-4-4-4444-40044000000-4-40000000000000000−2i22i2−2i22i22i2−2i22i2−2i2000000000000000000000000000000
χ734-4-4-4444-400-4-4000000440000000022−2222−22−2222−222200000000000000000000000000000000000000
χ744-4-4-4444-400-4-40000004400000000−2222−222222−2222−2200000000000000000000000000000000000000

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