Finite Group Databasebeta

← Group #504392

Character table — Group #504392

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222444444448888888844444488881616161616161616161616161616161644444488881616161616161616222244444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-111-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1
χ911111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-11
χ1011111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111-1
χ1111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1111111-1-11111-1-1-1-1-1-1-1-111-1-1111-1
χ1211111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-11
χ1311111111-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-111111-1-1111111-1-1-1-1-1-111-1-111-1-11-1
χ1411111111-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111-11
χ1511111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-111111-1-111-1-1-1-11111-1-111-1-1-1-111-11
χ1611111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-11-1
χ172222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-20000000000000000220000-2-2-2-200000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-20000000000000000-2-20000222200000000000000000000
χ19222222222222-2-2-2-20000000022-2-22200002222−2−2−2−22222−2−2−2−2-2-20000000022−2−222−2−2000000000000
χ20222222222222-2-2-2-20000000022-2-2220000−2−2−2−22222−2−2−2−22222-2-200000000−2−222−2−222000000000000
χ21222222222222-2-2-2-200000000-2-2-2-2-2-200002222−2−2−2−22222−2−2−2−22200000000−2−222−2−222000000000000
χ22222222222222-2-2-2-200000000-2-2-2-2-2-20000−2−2−2−22222−2−2−2−22222220000000022−2−222−2−2000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000002-20000-2-22200000000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000-22000022-2-200000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-200002222−2−2−2−2−2−2−2−22222-2200000000−2−22222−2−2000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-20000−2−2−2−222222222−2−2−2−2-220000000022−2−2−2−222000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-2222200002222−2−2−2−2−2−2−2−222222-20000000022−2−2−2−222000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-222220000−2−2−2−222222222−2−2−2−22-200000000−2−22222−2−2000000000000
χ29222-2-2-2-222i2i−2i−2i-222-222-2-2-2-222002i−2i002i2i−2i−2i0000000000000000000000000000000000002-22i−2i000000
χ30222-2-2-2-222i2i−2i−2i-222-222-2-2-2-222002i−2i002i2i−2i−2i000000000000000000000000000000000000-22−2i2i000000
χ31222-2-2-2-222i2i−2i−2i-222-2-2-22222-2-2002i−2i00−2i−2i2i2i0000000000000000002i2i−2i−2i0000000000002-20000000000
χ32222-2-2-2-222i2i−2i−2i-222-2-2-22222-2-2002i−2i00−2i−2i2i2i000000000000000000−2i−2i2i2i000000000000-220000000000
χ33222-2-2-2-22−2i−2i2i2i-222-222-2-2-2-22200−2i2i00−2i−2i2i2i0000000000000000000000000000000000002-2−2i2i000000
χ34222-2-2-2-22−2i−2i2i2i-222-222-2-2-2-22200−2i2i00−2i−2i2i2i000000000000000000000000000000000000-222i−2i000000
χ35222-2-2-2-22−2i−2i2i2i-222-2-2-22222-2-200−2i2i002i2i−2i−2i0000000000000000002i2i−2i−2i000000000000-220000000000
χ36222-2-2-2-22−2i−2i2i2i-222-2-2-22222-2-200−2i2i002i2i−2i−2i000000000000000000−2i−2i2i2i0000000000002-20000000000
χ3722-22-22-2-22-22-200002−222−2−22−22-2002-22−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ50000002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3822-22-22-2-22-22-200002−222−2−22−22-2002-22−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ50000002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ3922-22-22-2-22-22-200002−222−2−22−2-2200-222−22−2ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4022-22-22-2-22-22-200002−222−2−22−2-2200-222−22−2−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4122-22-22-2-22-22-20000−22−2−222−222-2002-2−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ4222-22-22-2-22-22-20000−22−2−222−222-2002-2−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ4322-22-22-2-22-22-20000−22−2−222−22-2200-22−22−22ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ70000002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ4422-22-22-2-22-22-20000−22−2−222−22-2200-22−22−22−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ70000002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ4522-22-22-2-2-22-2200002−222−2−22−22-200-22−22−22ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ50000002−2−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4622-22-22-2-2-22-2200002−222−2−22−22-200-22−22−22−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ50000002−2−