Finite Group Databasebeta

← Group #268461

Character table — Group #268461

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444224444444444444444488888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ3111111111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111
χ4111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111111111111-11-1-1-1-1-1
χ511111111111111111111111111-1-1-1-11111-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111111111-11-11-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ911111111111-1-1-1-111111-1-1-1-11111-1-1111111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-11-1
χ1011111111111-1-1-1-111111-1-1-1-11111-1-1111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-1-1-11
χ1111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1111-1
χ1211111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1-111-111-11
χ1311111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-11
χ1411111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-11-1
χ1511111111111-1-1-1-111111-1-1-1-111-1-111-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1111-11
χ1611111111111-1-1-1-111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-11111-1
χ17222222222222222-2-2-2-2222-2-2-2-20000000022-2220000000000000000000000000-20-20000
χ18222222222222222-2-2-2-2222-2-2-2-200000000-2-2-2-2-200000000000000000000000002020000
χ1922222222222-2-2-2-2-2-2-2-22-2-222-2-200000000222-2-2000000000000000000000000020-20000
χ2022222222222-2-2-2-2-2-2-2-22-2-222-2-200000000-2-22220000000000000000000000000-2020000
χ2122222222-2-2-222222222-2-2-222-2-22222000000-200000000000000000000000000-20-200000
χ2222222222-2-2-222222222-2-2-222-2-2-2-2-2-2000000-20000000000000000000000000020200000
χ2322222222-2-2-22222-2-2-2-2-2-2-2-2-222000022-2-20020000000000000000000000000000002-200
χ2422222222-2-2-22222-2-2-2-2-2-2-2-2-2220000-2-222002000000000000000000000000000000-2200
χ2522222222-2-2-2-2-2-2-22222-222-2-2-2-222-2-200000020000000000000000000000000020-200000
χ2622222222-2-2-2-2-2-2-22222-222-2-2-2-2-2-222000000200000000000000000000000000-20200000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000022-2-200-2000000000000000000000000000000-2200
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-2-22200-20000000000000000000000000000002-200
χ29222-2-2-2-220002i2i−2i−2i2-22-20002i−2i002-22i−2i0000000000000000022−2−2i2i2−i2−i222−2−2i2i2−i2−i200000000
χ30222-2-2-2-220002i2i−2i−2i2-22-20002i−2i002-22i−2i00000000000000000−2−222−i2−i2i2i2−2−222−i2−i2i2i200000000
χ31222-2-2-2-220002i2i−2i−2i2-22-20002i−2i00-22−2i2i0000000000000000022−2−2i2i2−i2−i2−2−222−i2−i2i2i200000000
χ32222-2-2-2-220002i2i−2i−2i2-22-20002i−2i00-22−2i2i00000000000000000−2−222−i2−i2i2i222−2−2i2i2−i2−i200000000
χ33222-2-2-2-22000−2i−2i2i2i2-22-2000−2i2i002-2−2i2i0000000000000000022−2−2−i2−i2i2i222−2−2−i2−i2i2i200000000
χ34222-2-2-2-22000−2i−2i2i2i2-22-2000−2i2i002-2−2i2i00000000000000000−2−222i2i2−i2−i2−2−222i2i2−i2−i200000000
χ35222-2-2-2-22000−2i−2i2i2i2-22-2000−2i2i00-222i−2i0000000000000000022−2−2−i2−i2i2i2−2−222i2i2−i2−i200000000
χ36222-2-2-2-22000−2i−2i2i2i2-22-2000−2i2i00-222i−2i00000000000000000−2−222i2i2−i2−i222−2−2−i2−i2i2i200000000
χ372-2222-2-2-22-2-22-22-2000022-20000000000002i−2i02i−2ii2i2−i2−i2i2i2−i2−i2000000002−22−22−22−200000000
