Finite Group Databasebeta

← Group #99993

Character table — Group #99993

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222444444444444444444444422444444888888888888888888888888224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111
χ91111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1ii−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1
χ101111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1ii−i−i−i−i−i−iiiiiii−i−iiiii−i−i−i−i-1-111−i−iii-1-111
χ111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1−i−iiiiiii−i−i−i−i−i−iii−i−i−i−iiiii-1-111ii−i−i-1-111
χ121111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-1−i−iii−i−i−i−iiiii−i−iii−i−i−i−iiiii11-1-1−i−iii11-1-1
χ131111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-11111ii−i−iiiii−i−i−i−iii−i−i−i−i−i−iiiii-1-111−i−iii11-1-1
χ141111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-11111ii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiii11-1-1ii−i−i-1-111
χ151111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-11111−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i11-1-1−i−iii-1-111
χ161111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-11111−i−iii−i−i−i−iiiii−i−iiiiiii−i−i−i−i-1-111ii−i−i11-1-1
χ1722222222222222-2-2222222-2-2-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ1822222222222222-2-2222222-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ192222222222-2-2-2-22222-2-2-2-222-2-222-2-222-2-2-2-222000000000000000000000000000000000000
χ202222222222-2-2-2-22222-2-2-2-222-2-222-2-2-2-22222-2-2000000000000000000000000000000000000
χ2122222222-2-222-2-222-2-222-2-222-2-2-2-22200000000222200000000-2-2-2-200000000000000000000
χ2222222222-2-222-2-222-2-222-2-222-2-2-2-22200000000-2-2-2-200000000222200000000000000000000
χ2322222222-2-222-2-2-2-2-2-222-2-2-2-22222-2-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ2422222222-2-222-2-2-2-2-2-222-2-2-2-22222-2-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2522222222-2-2-2-22222-2-2-2-2222222-2-2-2-200000000000000000000000022-2-2-2-222000000000000
χ2622222222-2-2-2-22222-2-2-2-2222222-2-2-2-2000000000000000000000000-2-22222-2-2000000000000
χ2722222222-2-2-2-222-2-2-2-2-2-222-2-2-2-22222000000002i2i−2i−2i00000000−2i−2i2i2i00000000000000000000
χ2822222222-2-2-2-222-2-2-2-2-2-222-2-2-2-2222200000000−2i−2i2i2i000000002i2i−2i−2i00000000000000000000
χ29222-22-2-2-22-22i−2i2i−2i002-22i−2i2i−2i00000000002i−2i002-21+i−1−i1−i−1+i000000001+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ30222-22-2-2-22-22i−2i2i−2i002-22i−2i2i−2i00000000002i−2i002-2−1−i1+i−1+i1−i00000000−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ31222-22-2-2-22-22i−2i2i−2i002-22i−2i2i−2i0000000000−2i2i00-221+i−1−i1−i−1+i000000001+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ32222-22-2-2-22-22i−2i2i−2i002-22i−2i2i−2i0000000000−2i2i00-22−1−i1+i−1+i1−i00000000−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ33222-22-2-2-22-2−2i2i−2i2i002-2−2i2i−2i2i00000000002i−2i00-221−i−1+i1+i−1−i000000001−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ34222-22-2-2-22-2−2i2i−2i2i002-2−2i2i−2i2i00000000002i−2i00-22−1+i1−i−1−i1+i00000000−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ35222-22-2-2-22-2−2i2i−2i2i002-2−2i2i−2i2i0000000000−2i2i002-21−i−1+i1+i−1−i000000001−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ36222-22-2-2-22-2−2i2i−2i2i002-2−2i2i−2i2i0000000000−2i2i002-2−1+i1−i−1−i1+i00000000−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ37222-22-2-2-2-222i−2i−2i2i00-222i−2i−2i2i000000002-2002i−2i001+i−1−i1−i−1+i00000000−1−i1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ38222-22-2-2-2-222i−2i−2i2i00-222i−2i−2i2i000000002-2002i−2i00−1−i1+i−1+i1−i000000001+i−1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ39222-22-2-2-2-222i−2i−2i2i00-222i−2i−2i2i00000000-2200