Finite Group Databasebeta

← Group #511521

Character table — Group #511521

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222444444444444444444444444444488888888888888161616161616161632323232
order12222222444488888888444444448888161616161616161616161616161616164488881616161616161616444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ51111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ61111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ71111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ81111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ911111111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-1111111-1-1-1-1-11
χ1011111111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-1-1-1-1-111111-1
χ1111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-1111111-1-11111-1-11-1
χ1211111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-11111-1-111-1-1-1-111-11
χ1311111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111111111-1-111-11-1-1
χ1411111111111111111111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-1-1-111-1-11-111
χ1511111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1111111-1-1-1-111-1-1-1-1-1-1-1111
χ1611111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1111111-1-1-1-1-1-11111111-1-1-1
χ17222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2000000000000000022-2-2-2-200000000000000000000
χ18222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-20000000000000000-2-2222200000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000002-2-2-22200000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222220000000000000000-2222-2-200000000000000000000
χ2122222222-2-2-2-200000000222222-2-200002222−2−2−2−22222−2−2−2−2-2-2000022−2−222−2−2000000000000
χ2222222222-2-2-2-200000000222222-2-20000−2−2−2−22222−2−2−2−22222-2-20000−2−222−2−222000000000000
χ2322222222-2-2-2-20000000022-2-2-2-2-2-200002222−2−2−2−22222−2−2−2−2220000−2−222−2−222000000000000
χ2422222222-2-2-2-20000000022-2-2-2-2-2-20000−2−2−2−22222−2−2−2−2222222000022−2−222−2−2000000000000
χ2522222222-2-2-2-200000000-2-222-2-22200002222−2−2−2−2−2−2−2−22222-22000022−2−2−2−222000000000000
χ2622222222-2-2-2-200000000-2-222-2-2220000−2−2−2−222222222−2−2−2−2-220000−2−22222−2−2000000000000
χ2722222222-2-2-2-200000000-2-2-2-2222200002222−2−2−2−2−2−2−2−222222-20000−2−22222−2−2000000000000
χ2822222222-2-2-2-200000000-2-2-2-222220000−2−2−2−222222222−2−2−2−22-2000022−2−2−2−222000000000000
χ29222-22-2-2-200002−222−2−22−22-22-22-20022−2−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5002−22−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ30222-22-2-2-200002−222−2−22−22-22-22-20022−2−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5002−22−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ31222-22-2-2-200002−222−2−22−22-2-22-220022−2−2ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ500−22−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ32222-22-2-2-200002−222−2−22−22-2-22-220022−2−2−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ500−22−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ33222-22-2-2-200002−222−2−22−2-222-2-2200−2−222ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5002−2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ34222-22-2-2-200002−222−2−22−2-222-2-2200−2−222−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5002−2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ35222-22-2-2-200002−222−2−22−2-22-222-200−2−222ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ500−222−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ36222-22-2-2-200002−222−2−22−2-22-222-200−2−222−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ500−222−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ37222-22-2-2-20000−22−2−222−222-22-22-200−2−222ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ700−22−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ38222-22-2-2-20000−22−2−222−222-22-22-200−2−222−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ700−22−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ39222-22-2-2-20000−22−2−222−222-2-22-2200−2−222ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7002−22−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ40222-22-2-2-20000−22−2−222−222-2-22-