Finite Group Databasebeta

← Group #98249

Character table — Group #98249

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
χ311111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-11111-1-111-1-11111-1-1111-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1-11111-1-111-1-11111-1-1111-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−i−iii−i−iii
χ1111111111-1-1-1-1-1-11111-1-111-1-11111-1-1111-1-1-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-111ii−i−i−i−iii
χ1211111111-1-1-1-1-1-11111-1-111-1-11111-1-1111-1-1-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111−i−iiiii−i−i
χ1311111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11-1-11111-1-111iiii−i−i−i−iiiii−i−i−i−i1-1-1-111−i−iii−i−iii
χ1411111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11-1-11111-1-111−i−i−i−iiiii−i−i−i−iiiii1-1-1-111ii−i−iii−i−i
χ1511111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11-1-111-1-11111iiii−i−i−i−i−i−i−i−iiiii-1111-1-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11-1-111-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1ii−i−i−i−iii
χ1722222222222222-2-2-2-22222-2-20000-2-2-200002222000000000000000000-2-2000000000000
χ1822222222222222-2-2-2-22222-2-20000-2-2-20000-2-2-2-200000000000000000022000000000000
χ1922222222222-2-2-222222-2-2-22-222222-2-2-2-2220000-2-2000000000000000000000000000000
χ2022222222222-2-2-222222-2-2-22-2-2-2-2-22-2-222-2-2000022000000000000000000000000000000
χ2122222222222-2-2-2-2-2-2-22-2-2-2-220000-22200000000000000000000000000002-22-200000000
χ2222222222222-2-2-2-2-2-2-22-2-2-2-220000-2220000000000000000000000000000-22-2200000000
χ2322222222-2-2-22222222-22-2-2-222222-22-2-2-2-2-2000022000000000000000000000000000000
χ2422222222-2-2-22222222-22-2-2-22-2-2-2-2-22-222220000-2-2000000000000000000000000000000
χ2522222222-2-2-2222-2-2-2-2-22-2-22-200002-2200000000000000000000000000002-2-2200000000
χ2622222222-2-2-2222-2-2-2-2-22-2-22-200002-220000000000000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-2000022-2-2000000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222000022-20000-2-2220000000000000000002-2000000000000
χ29222-2-22-2-222-222-20000-2-22-200000000000002-22-20022−2−222−2−222−2−222−2−200000000000000
χ30222-2-22-2-222-222-20000-2-22-200000000000002-22-200−2−222−2−222−2−222−2−22200000000000000
χ31222-2-22-2-222-222-20000-2-22-20000000000000-22-220022−2−222−2−2−2−222−2−22200000000000000
χ32222-2-22-2-222-222-20000-2-22-20000000000000-22-2200−2−222−2−22222−2−222−2−200000000000000
χ33222-2-22-2-2-2-22-2-220000222-200000000000002-2-2200i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000
χ34222-2-22-2-2-2-22-2-220000222-200000000000002-2-2200−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000
χ35222-2-22-2-2-2-22-2-220000222-20000000000000-222-200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000
χ36222-2-22-2-2-2-22-2-220000222-20000000000000-222-200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000
χ3722-22-2-2-222-2200022-2-2-2000-202i2i−2i−2i200002i−2i00000000000000i2−i2i2−i2i2−i2i2−i200000000002−22−2
χ3822-22-2-2-222-2200022-2-2-2000-202i2i−2i−2i200002i−2i00000000000000−i2i2−i2i2−i2i2−i2i20000000000−22−22
χ3922-22-2-2-222-2200022-2-2-2000-20−2i−2i2i2i20000−2i2i00000000000000i2−i2i2−i2i2−i2i2−i20000000000−22−22
χ4022-22-2-2-222-2200022-2-2-2000-20−2i−2i2i2i20000−2i2i00000000000000−i2i2−i2i2−i2i2−i2i200000000002−22−2
χ4122-22-2-2-22-22-200022-2-22000202i2i−2i−2i-20000−2i2i000000000000002−22−2−22−220000000000−i2i2i2−i2
χ4222-22-2-2-22-22-200022-2-22000202i2i−2i−2i-20000−2i2i00000000000000−22−222−22−20000000000i2−i2−i2i2
χ4322-22-2-2-22-22-200022-2-2200020−2i−2i2i2i-200002i−2i000000000000002−22−2−22−220000000000i2−i2−i2i2
χ4422-22-2-2-22-22-200022-2-2200020−2i−2i2i2i-200002i−2i00000000000000−22−222−22−20000000000−i2i2i2−i2
χ452-2-2-2-22220002-222-22-20-200022-22-20-20000000002-2i2−i2i2−i2i2−i2i2−i200000000000000i2−i2i2−i20000
χ462-2-2-2-22220002-222-22-20-200022-22-20-20000000002-2−i2i2−i2i2−i2i2−i2i200000000000000−i2i2−i2i20000
χ472-2-2-2-22220002-222-22-20-20002-22-220-2000000000-22i2−i2i2−i2i2−i2i2−i200000000000000−i2i2−i2i20000
χ482-2-2-2-22220002-222-22-20-20002-22-220-2000000000-22−i2i2−i2i2−i2i2−i2i200000000000000i2−i2i2−i20000
χ492-2-2-2-2222000-22-22-22-202000-22-22-202000000000-222−22−2−22−22000000000000002−2−220000
χ502-2-2-2-2222000-22-22-22-202000-22-22-202000000000-22−22−222−22−200000000000000−222−20000
χ512-2-2-2-2222000-22-22-22-202000-2-22-22020000000002-22−22−2−22−2200000000000000−222−20000
χ522-2-2-2-2222000-22-22-22-202000-2-22-22020000000002-2−22−222−22−2000000000000002−2−220000
χ53444-4-44-4-444-4-4-440000-44-440000000000000000000000000000000000000000000000000
χ54444-4-44-4-4-4-4444-400004-4-440000000000000000000000000000000000000000000000000
χ5544-44-4-4-444-44000-4-444-4000400000-4000000000000000000000000000000000000000000
χ5644-44-4-4-44-44-4000-4-4444000-4000004000000000000000000000000000000000000000000
χ5744-4-44-44-44-4-4000000040000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ5844-4-44-44-44-4-400000004000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ5944-4-44-44-4-4440000000-40000000000000000000000000000002-2-22-222-200000000000000
χ6044-4-44-44-4-4440000000-4000000000000000000000000000000-222-22-2-2200000000000000
χ614-44-44-4-440000004-4-440000004i−4i−4i4i0000000000000000000000000000000000000000000
χ624-44-44-4-440000004-4-44000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ634-44-44-4-44000000-444-400000000000004i−4i00000000000000000000000000000000000000
χ644-44-44-4-44000000-444-40000000000000−4i4i00000000000000000000000000000000000000
χ654-4-4444-4-40004-4-40000040000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000
χ664-4-4444-4-40004-4-4000004000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000
χ674-4-4444-4-4000-44400000-40000000000000000000002-2-22-222-20000000000000000000000
χ684-4-4444-4-4000-44400000-4000000000000000000000-222-22-2-220000000000000000000000
χ694-4-4-4-44440004-44-44-440-4000-400000400000000000000000000000000000000000000000
χ704-4-4-4-4444000-44-4-44-4404000400000-400000000000000000000000000000000000000000
χ718-888-8-88-8000000000000000000000000000000000000000000000000000000000000000

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