Finite Group Databasebeta

← Group #324154

Character table — Group #324154

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444422444488888888888888888888888888888888444488882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111111111-1-1-1-1-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-11-11-1
χ10111111111-1-1-1-1-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-11-11
χ11111111111-1-1-1-1-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-1-11-11
χ12111111111-1-1-1-1-1-1-1-11111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-1111-11-1
χ13111111111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111-11-1-1-1111-1-11
χ14111111111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-11-1111-1-1-111-1
χ15111111111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11-11-1-1-111-111-1
χ16111111111-1-1-1-1-1-1-1-11111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1111-1-11-1-11
χ172222222222222-2-2-2-222-2-2-2-2222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222-2-2-2-222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ19222222222-2-2-2-2222222-2-2-2-22-2-2-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ20222222222-2-2-2-2222222-2-2-2-22-2-2-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2122222222-222222222-2-22222-2-2-2-2-2-2-20000000000000000000000000000000022-2-200000000
χ2222222222-222222222-2-22222-2-2-2-2-2-2-200000000000000000000000000000000-2-22200000000
χ2322222222-22222-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000002i−2i2i−2i0000
χ2422222222-22222-2-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000−2i2i−2i2i0000
χ2522222222-2-2-2-2-22222-2-2-2-2-2-2-22222-2-20000000000000000000000000000000000002i−2i−2i2i0000
χ2622222222-2-2-2-2-22222-2-2-2-2-2-2-22222-2-2000000000000000000000000000000000000−2i2i2i−2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-2-22222-222-2-222000000000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-22222-222-2-22200000000000000000000000000000000-222-200000000
χ29222-22-2-2-2-222-2-200002-2000022-200002i2i−2i−2i2i2i−2i−2i00000000i2i2−i2−i2i2i2−i2−i222−2−222−2−2000000000000
χ30222-22-2-2-2-222-2-200002-2000022-200002i2i−2i−2i2i2i−2i−2i00000000−i2−i2i2i2−i2−i2i2i2−2−222−2−222000000000000
χ31222-22-2-2-2-222-2-200002-2000022-20000−2i−2i2i2i−2i−2i2i2i00000000i2i2−i2−i2i2i2−i2−i2−2−222−2−222000000000000
χ32222-22-2-2-2-222-2-200002-2000022-20000−2i−2i2i2i−2i−2i2i2i00000000−i2−i2i2i2−i2−i2i2i222−2−222−2−2000000000000
χ33222-22-2-2-2-2-2-22200002-200002-2200002i2i−2i−2i−2i−2i2i2i00000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ34222-22-2-2-2-2-2-22200002-200002-2200002i2i−2i−2i−2i−2i2i2i00000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ35222-22-2-2-2-2-2-22200002-200002-220000−2i−2i2i2i2i2i−2i−2i00000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ36222-22-2-2-2-2-2-22200002-200002-220000−2i−2i2i2i2i2i−2i−2i00000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ372-222-2-22-2-200002i2i−2i−2i220000-200002i−2i2-22-2000000002i2i−2i−2i2−22−2i2−i2i2−i22−22−2i2−i2i2−i2000000000000
χ382-222-2-22-2-200002i2i−2i−2i220000-200002i−2i2-22-2000000002i2i−2i−2i−22−22−i2i2−i2i2−22−22−i2i2−i2i2000000000000
χ392-222-2-22-2-200002i2i−2i−2i220000-200002i−2i-22-2200000000−2i−2i2i2i2−22−2i2−i2i2−i2−22−22−i2i2−i2i2000000000000
χ402-222-2-22-2-200002i2i−2i−2i220000-200002i−2i-22-2200000000−2i−2i2i2i−22−22−i2i2−i2i22−22−2i2−i2i2−i2000000000000
