Finite Group Databasebeta

← Group #507774

Character table — Group #507774

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222224444444444448888888822444444888888888888161616161616161616161616161616162244444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ511111111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ611111111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ711111111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-11111-1-1
χ101111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-111
χ111111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111
χ121111111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ141111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ151111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-1
χ161111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ192222222222-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2122222222-2-222222222-2-20000000022-2-2-2-2-2-200000000000022−2−222−2−222−2−222−2−20000000000000000
χ2222222222-2-222222222-2-20000000022-2-2-2-2-2-2000000000000−2−222−2−222−2−222−2−2220000000000000000
χ2322222222-2-22222-2-2-2-2-2-200000000-2-2-2-2222200000000000022−2−222−2−2−2−222−2−2220000000000000000
χ2422222222-2-22222-2-2-2-2-2-200000000-2-2-2-22222000000000000−2−222−2−22222−2−222−2−20000000000000000
χ2522222222-2-2-2-2-2-22222-2-200000000-2-222-2-22200000000000022−2−2−2−22222−2−2−2−2220000000000000000
χ2622222222-2-2-2-2-2-22222-2-200000000-2-222-2-222000000000000−2−22222−2−2−2−22222−2−20000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-200000000000022−2−2−2−222−2−22222−2−20000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200000000222222-2-2000000000000−2−22222−2−222−2−2−2−2220000000000000000
χ29222-2-22-2-20022-2-222-2-2002222−2−2−2−22-200000022−2−222−2−222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ30222-2-22-2-20022-2-222-2-2002222−2−2−2−22-200000022−2−222−2−222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ31222-2-22-2-20022-2-222-2-200−2−2−2−222222-2000000−2−222−2−222−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ32222-2-22-2-20022-2-222-2-200−2−2−2−222222-2000000−2−222−2−222−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ33222-2-22-2-20022-2-2-2-222002222−2−2−2−2-2200000022−2−2−2−222−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ34222-2-22-2-20022-2-2-2-222002222−2−2−2−2-2200000022−2−2−2−222−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ35222-2-22-2-20022-2-2-2-22200−2−2−2−22222-22000000−2−22222−2−222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ36222-2-22-2-20022-2-2-2-22200−2−2−2−22222-22000000−2−22222−2−222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ37222-2-22-2-200-2-22222-2-2002222−2−2−2−2-22000000−2−22222−2−2−2−222ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ38222-2-22-2-200-2-22222-2-2002222−2−2−2−2-22000000−2−22222−2−2−2−222−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ39222-2-22-2-200-2-22222-2-200−2−2−2−22222-2200000022−2−2−2−22222−2−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ40222-2-22-2-200-2-22222-2-200−2−2−2−22222-2200000022−2−2−2−22222−2−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ41222-2-22-2-200-2-222-2-222002222−2−2−2−22-2000000−2−222−2−22222−2−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000000000
χ42222-2-22-2-200-2-222-2-222002222−2−2−2−22-2000000−2−222−2−22222−2−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000000000
χ43222-2-22-2-200-2-222-2-22200−2−2−2−222222-200000022−2−222−2−2−2−222ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000000000
χ44222-2-22-2-200-2-222-2-22200−2−2−2−222222-200000022−2−222−2−2−2−222−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000000000
χ4522-22-2-22-22-200002i−2i2i−2i2-222-2-222-2-200002i−2i0000002i−2i2i−2i00000000000000000000000000002-200002i−2i
