Finite Group Databasebeta

← Group #124757

Character table — Group #124757

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222224444444444448888888822444444888888888888161616161616161616161616161616162244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111ii−i−iii−i−i
χ101111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1−i−iii−i−iii
χ111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111−i−iii−i−iii
χ121111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i
χ131111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-111-1-1ii−i−i−i−iii
χ141111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i
χ151111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-111-1-1−i−iiiii−i−i
χ161111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-111ii−i−i−i−iii
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222200000000000000000000000000000000
χ192222222222-2-2222222-2-222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ202222222222-2-2-2-2-2-222-2-22222222222-2-222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2122222222-2-2222222-2-22200000000-2-2-2-222-2-200000000000022−2−222−2−222−2−222−2−20000000000000000
χ2222222222-2-2222222-2-22200000000-2-2-2-222-2-2000000000000−2−222−2−222−2−222−2−2220000000000000000
χ2322222222-2-222-2-2-2-2-2-222000000002222-2-2-2-200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ2422222222-2-222-2-2-2-2-2-222000000002222-2-2-2-2000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2522222222-2-2-2-22222-2-2-2-20000000022-2-2-2-222000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2622222222-2-2-2-22222-2-2-2-20000000022-2-2-2-222000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2222222000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2222222000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ29222-2-2-2-22002i−2i22-2-2002i−2ii2i2−i2−i2i2i2−i2−i200002i−2i0022−2−222−2−2i2i2−i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000000000
χ30222-2-2-2-22002i−2i22-2-2002i−2ii2i2−i2−i2i2i2−i2−i200002i−2i0022−2−222−2−2i2i2−i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000000000
χ31222-2-2-2-22002i−2i22-2-2002i−2i−i2−i2i2i2−i2−i2i2i200002i−2i00−2−222−2−222−i2−i2i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000000000
χ32222-2-2-2-22002i−2i22-2-2002i−2i−i2−i2i2i2−i2−i2i2i200002i−2i00−2−222−2−222−i2−i2i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000000000
χ33222-2-2-2-22002i−2i-2-222002i−2ii2i2−i2−i2i2i2−i2−i20000−2i2i0022−2−2−2−222−i2−i2i2i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ30000000000000000
χ34222-2-2-2-22002i−2i-2-222002i−2ii2i2−i2−i2i2i2−i2−i20000−2i2i0022−2−2−2−222−i2−i2i2i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ30000000000000000
χ35222-2-2-2-22002i−2i-2-222002i−2i−i2−i2i2i2−i2−i2i2i20000−2i2i00−2−22222−2−2i2i2−i2−i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ70000000000000000
χ36222-2-2-2-22002i−2i-2-222002i−2i−i2−i2i2i2−i2−i2i2i20000−2i2i00−2−22222−2−2i2i2−i2−i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ70000000000000000
χ37222-2-2-2-2200−2i2i22-2-200−2i2ii2i2−i2−i2i2i2−i2−i20000−2i2i00−2−222−2−222i2i2−i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000000000
χ38222-2-2-2-2200−2i2i22-2-200−2i2ii2i2−i2−i2i2i2−i2−i20000−2i2i00−2−222−2−222i2i2−i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000000000
χ39222-2-2-2-2200−2i2i22-2-200−2i2i−i2−i2i2i2−i2−i2i2i20000−2i2i0022−2−222−2−2−i2−i2i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000000000
χ40222-2-2-2-2200−2i2i22-2-200−2i2i−i2−i2i2i2−i2−i2i2i20000−2i2i0022−2−222−2−2−i2−i2i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000000000
χ41222-2-2-2-2200−2i2i-2-22200−2i2ii2i2−i2−i2i2i2−i2−i200002i−2i00−2−22222−2−2−i2−i2i2i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ30000000000000000
χ42222-2-2-2-2200−2i2i-2-22200−2i2ii2i2−i2−i2i2i2−i2−i200002i−2i00−2−22222−2−2−i2−i2i2i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ30000000000000000
χ43222-2-2-2-2200−2i2i-2-22200−2i2i−i2−i2i2i2−i2−i2i2i200002i−2i0022−2−2−2−222i2i2−i2−i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ70000000000000000
χ44222-2-2-2-2200−2i2i-2-22200−2i2i−i2−i2i2i2−i2−i2i2i200002i−2i0022−2−2−2−222i2i2−i2−i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ70000000000000000
