Finite Group Databasebeta

← Group #97614

Character table — Group #97614

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888444488888888
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
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
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
χ9111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111ii−i−iii−i−i
χ10111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111−i−iii−i−iii
χ11111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii−i−iii
χ12111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−iii−i−i
χ13111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i−i−iii
χ14111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−iiiii−i−i
χ15111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111−i−iiiii−i−i
χ16111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111ii−i−i−i−iii
χ172222222222222222-2-2-2-22222-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000
χ182222222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-222000000000000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222000000000000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000000000000000
χ2122222222-2-2-2-222-2-2222222-2-2-2-222-2-20000000022-2-222-2-20000000000000000000000000000
χ2222222222-2-2-2-222-2-2222222-2-2-2-222-2-200000000-2-222-2-2220000000000000000000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-222-2-222-2-222000000000000000000000000000000002-22-200000000
χ2422222222-2-2-2-222-2-2-2-2-2-222-2-222-2-22200000000000000000000000000000000-22-2200000000
χ2522222222-2-2-2-2-2-2222222-2-222-2-2-2-2220000000022-2-2-2-2220000000000000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-222-2-2-2-22200000000-2-22222-2-20000000000000000000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-2000000000000000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-222-2-2-2-2-2-2222222-2-200000000000000000000000000000000-222-200000000
χ29222-22-2-2-222-2-222220000-2-2-2-20000002-2002-2000000000022−2−222−2−222−2−222−2−2000000000000
χ30222-22-2-2-222-2-222220000-2-2-2-20000002-2002-20000000000−2−222−2−222−2−222−2−222000000000000
χ31222-22-2-2-222-2-222220000-2-2-2-2000000-2200-22000000000022−2−222−2−2−2−222−2−222000000000000
χ32222-22-2-2-222-2-222220000-2-2-2-2000000-2200-220000000000−2−222−2−22222−2−222−2−2000000000000
χ33222-22-2-2-222-2-2-2-2-2-2000022220000002-200-220000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ34222-22-2-2-222-2-2-2-2-2-2000022220000002-200-220000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ35222-22-2-2-222-2-2-2-2-2-200002222000000-22002-20000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ36222-22-2-2-222-2-2-2-2-2-200002222000000-22002-20000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ372-222-2-2-222-22-22i−2i2i−2i22-2-22i−2i2i−2i2-22i−2i2i−2i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ382-222-2-2-222-22-22i−2i2i−2i22-2-22i−2i2i−2i2-22i−2i2i−2i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ392-222-2-2-222-22-22i−2i2i−2i-2-2222i−2i2i−2i-22−2i2i−2i2i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ402-222-2-2-222-22-22i−2i2i−2i-2-2222i−2i2i−2i-22−2i2i−2i2i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ412-222-2-2-222-22-2−2i2i−2i2i22-2-2−2i2i−2i2i2-2−2i2i−2i2i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ422-222-2-2-222-22-2−2i2i−2i2i22-2-2−2i2i−2i2i2-2−2i2i−2i2i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ432-222-2-2-222-22-2−2i2i−2i2i-2-222−2i2i−2i2i-222i−2i2i−2i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ442-222-2-2-222-22-2−2i2i−2i2i-2-222−2i2i−2i2i-222i−2i2i−2i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ452-222-2-2-22-22-222i−2i−2i2i22-2-22i−2i−2i2i-222i−2i−2i2i0000000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000
χ462-222-2-2-22-22-222i−2i−2i2i22-2-22i−2i−2i2i-222i−2i−2i2i000000000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000
χ472-222-2-2-22-22-222i−2i−2i2i-2-2222i−2i−2i2i2-2−2i2i2i−2i00000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000000000000000000
χ482-222-2-2-22-22-222i−2i−2i2i-2-2222i−2i−2i2i2-2−2i2i2i−2i0000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000000000000000000
χ492-222-2-2-22-22-22−2i2i2i−2i22-2-2−2i2i2i−2i-22−2i2i2i−2i0000000000000000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000
χ502-222-2-2-22-22-22−2i2i2i−2i22-2-2−2i2i2i−2i-22−2i2i2i−2i000000000000000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000
χ512-222-2-2-22-22-22−2i2i2i−2i-2-222−2i2i2i−2i2-22i−2i−2i2i00000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000000000000000000
χ522-222-2-2-22-22-22−2i2i2i−2i-2-222−2i2i2i−2i2-22i−2i−2i2i0000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000000000000000000
χ532-22-2-222-2-222-22i−2i−2i2i0000−2i2i2i−2i000000002i−2i002-2000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ542-22-2-222-2-222-22i−2i−2i2i0000−2i2i2i−2i000000002i−2i002-200000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ552-22-2-222-2-222-22i−2i−2i2i0000−2i2i2i−2i00000000−2i2i00-22000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000000000
χ562-22-2-222-2-222-22i−2i−2i2i0000−2i2i2i−2i00000000−2i2i00-2200000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i000000000000
χ572-22-2-222-2-222-2−2i2i2i−2i00002i−2i−2i2i000000002i−2i00-22000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ582-22-2-222-2-222-2−2i2i2i−2i00002i−2i−2i2i000000002i−2i00-2200000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ592-22-2-222-2-222-2−2i2i2i−2i00002i−2i−2i2i00000000−2i2i002-2000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i000000000000
χ602-22-2-222-2-222-2−2i2i2i−2i00002i−2i−2i2i00000000−2i2i002-200000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000000000
χ61444-44-4-4-4-4-44444-4-40000-4-44400000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4-444-4-444000044-4-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-44000000004-44-4000000000000000000004i−4i00000000000000000000000000000000
χ6444-4-4-44-44000000004-44-400000000000000000000−4i4i00000000000000000000000000000000
χ6544-4-4-44-4400000000-44-440000000000000000004i−4i0000000000000000000000000000000000
χ6644-4-4-44-4400000000-44-44000000000000000000−4i4i0000000000000000000000000000000000
χ674-44-4-444-44-4-444i−4i4i−4i0000−4i4i−4i4i00000000000000000000000000000000000000000000000000
χ684-44-4-444-44-4-44−4i4i−4i4i00004i−4i4i−4i00000000000000000000000000000000000000000000000000
χ694-4-4-44-444000000004-4-4400000000000000000000004-4000000000000000000000000000000
χ704-4-4-44-444000000004-4-440000000000000000000000-44000000000000000000000000000000
χ714-4-4-44-44400000000-444-40000000000000000000000004-40000000000000000000000000000
χ724-4-4-44-44400000000-444-4000000000000000000000000-440000000000000000000000000000
χ7388-88-8-88-8000000000000000000000000000000000000000000000000000000000000000000
χ748-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000000

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