Finite Group Databasebeta

← Group #97598

Character table — Group #97598

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444422224444444444448888888888888888224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111ii−i−iii−i−i
χ101111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111−i−iii−i−iii
χ111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i−i−iii
χ121111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iiiii−i−i
χ131111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii−i−iii
χ141111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−iii−i−i
χ151111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiiii−i−i
χ161111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−i−iii
χ17222222222222-2-2-2-222222222-2-2-2-2-2-2000022-2-2220000-2-20000000000000000000000000000
χ18222222222222-2-2-2-222222222-2-2-2-2-2-20000-2-222-2-20000220000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222000022-2-2-2-20000220000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000-2-222220000-2-20000000000000000000000000000
χ2122222222-2-2-2-2222222-2-222-2-2-2-222-2-222-2-200000022-2-2000000000000000000000000000000
χ2222222222-2-2-2-2222222-2-222-2-2-2-222-2-2-2-222000000-2-222000000000000000000000000000000
χ2322222222-2-2-2-22222-2-222-2-222-2-2-2-22222-2-2000000-2-222000000000000000000000000000000
χ2422222222-2-2-2-22222-2-222-2-222-2-2-2-222-2-22200000022-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-2-222-2-222000000000000000000000000000000002-22-200000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-2-222-2-22200000000000000000000000000000000-22-2200000000
χ2722222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2000000000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-200000000000000000000000000000000-222-200000000
χ29222-2-22-2-222-2-200002i−2i2i−2i2i−2i2i−2i00000000002i−2i002-20000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ30222-2-22-2-222-2-200002i−2i2i−2i2i−2i2i−2i00000000002i−2i002-2000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ31222-2-22-2-222-2-200002i−2i2i−2i2i−2i2i−2i0000000000−2i2i00-220000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ32222-2-22-2-222-2-200002i−2i2i−2i2i−2i2i−2i0000000000−2i2i00-22000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ33222-2-22-2-222-2-20000−2i2i−2i2i−2i2i−2i2i00000000002i−2i00-220000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ34222-2-22-2-222-2-20000−2i2i−2i2i−2i2i−2i2i00000000002i−2i00-22000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ35222-2-22-2-222-2-20000−2i2i−2i2i−2i2i−2i2i0000000000−2i2i002-20000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ36222-2-22-2-222-2-20000−2i2i−2i2i−2i2i−2i2i0000000000−2i2i002-2000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ372-2222-2-2-22-22-222-2-22i−2i2i−2i−2i2i−2i2i2-22i−2i2i−2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000
χ382-2222-2-2-22-22-222-2-22i−2i2i−2i−2i2i−2i2i2-22i−2i2i−2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000
χ392-2222-2-2-22-22-222-2-2−2i2i−2i2i2i−2i2i−2i2-2−2i2i−2i2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000
χ402-2222-2-2-22-22-222-2-2−2i2i−2i2i2i−2i2i−2i2-2−2i2i−2i2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000
χ412-2222-2-2-22-22-2-2-2222i−2i2i−2i−2i2i−2i2i-22−2i2i−2i2i00000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ422-2222-2-2-22-22-2-2-2222i−2i2i−2i−2i2i−2i2i-22−2i2i−2i2i0000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ432-2222-2-2-22-22-2-2-222−2i2i−2i2i2i−2i2i−2i-222i−2i2i−2i00000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ442-2222-2-2-22-22-2-2-222−2i2i−2i2i2i−2i2i−2i-222i−2i2i−2i0000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ452-2222-2-2-2-22-2222-2-22i−2i−2i2i−2i2i2i−2i-222i−2i−2i2i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ462-2222-2-2-2-22-2222-2-22i−2i−2i2i−2i2i2i−2i-222i−2i−2i2i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ472-2222-2-2-2-22-2222-2-2−2i2i2i−2i2i−2i−2i2i-22−2i2i2i−2i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ482-2222-2-2-2-22-2222-2-2−2i2i2i−2i2i−2i−2i2i-22−2i2i2i−2i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ492-2222-2-2-2-22-22-2-2222i−2i−2i2i−2i2i2i−2i2-2−2i2i2i−2i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ502-2222-2-2-2-22-22-2-2222i−2i−2i2i−2i2i2i−2i2-2−2i2i2i−2i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ512-2222-2-2-2-22-22-2-222−2i2i2i−2i2i−2i−2i2i2-22i−2i−2i2i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ522-2222-2-2-2-22-22-2-222−2i2i2i−2i2i−2i−2i2i2-22i−2i−2i2i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ532-22-2-2-2222-2-2200002222-2-2-2-20000000000002-20000002-2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ542-22-2-2-2222-2-2200002222-2-2-2-20000000000002-20000002-2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ552-22-2-2-2222-2-2200002222-2-2-2-2000000000000-22000000-22i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ562-22-2-2-2222-2-2200002222-2-2-2-2000000000000-22000000-22−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ572-22-2-2-2222-2-220000-2-2-2-222220000000000002-2000000-222−2−22−222−22−2−22−222−2000000000000
χ582-22-2-2-2222-2-220000-2-2-2-222220000000000002-2000000-22−222−22−2−22−222−22−2−22000000000000
χ592-22-2-2-2222-2-220000-2-2-2-22222000000000000-220000002-22−2−22−222−2−222−22−2−22000000000000
χ602-22-2-2-2222-2-220000-2-2-2-22222000000000000-220000002-2−222−22−2−222−2−22−222−2000000000000
χ61444-4-44-4-4-4-44400004i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-4-4440000−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ6344-44-4-44-400004-44-4000000000000000000000000004i−4i000000000000000000000000000000
χ6444-44-4-44-400004-44-400000000000000000000000000−4i4i000000000000000000000000000000
χ6544-44-4-44-40000-44-440000000000000000000000004i−4i00000000000000000000000000000000
χ6644-44-4-44-40000-44-44000000000000000000000000−4i4i00000000000000000000000000000000
χ674-44-4-4-444-444-4000044-4-4-4-44400000000000000000000000000000000000000000000000000
χ684-44-4-4-444-444-40000-4-44444-4-400000000000000000000000000000000000000000000000000
χ694-4-44-44-4400004-4-44000000000000004-4000000000000000000000000000000000000000000
χ704-4-44-44-4400004-4-4400000000000000-44000000000000000000000000000000000000000000
χ714-4-44-44-440000-444-400000000000000004-40000000000000000000000000000000000000000
χ724-4-44-44-440000-444-40000000000000000-440000000000000000000000000000000000000000
χ7388-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8-8888-8000000000000000000000000000000000000000000000000000000000000000000

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