−2i2i001+i−1−i1−i−1+i00000000−1−i1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ40222-22-2-2-2-222i−2i−2i2i00-222i−2i−2i2i00000000-2200−2i2i00−1−i1+i−1+i1−i000000001+i−1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ41222-22-2-2-2-22−2i2i2i−2i00-22−2i2i2i−2i000000002-200−2i2i001−i−1+i1+i−1−i00000000−1+i1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ42222-22-2-2-2-22−2i2i2i−2i00-22−2i2i2i−2i000000002-200−2i2i00−1+i1−i−1−i1+i000000001−i−1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ43222-22-2-2-2-22−2i2i2i−2i00-22−2i2i2i−2i00000000-22002i−2i001−i−1+i1+i−1−i00000000−1+i1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ44222-22-2-2-2-22−2i2i2i−2i00-22−2i2i2i−2i00000000-22002i−2i00−1+i1−i−1−i1+i000000001−i−1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ4522-22-22-2-22-22i−2i2i−2i2i−2i-22−2i2i−2i2i2i−2i2-22i−2i2-200000000000000000000000000000000000000002-22i−2i
χ4622-22-22-2-22-22i−2i2i−2i2i−2i-22−2i2i−2i2i2i−2i2-22i−2i2-20000000000000000000000000000000000000000-22−2i2i
χ4722-22-22-2-22-22i−2i2i−2i−2i2i-22−2i2i−2i2i−2i2i-22−2i2i-22000000000000000000000000000000002-22i−2i00000000
χ4822-22-22-2-22-22i−2i2i−2i−2i2i-22−2i2i−2i2i−2i2i-22−2i2i-2200000000000000000000000000000000-22−2i2i00000000
χ4922-22-22-2-22-2−2i2i−2i2i2i−2i-222i−2i2i−2i2i−2i-222i−2i-22000000000000000000000000000000002-2−2i2i00000000
χ5022-22-22-2-22-2−2i2i−2i2i2i−2i-222i−2i2i−2i2i−2i-222i−2i-2200000000000000000000000000000000-222i−2i00000000
χ5122-22-22-2-22-2−2i2i−2i2i−2i2i-222i−2i2i−2i−2i2i2-2−2i2i2-200000000000000000000000000000000000000002-2−2i2i
χ5222-22-22-2-22-2−2i2i−2i2i−2i2i-222i−2i2i−2i−2i2i2-2−2i2i2-20000000000000000000000000000000000000000-222i−2i
χ5322-22-22-2-2-222i−2i−2i2i2i−2i2-2−2i2i2i−2i2i−2i-22−2i2i2-20000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000000000000
χ5422-22-22-2-2-222i−2i−2i2i2i−2i2-2−2i2i2i−2i2i−2i-22−2i2i2-2000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000000000000
χ5522-22-22-2-2-222i−2i−2i2i−2i2i2-2−2i2i2i−2i−2i2i2-22i−2i-220000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ5622-22-22-2-2-222i−2i−2i2i−2i2i2-2−2i2i2i−2i−2i2i2-22i−2i-22000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ5722-22-22-2-2-22−2i2i2i−2i2i−2i2-22i−2i−2i2i2i−2i2-2−2i2i-220000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ5822-22-22-2-2-22−2i2i2i−2i2i−2i2-22i−2i−2i2i2i−2i2-2−2i2i-22000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ5922-22-22-2-2-22−2i2i2i−2i−2i2i2-22i−2i−2i2i−2i2i-222i−2i2-20000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000000000000
χ6022-22-22-2-2-22−2i2i2i−2i−2i2i2-22i−2i−2i2i−2i2i-222i−2i2-2000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000000000000
χ6144-4-4-4-44444444400-4-4-4-4-4-40000000000000000000000000000000000000000000000000000
χ6244-4-4-4-44444-4-4-4-400-4-444440000000000000000000000000000000000000000000000000000
χ6344-4-4-4-444-4-444-4-40044-4-4440000000000000000000000000000000000000000000000000000
χ6444-4-4-4-444-4-4-4-444004444-4-40000000000000000000000000000000000000000000000000000
χ654-444-4-44-40000004i−4i000000−4i4i0000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ664-444-4-44-40000004i−4i000000−4i4i000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ674-444-4-44-4000000−4i4i0000004i−4i0000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ684-444-4-44-4000000−4i4i0000004i−4i000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ694-4-444-4-4400000044000000-4-40000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ704-4-444-4-4400000044000000-4-4000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ714-4-444-4-44000000-4-4000000440000000000000000002-2-222-2-22000000000000000000000000
χ724-4-444-4-44000000-4-400000044000000000000000000-222-2-222-2000000000000000000000000
χ738-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.