2200−2−222−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7002−22−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ41222-22-2-2-20000−22−2−222−22-222-2-220022−2−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ700−222−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ42222-22-2-2-20000−22−2−222−22-222-2-220022−2−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ700−222−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ43222-22-2-2-20000−22−2−222−22-22-222-20022−2−2ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7002−2−22−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ44222-22-2-2-20000−22−2−222−22-22-222-20022−2−2−ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ3−ζ5ζ−ζ7ζ−ζ7−ζ+ζ7−ζ+ζ7ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ3+ζ5−ζ+ζ7−ζ+ζ7ζ−ζ7ζ−ζ7002−2−22ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ4522-22-22-2-22-22-2222-22-2-2-20000000000002-22-22-22-200000000000000000000002-22-200000000
χ4622-22-22-2-22-22-2222-22-2-2-20000000000002-22-22-22-20000000000000000000000-22-2200000000
χ4722-22-22-2-22-22-2222-22-2-2-2000000000000-22-22-22-2200000000000000000000002-2-2200000000
χ4822-22-22-2-22-22-2222-22-2-2-2000000000000-22-22-22-220000000000000000000000-222-200000000
χ492-22-2-22-22-222-222-22-22-2-2000000000000000000002-22-22-22-20000000000000000002i−2i2i−2i0000
χ502-22-2-22-22-222-222-22-22-2-2000000000000000000002-22-22-22-2000000000000000000−2i2i−2i2i0000
χ512-22-2-22-22-222-222-22-22-2-200000000000000000000-22-22-22-220000000000000000002i−2i−2i2i0000
χ522-22-2-22-22-222-222-22-22-2-200000000000000000000-22-22-22-22000000000000000000−2i2i2i−2i0000
χ5344-44-44-4-44-44-4-4-4-44-4444000000000000000000000000000000000000000000000000000000
χ5444-44-44-4-4-44-440000000000000000000022−2222−22−2222−22220000000000000000000000000000000000
χ5544-44-44-4-4-44-4400000000000000000000−2222−222222−2222−220000000000000000000000000000000000
χ5644-4-4-4-444000022−2222−22−2222−22220000000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ50000000000000000000000000000000000
χ5744-4-4-4-444000022−2222−22−2222−2222000000000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ50000000000000000000000000000000000
χ5844-4-4-4-4440000−2222−222222−2222−220000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ70000000000000000000000000000000000
χ5944-4-4-4-4440000−2222−222222−2222−22000000000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ70000000000000000000000000000000000
χ604-444-4-44-4000022−22−222222−22−2222000000000000000000002ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ72ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ500000000000000000000000000
χ614-444-4-44-4000022−22−222222−22−222200000000000000000000−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ7−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ500000000000000000000000000
χ624-444-4-44-40000−222222−22−222222−22000000000000000000002ζ3−2ζ5−2ζ3+2ζ5−2ζ3+2ζ52ζ3−2ζ5−2ζ+2ζ72ζ−2ζ72ζ−2ζ7−2ζ+2ζ700000000000000000000000000
χ634-444-4-44-40000−222222−22−222222−2200000000000000000000−2ζ3+2ζ52ζ3−2ζ52ζ3−2ζ5−2ζ3+2ζ52ζ−2ζ7−2ζ+2ζ7−2ζ+2ζ72ζ−2ζ700000000000000000000000000
χ644-44-4-44-444-4-44000000000000000000000000000022−2222−22−2222−222200000000000000000000000000
χ654-44-4-44-444-4-440000000000000000000000000000−2222−222222−2222−2200000000000000000000000000
χ664-44-4-44-44-444-4-4-44-44-444000000000000000000000000000000000000000000000000000000
χ674-4-444-4-44000022−22−22−22222222−220000004i−4i2i2−2i22i2−2i2000000000000000000000000000000000000000000
χ684-4-444-4-44000022−22−22−22222222−22000000−4i4i−2i22i2−2i22i2000000000000000000000000000000000000000000
χ694-4-444-4-440000−22222222−22−22−22220000004i−4i−2i22i2−2i22i2000000000000000000000000000000000000000000
χ704-4-444-4-440000−22222222−22−22−2222000000−4i4i2i2−2i22i2−2i2000000000000000000000000000000000000000000
χ714-4-4-4444-444-4-400000000000000004i−4i−4i4i000000000000000000000000000000000000000000
χ724-4-4-4444-444-4-40000000000000000−4i4i4i−4i000000000000000000000000000000000000000000
χ734-4-4-4444-4-4-44444-4-4-4-444000000000000000000000000000000000000000000000000000000
χ744-4-4-4444-4-4-444-4-44444-4-4000000000000000000000000000000000000000000000000000000

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