χ382-2222-2-2-22-2-22-22-2000022-20000000000002i−2i02i−2i−i2−i2i2i2−i2−i2i2i200000000−22−22−22−2200000000
χ392-2222-2-2-22-2-22-22-2000022-2000000000000−2i2i0−2i2ii2i2−i2−i2i2i2−i2−i200000000−22−22−22−2200000000
χ402-2222-2-2-22-2-22-22-2000022-2000000000000−2i2i0−2i2i−i2−i2i2i2−i2−i2i2i2000000002−22−22−22−200000000
χ412-2222-2-2-22-2-2-22-2200002-220000000000002i−2i0−2i2ii2i2−i2−i2−i2−i2i2i2000000002−22−2−22−2200000000
χ422-2222-2-2-22-2-2-22-2200002-220000000000002i−2i0−2i2i−i2−i2i2i2i2i2−i2−i200000000−22−222−22−200000000
χ432-2222-2-2-22-2-2-22-2200002-22000000000000−2i2i02i−2ii2i2−i2−i2−i2−i2i2i200000000−22−222−22−200000000
χ442-2222-2-2-22-2-2-22-2200002-22000000000000−2i2i02i−2i−i2−i2i2i2i2i2−i2−i2000000002−22−2−22−2200000000
χ452-2-22-22-2222-2000022-2-2-200002-200002-22-20000000002i−2i2i−2i00002i−2i2i−2i0000000000000000
χ462-2-22-22-2222-2000022-2-2-200002-200002-22-2000000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000
χ472-2-22-22-2222-2000022-2-2-200002-20000-22-220000000002i−2i2i−2i0000−2i2i−2i2i0000000000000000
χ482-2-22-22-2222-2000022-2-2-200002-20000-22-22000000000−2i2i−2i2i00002i−2i2i−2i0000000000000000
χ492-2-22-22-22-2-220000-2-222200002-200002-2-22000002-22-200002-22-200000000000000000000
χ502-2-22-22-22-2-220000-2-222200002-200002-2-2200000-22-220000-22-2200000000000000000000
χ512-2-22-22-22-2-220000-2-222200002-20000-222-2000002-22-20000-22-2200000000000000000000
χ522-2-22-22-22-2-220000-2-222200002-20000-222-200000-22-2200002-22-200000000000000000000
χ53444-4-4-4-440004i4i−4i−4i-44-44000−4i4i00000000000000000000000000000000000000000000000
χ54444-4-4-4-44000−4i−4i4i4i-44-440004i−4i00000000000000000000000000000000000000000000000
χ5544-44-4-44-44-4400000000-40000000000000000000000022−22−2222000000000000000000000000
χ5644-44-4-44-44-4400000000-400000000000000000000000−222222−22000000000000000000000000
χ5744-44-4-44-4-44-400000000400000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ5844-44-4-44-4-44-40000000040000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ594-4444-4-4-4-4444-44-40000-4-440000000000000000000000000000000000000000000000000
χ604-4444-4-4-4-444-44-440000-44-40000000000000000000000000000000000000000000000000
χ614-44-4-444-40004i−4i−4i4i00000000000000000000000000000000000000002-2-222i−2i−2i2i00000000
χ624-44-4-444-40004i−4i−4i4i0000000000000000000000000000000000000000-222-2−2i2i2i−2i00000000
χ634-44-4-444-4000−4i4i4i−4i00000000000000000000000000000000000000002-2-22−2i2i2i−2i00000000
χ644-44-4-444-4000−4i4i4i−4i0000000000000000000000000000000000000000-222-22i−2i−2i2i00000000
χ654-4-44-44-4444-40000-4-444-40000-44000000000000000000000000000000000000000000000
χ664-4-44-44-44-4-44000044-4-440000-44000000000000000000000000000000000000000000000
χ674-4-4-44-44400000004-4-440000000000000000000000000000000022−22−22220000000000000000
χ684-4-4-44-44400000004-4-4400000000000000000000000000000000−222222−220000000000000000
χ694-4-4-44-4440000000-444-4000000000000000000000000000022−22−222200000000000000000000
χ704-4-4-44-4440000000-444-40000000000000000000000000000−222222−2200000000000000000000
χ7188-8-888-8-8000000000000000000000000000000000000000000000000000000000000000

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