Finite Group Databasebeta

← Group #98230

Character table — Group #98230

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422444444444888888888888888844444488888888
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
χ511111111111111111111111-1-1-1-1111-1-11-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111-1-1-1-1111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ711111111111111111111111-1-1-1-1111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ811111111111111111111111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii-11-1-111ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-1-111−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-111iiii−i−i−i−iiiii−i−i−i−i1-1-1-111−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111-1-111−i−i−i−iiiii−i−i−i−iiiii1-1-1-111ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-11111iiii−i−i−i−i−i−i−i−iiiii-1111-1-1−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1111-1-1ii−i−i−i−iii
χ17222222222222222-2-2-22-2-2-2-222222-22-2-2-2-2-2000022000000000000000000000000000000
χ18222222222222222-2-2-22-2-2-2-2-2-2-2-22-2222-2220000-2-2000000000000000000000000000000
χ19222222222222-2-2-2222-222-2-22222-22-2-2-2-2220000-2-2000000000000000000000000000000
χ20222222222222-2-2-2222-222-2-2-2-2-2-2-22-222-2-2-2000022000000000000000000000000000000
χ2122222222-2-2-2-222222222-2220000-2-2-200-2002222000000000000000000-2-2000000000000
χ2222222222-2-2-2-222222222-2220000-2-2-200-200-2-2-2-200000000000000000022000000000000
χ2322222222-2-2-2-2222-2-2-22-22-2-20000-22-2002000000000000000000000000002-22-200000000
χ2422222222-2-2-2-2222-2-2-22-22-2-20000-22-200200000000000000000000000000-22-2200000000
χ2522222222-2-2-2-2-2-2-2222-22-2-2-200002-22002000000000000000000000000002-2-2200000000
χ2622222222-2-2-2-2-2-2-2222-22-2-2-200002-2200200000000000000000000000000-222-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222000022200-20022-2-2000000000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222000022200-200-2-2220000000000000000002-2000000000000
χ29222-2-2-2-2222-2-200022-20-2-2002i2i−2i−2i0200002i−2i000000i2i2−i2−i2i2i2−i2−i2000000000000002−22−20000
χ30222-2-2-2-2222-2-200022-20-2-2002i2i−2i−2i0200002i−2i000000−i2−i2i2i2−i2−i2i2i200000000000000−22−220000
χ31222-2-2-2-2222-2-200022-20-2-200−2i−2i2i2i020000−2i2i000000i2i2−i2−i2i2i2−i2−i200000000000000−22−220000
χ32222-2-2-2-2222-2-200022-20-2-200−2i−2i2i2i020000−2i2i000000−i2−i2i2i2−i2−i2i2i2000000000000002−22−20000
χ33222-2-2-2-2222-2-2000-2-22022002i2i−2i−2i0-20000−2i2i00000022−2−2−2−22200000000000000−i2i2i2−i20000
χ34222-2-2-2-2222-2-2000-2-22022002i2i−2i−2i0-20000−2i2i000000−2−22222−2−200000000000000i2−i2−i2i20000
χ35222-2-2-2-2222-2-2000-2-2202200−2i−2i2i2i0-200002i−2i00000022−2−2−2−22200000000000000i2−i2−i2i20000
χ36222-2-2-2-2222-2-2000-2-2202200−2i−2i2i2i0-200002i−2i000000−2−22222−2−200000000000000−i2i2i2−i20000
χ3722-2-2-222-22-22-222-2000-200002i−2i2i−2i-2020000000002i−2i0000000022−2−222−2−20000000000i2−i2i2−i2
χ3822-2-2-222-22-22-222-2000-200002i−2i2i−2i-2020000000002i−2i00000000−2−222−2−2220000000000−i2i2−i2i2
χ3922-2-2-222-22-22-222-2000-20000−2i2i−2i2i-202000000000−2i2i0000000022−2−222−2−20000000000−i2i2−i2i2
χ4022-2-2-222-22-22-222-2000-20000−2i2i−2i2i-202000000000−2i2i00000000−2−222−2−2220000000000i2−i2i2−i2
χ4122-2-2-222-22-22-2-2-22000200002i−2i2i−2i20-2000000000−2i2i00000000i2i2−i2−i2−i2−i2i2i20000000000−222−2
χ4222-2-2-222-22-22-2-2-22000200002i−2i2i−2i20-2000000000−2i2i00000000−i2−i2i2i2i2i2−i2−i200000000002−2−22
χ4322-2-2-222-22-22-2-2-2200020000−2i2i−2i2i20-20000000002i−2i00000000i2i2−i2−i2−i2−i2i2i200000000002−2−22
χ4422-2-2-222-22-22-2-2-2200020000−2i2i−2i2i20-20000000002i−2i00000000−i2−i2i2i2i2i2−i2−i20000000000−222−2
χ452-2-2-22-22200002-222-22-2-202-20000000000002-22-200i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000
χ462-2-2-22-22200002-222-22-2-202-20000000000002-22-200−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000
χ472-2-2-22-22200002-222-22-2-202-2000000000000-22-2200i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000
χ482-2-2-22-22200002-222-22-2-202-2000000000000-22-2200−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000
χ492-2-2-22-2220000-22-2-22-22202-20000000000002-2-22002−22−2−22−222−22−2−22−2200000000000000
χ502-2-2-22-2220000-22-2-22-22202-20000000000002-2-2200−22−222−22−2−22−222−22−200000000000000
χ512-2-2-22-2220000-22-2-22-22202-2000000000000-222-2002−22−2−22−22−22−222−22−200000000000000
χ522-2-2-22-2220000-22-2-22-22202-2000000000000-222-200−22−222−22−22−22−2−22−2200000000000000
χ53444-4-4-4-44-4-44400044-40-440000000-4000000000000000000000000000000000000000000
χ54444-4-4-4-44-4-444000-4-4404-400000004000000000000000000000000000000000000000000
χ5544-444-4-4-44-4-44000000000004-4-4400000000000000000000000000000000000000000000
χ5644-444-4-4-44-4-4400000000000-444-400000000000000000000000000000000000000000000
χ5744-444-4-4-4-444-40000000000000000004-4000000000000000000000000000000000000000
χ5844-444-4-4-4-444-4000000000000000000-44000000000000000000000000000000000000000
χ5944-4-4-444-4-44-4444-4000-40000000040-400000000000000000000000000000000000000000
χ6044-4-4-444-4-44-44-4-44000400000000-40400000000000000000000000000000000000000000
χ614-444-4-44-400004-4-400040000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ624-444-4-44-400004-4-40004000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ634-444-4-44-40000-444000-40000000000000000000000000000002-2-22-222-200000000000000
χ644-444-4-44-40000-444000-4000000000000000000000000000000-222-22-2-2200000000000000
χ654-4-44-44-4400000004-4-4040000000000000000000002-2-222-2-220000000000000000000000
χ664-4-44-44-4400000004-4-404000000000000000000000-222-2-222-20000000000000000000000
χ674-4-44-44-440000000-4440-40000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ684-4-44-44-440000000-4440-4000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ694-4-4-44-44400004-44-44-4-440-44000000000000000000000000000000000000000000000000
χ704-4-4-44-4440000-44-44-444-40-44000000000000000000000000000000000000000000000000
χ718-88-888-8-8000000000000000000000000000000000000000000000000000000000000000

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