Finite Group Databasebeta

← Group #98248

Character table — Group #98248

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444444444444444888888888888888844444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-111-1-1-1-111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1111iiii−i−i−i−iiiii−i−i−i−i1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1111−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−i−iii−i−iii
χ1111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111iiii−i−i−i−i−i−i−i−iiiii-11-1-111ii−i−i−i−iii
χ1211111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111−i−i−i−iiiiiiiii−i−i−i−i-11-1-111−i−iiiii−i−i
χ1311111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-11-1-1iiii−i−i−i−iiiii−i−i−i−i1-1-1-111−i−iii−i−iii
χ1411111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-11-1-1−i−i−i−iiiii−i−i−i−iiiii1-1-1-111ii−i−iii−i−i
χ1511111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii-1111-1-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1ii−i−i−i−iii
χ1722222222222222-2-2-2-222-2-2220000-2-200002222-2000000000000000000-2-2000000000000
χ1822222222222222-2-2-2-222-2-2220000-2-20000-2-2-2-2-200000000000000000022000000000000
χ1922222222222-2-2-222222-22-2-2-222222-222-2-20000-2-2-2000000000000000000000000000000
χ2022222222222-2-2-222222-22-2-2-2-2-2-2-22-2-2-2220000-222000000000000000000000000000000
χ2122222222222-2-2-2-2-2-2-22-2-22-2-20000-22000000002000000000000000000002-22-200000000
χ2222222222222-2-2-2-2-2-2-22-2-22-2-20000-2200000000200000000000000000000-22-2200000000
χ2322222222-2-2-22222222-22-22-2-22222-22-2-2220000-2-2-2000000000000000000000000000000
χ2422222222-2-2-22222222-22-22-2-2-2-2-2-2-2222-2-20000-222000000000000000000000000000000
χ2522222222-2-2-2222-2-2-2-2-222-2-2-200002-2000000002000000000000000000002-2-2200000000
χ2622222222-2-2-2222-2-2-2-2-222-2-2-200002-200000000200000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000022000022-2-2-2000000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222220000220000-2-222-20000000000000000002-2000000000000
χ29222-2-22-2-222-222-20000-2-2002-200000000002-22-200022−2−222−2−222−2−222−2−200000000000000
χ30222-2-22-2-222-222-20000-2-2002-200000000002-22-2000−2−222−2−222−2−222−2−22200000000000000
χ31222-2-22-2-222-222-20000-2-2002-20000000000-22-2200022−2−222−2−2−2−222−2−22200000000000000
χ32222-2-22-2-222-222-20000-2-2002-20000000000-22-22000−2−222−2−22222−2−222−2−200000000000000
χ33222-2-22-2-2-2-22-2-22000022002-200000000002-2-22000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ34222-2-22-2-2-2-22-2-22000022002-200000000002-2-22000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ35222-2-22-2-2-2-22-2-22000022002-20000000000-222-2000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ36222-2-22-2-2-2-22-2-22000022002-20000000000-222-2000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ3722-22-2-2-220002-2222-2-20-20-2002i2i−2i−2i02002i−2i0000000i2−i2i2−i2i2−i2i2−i2000000000000002−22−20000
χ3822-22-2-2-220002-2222-2-20-20-2002i2i−2i−2i02002i−2i0000000−i2i2−i2i2−i2i2−i2i200000000000000−22−220000
χ3922-22-2-2-220002-2222-2-20-20-200−2i−2i2i2i0200−2i2i0000000i2−i2i2−i2i2−i2i2−i200000000000000−22−220000
χ4022-22-2-2-220002-2222-2-20-20-200−2i−2i2i2i0200−2i2i0000000−i2i2−i2i2−i2i2−i2i2000000000000002−22−20000
χ4122-22-2-2-22000-22-222-2-20202002i2i−2i−2i0-200−2i2i00000002−22−2−22−2200000000000000−i2i2i2−i20000
χ4222-22-2-2-22000-22-222-2-20202002i2i−2i−2i0-200−2i2i0000000−22−222−22−200000000000000i2−i2−i2i20000
χ4322-22-2-2-22000-22-222-2-2020200−2i−2i2i2i0-2002i−2i00000002−22−2−22−2200000000000000i2−i2−i2i20000
χ4422-22-2-2-22000-22-222-2-2020200−2i−2i2i2i0-2002i−2i0000000−22−222−22−200000000000000−i2i2i2−i20000
χ452-22-22-2-222-220002-22-2-20-20002i−2i2i−2i202i−2i00000000000000000i2−i2i2−i2i2−i2i2−i200000000002−22−2
χ462-22-22-2-222-220002-22-2-20-20002i−2i2i−2i202i−2i00000000000000000−i2i2−i2i2−i2i2−i2i20000000000−22−22
χ472-22-22-2-222-220002-22-2-20-2000−2i2i−2i2i20−2i2i00000000000000000i2−i2i2−i2i2−i2i2−i20000000000−22−22
χ482-22-22-2-222-220002-22-2-20-2000−2i2i−2i2i20−2i2i00000000000000000−i2i2−i2i2−i2i2−i2i200000000002−22−2
χ492-22-22-2-22-22-20002-22-22020002i−2i2i−2i-20−2i2i000000000000000002−22−2−22−220000000000−i2i2i2−i2
χ502-22-22-2-22-22-20002-22-22020002i−2i2i−2i-20−2i2i00000000000000000−22−222−22−20000000000i2−i2−i2i2
χ512-22-22-2-22-22-20002-22-2202000−2i2i−2i2i-202i−2i000000000000000002−22−2−22−220000000000i2−i2−i2i2
χ522-22-22-2-22-22-20002-22-2202000−2i2i−2i2i-202i−2i00000000000000000−22−222−22−20000000000−i2i2i2−i2
χ53444-4-44-4-444-4-4-440000-4400-4400000000000000000000000000000000000000000000000
χ54444-4-44-4-4-4-4444-400004-400-4400000000000000000000000000000000000000000000000
χ5544-44-4-4-440004-44-4-4440-4040000000-400000000000000000000000000000000000000000
χ5644-44-4-4-44000-44-4-4-444040-40000000400000000000000000000000000000000000000000
χ5744-4-44-44-40004-4-40000040000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ5844-4-44-44-40004-4-4000004000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ5944-4-44-44-4000-44400000-40000000000000000000002-2-22-222-20000000000000000000000
χ6044-4-44-44-4000-44400000-4000000000000000000000-222-22-2-220000000000000000000000
χ614-444-4-44-44-4-4000000040000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ624-444-4-44-44-4-400000004000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ634-444-4-44-4-4440000000-40000000000000000000000000000002-2-22-222-200000000000000
χ644-444-4-44-4-4440000000-4000000000000000000000000000000-222-22-2-2200000000000000
χ654-44-44-4-444-44000-44-44-4040000000-4000000000000000000000000000000000000000000
χ664-44-44-4-44-44-4000-44-4440-400000004000000000000000000000000000000000000000000
χ674-4-4-4-44440000004-4-440000004-4-440000000000000000000000000000000000000000000
χ684-4-4-4-44440000004-4-44000000-444-40000000000000000000000000000000000000000000
χ694-4-4-4-4444000000-444-40000000000000000000004-4000000000000000000000000000000
χ704-4-4-4-4444000000-444-4000000000000000000000-44000000000000000000000000000000
χ718-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000

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