χ4622-22-2-22-22-200002i−2i2i−2i2-222-2-222-2-200002i−2i0000002i−2i2i−2i0000000000000000000000000000-220000−2i2i
χ4722-22-2-22-22-200002i−2i2i−2i2-2-2-222-2-22200002i−2i000000−2i2i−2i2i000000000000000000000000002i−2i00002-200
χ4822-22-2-22-22-200002i−2i2i−2i2-2-2-222-2-22200002i−2i000000−2i2i−2i2i00000000000000000000000000−2i2i0000-2200
χ4922-22-2-22-22-20000−2i2i−2i2i2-222-2-222-2-20000−2i2i000000−2i2i−2i2i00000000000000000000000000002-20000−2i2i
χ5022-22-2-22-22-20000−2i2i−2i2i2-222-2-222-2-20000−2i2i000000−2i2i−2i2i0000000000000000000000000000-2200002i−2i
χ5122-22-2-22-22-20000−2i2i−2i2i2-2-2-222-2-2220000−2i2i0000002i−2i2i−2i000000000000000000000000002i−2i0000-2200
χ5222-22-2-22-22-20000−2i2i−2i2i2-2-2-222-2-2220000−2i2i0000002i−2i2i−2i00000000000000000000000000−2i2i00002-200
χ532-22-22-22-2-222i−2i2i−2i00002-22-22-22-22-2002i−2i00002i−2i2i−2i0000000000000000000000002-22i−2i000000000000
χ542-22-22-22-2-222i−2i2i−2i00002-22-22-22-22-2002i−2i00002i−2i2i−2i000000000000000000000000-22−2i2i000000000000
χ552-22-22-22-2-222i−2i2i−2i00002-2-22-22-22-22002i−2i0000−2i2i−2i2i00000000000000000000000000002-200002i−2i0000
χ562-22-22-22-2-222i−2i2i−2i00002-2-22-22-22-22002i−2i0000−2i2i−2i2i0000000000000000000000000000-220000−2i2i0000
χ572-22-22-22-2-22−2i2i−2i2i00002-22-22-22-22-200−2i2i0000−2i2i−2i2i0000000000000000000000002-2−2i2i000000000000
χ582-22-22-22-2-22−2i2i−2i2i00002-22-22-22-22-200−2i2i0000−2i2i−2i2i000000000000000000000000-222i−2i000000000000
χ592-22-22-22-2-22−2i2i−2i2i00002-2-22-22-22-2200−2i2i00002i−2i2i−2i00000000000000000000000000002-20000−2i2i0000
χ602-22-22-22-2-22−2i2i−2i2i00002-2-22-22-22-2200−2i2i00002i−2i2i−2i0000000000000000000000000000-2200002i−2i0000
χ6144-44-4-44-4-4400004i−4i4i−4i-44000000000000−4i4i0000000000000000000000000000000000000000000000
χ6244-44-4-44-4-440000−4i4i−4i4i-440000000000004i−4i0000000000000000000000000000000000000000000000
χ6344-4-44-4-440000004i−4i−4i4i002222−22−22−22−2222220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ6444-4-44-4-440000004i−4i−4i4i00−22−2222222222−22−22000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ6544-4-44-4-44000000−4i4i4i−4i002222−22−22−22−222222000000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ6644-4-44-4-44000000−4i4i4i−4i00−22−2222222222−22−220000000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ674-444-4-4-44004i−4i−4i4i00000022−2222−22−2222−2222000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ684-444-4-4-44004i−4i−4i4i000000−2222−222222−2222−2200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ694-444-4-4-4400−4i4i4i−4i00000022−2222−22−2222−222200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ704-444-4-4-4400−4i4i4i−4i000000−2222−222222−2222−22000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ714-44-44-44-44-44i−4i4i−4i0000-440000000000−4i4i000000000000000000000000000000000000000000000000
χ724-44-44-44-44-4−4i4i−4i4i0000-4400000000004i−4i000000000000000000000000000000000000000000000000
χ734-4-4444-4-400000000000022−22−2222−222222−220000004i−4i000000002i2−2i22i2−2i200000000000000000000000000000000
χ744-4-4444-4-400000000000022−22−2222−222222−22000000−4i4i00000000−2i22i2−2i22i200000000000000000000000000000000
χ754-4-4444-4-4000000000000−222222−2222−22−22220000004i−4i00000000−2i22i2−2i22i200000000000000000000000000000000
χ764-4-4444-4-4000000000000−222222−2222−22−2222000000−4i4i000000002i2−2i22i2−2i200000000000000000000000000000000
χ774-4-4-4-44444400000000-4-40000000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ784-4-4-4-44444400000000-4-4000000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ794-4-4-4-4444-4-400000000444-4-444-4-440000000000000000000000000000000000000000000000000000
χ804-4-4-4-4444-4-40000000044-444-4-444-40000000000000000000000000000000000000000000000000000

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