χ412-222-2-22-2-20000−2i−2i2i2i220000-20000−2i2i2-22-200000000−2i−2i2i2i2−22−2−i2i2−i2i22−22−2−i2i2−i2i2000000000000
χ422-222-2-22-2-20000−2i−2i2i2i220000-20000−2i2i2-22-200000000−2i−2i2i2i−22−22i2−i2i2−i2−22−22i2−i2i2−i2000000000000
χ432-222-2-22-2-20000−2i−2i2i2i220000-20000−2i2i-22-22000000002i2i−2i−2i2−22−2−i2i2−i2i2−22−22i2−i2i2−i2000000000000
χ442-222-2-22-2-20000−2i−2i2i2i220000-20000−2i2i-22-22000000002i2i−2i−2i−22−22i2−i2i2−i22−22−2−i2i2−i2i2000000000000
χ452-22-2-22-222000000002-222-2-2-2002-2002i−2i−2i2i00002i2i−2i−2i000000002-2-220000−2i2i2i−2i000000000000
χ462-22-2-22-222000000002-222-2-2-2002-2002i−2i−2i2i00002i2i−2i−2i00000000-222-200002i−2i−2i2i000000000000
χ472-22-2-22-222000000002-222-2-2-2002-200−2i2i2i−2i0000−2i−2i2i2i000000002-2-2200002i−2i−2i2i000000000000
χ482-22-2-22-222000000002-222-2-2-2002-200−2i2i2i−2i0000−2i−2i2i2i00000000-222-20000−2i2i2i−2i000000000000
χ492-22-2-22-222000000002-2-2-222-200-22002i−2i−2i2i0000−2i−2i2i2i00002i−2i−2i2i00002-2-220000000000000000
χ502-22-2-22-222000000002-2-2-222-200-22002i−2i−2i2i0000−2i−2i2i2i0000−2i2i2i−2i0000-222-20000000000000000
χ512-22-2-22-222000000002-2-2-222-200-2200−2i2i2i−2i00002i2i−2i−2i00002i−2i−2i2i0000-222-20000000000000000
χ522-22-2-22-222000000002-2-2-222-200-2200−2i2i2i−2i00002i2i−2i−2i0000−2i2i2i−2i00002-2-220000000000000000
χ53444-44-4-4-4444-4-40000-440000-4-44000000000000000000000000000000000000000000000000
χ54444-44-4-4-44-4-4440000-440000-44-4000000000000000000000000000000000000000000000000
χ5544-44-4-4-4404i−4i4i−4i4i−4i4i−4i004-44-4000000000000000000000000000000000000000000000000000
χ5644-44-4-4-4404i−4i4i−4i−4i4i−4i4i00-44-44000000000000000000000000000000000000000000000000000
χ5744-44-4-4-440−4i4i−4i4i4i−4i4i−4i00-44-44000000000000000000000000000000000000000000000000000
χ5844-44-4-4-440−4i4i−4i4i−4i4i−4i4i004-44-4000000000000000000000000000000000000000000000000000
χ5944-4-4-444-404i−4i−4i4i000000000000000000000000022−2222−222i2−2i22i2−2i20000000000000000000000000000
χ6044-4-4-444-404i−4i−4i4i0000000000000000000000000−2222−2222−2i22i2−2i22i20000000000000000000000000000
χ6144-4-4-444-40−4i4i4i−4i000000000000000000000000022−2222−22−2i22i2−2i22i20000000000000000000000000000
χ6244-4-4-444-40−4i4i4i−4i0000000000000000000000000−2222−22222i2−2i22i2−2i20000000000000000000000000000
χ634-444-4-44-4400004i4i−4i−4i-4-4000040000−4i4i00000000000000000000000000000000000000000000
χ644-444-4-44-440000−4i−4i4i4i-4-40000400004i−4i00000000000000000000000000000000000000000000
χ654-44-4-44-44-400000000-4444-4-4400-440000000000000000000000000000000000000000000000
χ664-44-4-44-44-400000000-44-4-4444004-40000000000000000000000000000000000000000000000
χ674-4-4444-4-4000004-4-44000000000000000002i2−2i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000
χ684-4-4444-4-4000004-4-4400000000000000000−2i22i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000
χ694-4-4444-4-400000-444-4000000000000000002i2−2i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ704-4-4444-4-400000-444-400000000000000000−2i22i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ714-4-4-44-444000000000004-4-440000000000022−22−22220000−222222−220000000000000000000000000000
χ724-4-4-44-444000000000004-4-4400000000000−222222−22000022−22−22220000000000000000000000000000
χ734-4-4-44-44400000000000-444-40000000000022−22−2222000022−22−22220000000000000000000000000000
χ744-4-4-44-44400000000000-444-400000000000−222222−220000−222222−220000000000000000000000000000

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