χ4522-22-22-2-22-22i−2i00002-2−2i2i2i−2i2i−2i2i−2i2i−2i0000002i−2i2-22-200000000000000000000000000002-22i−2i00000000
χ4622-22-22-2-22-22i−2i00002-2−2i2i2i−2i2i−2i2i−2i2i−2i0000002i−2i2-22-20000000000000000000000000000-22−2i2i00000000
χ4722-22-22-2-22-22i−2i00002-2−2i2i−2i2i−2i2i−2i2i−2i2i0000002i−2i-22-220000000000000000000000002-22i−2i000000000000
χ4822-22-22-2-22-22i−2i00002-2−2i2i−2i2i−2i2i−2i2i−2i2i0000002i−2i-22-22000000000000000000000000-22−2i2i000000000000
χ4922-22-22-2-22-2−2i2i00002-22i−2i2i−2i2i−2i2i−2i2i−2i000000−2i2i-22-220000000000000000000000002-2−2i2i000000000000
χ5022-22-22-2-22-2−2i2i00002-22i−2i2i−2i2i−2i2i−2i2i−2i000000−2i2i-22-22000000000000000000000000-222i−2i000000000000
χ5122-22-22-2-22-2−2i2i00002-22i−2i−2i2i−2i2i−2i2i−2i2i000000−2i2i2-22-200000000000000000000000000002-2−2i2i00000000
χ5222-22-22-2-22-2−2i2i00002-22i−2i−2i2i−2i2i−2i2i−2i2i000000−2i2i2-22-20000000000000000000000000000-222i−2i00000000
χ532-2-222-2-2222002-22-2-2-2002i−2i2i−2i−2i2i−2i2i002-20000000000002i−2i2i−2i0000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ542-2-222-2-2222002-22-2-2-2002i−2i2i−2i−2i2i−2i2i002-20000000000002i−2i2i−2i000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ552-2-222-2-2222002-22-2-2-200−2i2i−2i2i2i−2i2i−2i002-2000000000000−2i2i−2i2i0000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ562-2-222-2-2222002-22-2-2-200−2i2i−2i2i2i−2i2i−2i002-2000000000000−2i2i−2i2i000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ572-2-222-2-222200-22-22-2-2002i−2i2i−2i−2i2i−2i2i00-22000000000000−2i2i−2i2i0000000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i
χ582-2-222-2-222200-22-22-2-2002i−2i2i−2i−2i2i−2i2i00-22000000000000−2i2i−2i2i000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i
χ592-2-222-2-222200-22-22-2-200−2i2i−2i2i2i−2i2i−2i00-220000000000002i−2i2i−2i0000000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i
χ602-2-222-2-222200-22-22-2-200−2i2i−2i2i2i−2i2i−2i00-220000000000002i−2i2i−2i000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i
χ6144-44-44-4-4-444i−4i0000-44−4i4i00000000000000−4i4i00000000000000000000000000000000000000000000
χ6244-44-44-4-4-44−4i4i0000-444i−4i000000000000004i−4i00000000000000000000000000000000000000000000
χ6344-4-44-44-40044000000-4-422−22−222222−22−22220000000022−22−22220000000000000000000000000000000000000000
χ6444-4-44-44-40044000000-4-4−222222−22−222222−2200000000−222222−220000000000000000000000000000000000000000
χ6544-4-44-44-400-4-40000004422−22−222222−22−222200000000−222222−220000000000000000000000000000000000000000
χ6644-4-44-44-400-4-400000044−222222−22−222222−220000000022−22−22220000000000000000000000000000000000000000
χ674-444-4-44-44-4000000-44004444-4-4-4-40000000000000000000000000000000000000000000000000000
χ684-444-4-44-44-4000000-4400-4-4-4-444440000000000000000000000000000000000000000000000000000
χ694-444-4-44-4-440000004-400000000000000000000004i−4i4i−4i000000000000000000000000000000000000
χ704-444-4-44-4-440000004-40000000000000000000000−4i4i−4i4i000000000000000000000000000000000000
χ714-44-444-4-40000000000002i22i2−2i2−2i2−2i2−2i22i22i24-400000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ724-44-444-4-40000000000002i22i2−2i2−2i2−2i2−2i22i22i2-440000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ734-44-444-4-4000000000000−2i2−2i22i22i22i22i2−2i2−2i24-40000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ744-44-444-4-4000000000000−2i2−2i22i22i22i22i2−2i2−2i2-4400000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ754-4-444-4-44-4-4004-44-444000000000000-44000000000000000000000000000000000000000000000000
χ764-4-444-4-44-4-400-44-44440000000000004-4000000000000000000000000000000000000000000000000
χ774-4-4-4-444400004-4-44000022−22−2222−222222−22000000000000000022−22−222200000000000000000000000000000000
χ784-4-4-4-444400004-4-440000−222222−2222−22−22220000000000000000−222222−2200000000000000000000000000000000
χ794-4-4-4-44440000-444-4000022−22−2222−222222−220000000000000000−222222−2200000000000000000000000000000000
χ804-4-4-4-44440000-444-40000−222222−2222−22−2222000000000000000022−22−222200000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.