Finite Group Databasebeta

← Group #97229

Character table — Group #97229

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111111144444444448888881616161616161616161616161616161616161616161616161616
order12222222222222444444444424444444444444444488888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-11-11-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-111-1-11-111-1-1-11-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-111-1-11-111-1-1-11-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-111-1-1-11-1-111-1-1-111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-111-1-1-11-1-111-1-1-11-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-11ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-11−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-111111-1ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-111111-1−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-11-111ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-11-111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-222-2-2-2-2000000-20200000000000000000
χ1822222222222222-2-2-2-2-2-2-2-22200000020-200000000000000000
χ192222222222-2-2-2-2222222-2-2-2-200000020-200000000000000000
χ202222222222-2-2-2-22222-2-2-2-222000000-20200000000000000000
χ2122222222-2-22-22-22-22-2002-20002002-2000-20000000000000000
χ2222222222-2-22-22-22-22-2002-2000-200-2200020000000000000000
χ2322222222-2-22-22-2-22-2200-2200202-2000-2000000000000000000
χ2422222222-2-22-22-2-22-2200-2200-20-220002000000000000000000
χ2522222222-2-2-22-222-22-200-220020-22000-2000000000000000000
χ2622222222-2-2-22-222-22-200-2200-202-20002000000000000000000
χ2722222222-2-2-22-22-22-22002-2000200-22000-20000000000000000
χ2822222222-2-2-22-22-22-22002-2000-2002-200020000000000000000
χ2944-444-4-4-400040-4000000000000000000002-22-2000000000000
χ3044-444-4-4-400040-400000000000000000000-22-22000000000000
χ3144-444-4-4-4000-404000000000000000000002i−2i−2i2i000000000000
χ3244-444-4-4-4000-40400000000000000000000−2i2i2i−2i000000000000
χ3344-4-4-44-44000000040-40000000000000000000000002i−2i2i−2i0000
χ3444-4-4-44-44000000040-4000000000000000000000000−2i2i−2i2i0000
χ3544-4-4-44-440000000-4040000000000000000000000002-2-220000
χ3644-4-4-44-440000000-404000000000000000000000000-222-20000
χ374-444-44-4-40040-400000000000000000000000002-22-200000000
χ384-444-44-4-40040-40000000000000000000000000-22-2200000000
χ394-444-44-4-400-40400000000000000000000000002i−2i−2i2i00000000
χ404-444-44-4-400-4040000000000000000000000000−2i2i2i−2i00000000
χ414-44-44-4-4400000040-4000000000000000000000000000002i−2i2i−2i
χ424-44-44-4-4400000040-400000000000000000000000000000−2i2i−2i2i
χ434-44-44-4-44000000-404000000000000000000000000000002-2-22
χ444-44-44-4-44000000-40400000000000000000000000000000-222-2
χ454-4-44-4-4444-40000000000004-400000000000000000000000000
χ464-4-44-4-4444-4000000000000-4400000000000000000000000000
χ474-4-44-4-444-44000000004-4000000000000000000000000000000
χ484-4-44-4-444-4400000000-44000000000000000000000000000000
χ49888-8-8-88-8000000000000000000000000000000000000000000
χ508-8-8-8888-8000000000000000000000000000000000000000000

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