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4722-22-22-2-2-22-2200002−222−2−22−2-22002-2−22−22ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5000000−222−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ4822-22-22-2-2-22-2200002−222−2−22−2-22002-2−22−22−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5000000−222−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ4922-22-22-2-2-22-220000−22−2−222−222-200-222−22−2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7000000−222−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ5022-22-22-2-2-22-220000−22−2−222−222-200-222−22−2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7000000−222−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ5122-22-22-2-2-22-220000−22−2−222−22-22002-22−22−2ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ7−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ70000002−2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ5222-22-22-2-2-22-220000−22−2−222−22-22002-22−22−2−ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ3+ζ5ζ+ζ7ζ+ζ7−ζ−ζ7−ζ−ζ7ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ3−ζ5−ζ−ζ7−ζ−ζ7ζ+ζ7ζ+ζ70000002−2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ532-2-222-2-22000022-2-2222-22-2-2-200000000002-22-22-22-200000000002i−2i2i−2i0000000000000000002i−2i0000
χ542-2-222-2-22000022-2-2222-22-2-2-200000000002-22-22-22-20000000000−2i2i−2i2i000000000000000000−2i2i0000
χ552-2-222-2-22000022-2-2222-22-2-2-20000000000-22-22-22-2200000000002i−2i2i−2i000000000000000000−2i2i0000
χ562-2-222-2-22000022-2-2222-22-2-2-20000000000-22-22-22-220000000000−2i2i−2i2i0000000000000000002i−2i0000
χ572-2-2-2-22220000-22-22-2-22-22-2220000000000000000002-22-22-22-2002-2-22000000000000000000002-200
χ582-2-2-2-22220000-22-22-2-22-22-2220000000000000000002-22-22-22-200-222-200000000000000000000-2200
χ592-2-2-2-22220000-22-22-2-22-22-222000000000000000000-22-22-22-22002-2-2200000000000000000000-2200
χ602-2-2-2-22220000-22-22-2-22-22-222000000000000000000-22-22-22-2200-222-2000000000000000000002-200
χ61444-4-4-4-444i4i−4i−4i4-4-440000000000−4i4i0000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44−4i−4i4i4i4-4-4400000000004i−4i0000000000000000000000000000000000000000000000000000
χ6344-4-44-44-44i−4i−4i4i000022−22−22−22222222−220000002i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ6444-4-44-44-44i−4i−4i4i0000−22222222−22−22−2222000000−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ6544-4-44-44-4−4i4i4i−4i000022−22−22−22222222−22000000−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ6644-4-44-44-4−4i4i4i−4i0000−22222222−22−22−22220000002i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ674-444-4-44-40000000022−2222−22−2222−222200000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ500000000000000000000000000000000000000
χ684-444-4-44-40000000022−2222−22−2222−22220000000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ500000000000000000000000000000000000000
χ694-444-4-44-400000000−2222−222222−2222−2200000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ700000000000000000000000000000000000000
χ704-444-4-44-400000000−2222−222222−2222−220000000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ700000000000000000000000000000000000000
χ714-44-444-4-40000000022−22−222222−22−22220000000000000000002ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7000000000000000000000000000000
χ724-44-444-4-40000000022−22−222222−22−2222000000000000000000−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ7000000000000000000000000000000
χ734-44-444-4-400000000−222222−22−222222−220000000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5−2ζ3−2ζ52ζ3+2ζ5000000000000000000000000000000
χ744-44-444-4-400000000−222222−22−222222−22000000000000000000−2ζ−2ζ72ζ+2ζ72ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ52ζ3+2ζ5−2ζ3−2ζ5000000000000000000000000000000
χ754-4-444-4-44000044-4-4-4-4-44-444400000000000000000000000000000000000000000000000000000000
χ764-4-444-4-440000-4-44400000000000000000022−2222−22−2222−222200000000000000000000000000000000000000
χ774-4-444-4-440000-4-444000000000000000000−2222−222222−2222−2200000000000000000000000000000000000000
χ784-4-4-4-444400004-44-40000000000000000000000000022−2222−22−2222−2222000000000000000000000000000000
χ794-4-4-4-444400004-44-400000000000000000000000000−2222−222222−2222−22000000000000000000000000000000
χ804-4-4-4-44440000-44-4444-44-44-4-400000000000000000000000000000000000000000000000000000000

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