Finite Group Databasebeta

← Group #508809

Character table — Group #508809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888444444444488888888888816161616161616161616161616161616444444442444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ911111111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ1111111111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ1211111111-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1
χ1311111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ19222222222222-2-2-2-200000000-2-22222-2-2-2-200000000000022−2−222−2−222−2−222−2−2000000000000
χ20222222222222-2-2-2-200000000-2-22222-2-2-2-2000000000000−2−222−2−222−2−222−2−222000000000000
χ21222222222222-2-2-2-200000000-2-2-2-2-2-2222200000000000022−2−222−2−2−2−222−2−222000000000000
χ22222222222222-2-2-2-200000000-2-2-2-2-2-22222000000000000−2−222−2−22222−2−222−2−2000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-222220000000000000000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222222222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-2-2-22200000000000022−2−2−2−22222−2−2−2−222000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-2-2-222000000000000−2−22222−2−2−2−22222−2−2000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022-2-22222-2-200000000000022−2−2−2−222−2−22222−2−2000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022-2-22222-2-2000000000000−2−22222−2−222−2−2−2−222000000000000
χ29222-2-2-22-22i2i−2i−2i22-2-222-2-222-2-22i−2i000000002i2i−2i−2i00000000000000000000000000002i−2i2-20000
χ30222-2-2-22-22i2i−2i−2i22-2-222-2-222-2-22i−2i000000002i2i−2i−2i0000000000000000000000000000−2i2i-220000
χ31222-2-2-22-22i2i−2i−2i22-2-2-2-222-2-2222i−2i00000000−2i−2i2i2i0000000000000000000000002i−2i2-200000000
χ32222-2-2-22-22i2i−2i−2i22-2-2-2-222-2-2222i−2i00000000−2i−2i2i2i000000000000000000000000−2i2i-2200000000
χ33222-2-2-22-2−2i−2i2i2i22-2-222-2-222-2-2−2i2i00000000−2i−2i2i2i00000000000000000000000000002i−2i-220000
χ34222-2-2-22-2−2i−2i2i2i22-2-222-2-222-2-2−2i2i00000000−2i−2i2i2i0000000000000000000000000000−2i2i2-20000
χ35222-2-2-22-2−2i−2i2i2i22-2-2-2-222-2-222−2i2i000000002i2i−2i−2i0000000000000000000000002i−2i-2200000000
χ36222-2-2-22-2−2i−2i2i2i22-2-2-2-222-2-222−2i2i000000002i2i−2i−2i000000000000000000000000−2i2i2-200000000
χ372-2-2-2-22222-22-200002−22−22−22−20000002-22-22−22−222−2−222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ382-2-2-2-22222-22-200002−22−22−22−20000002-22-22−22−222−2−222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ392-2-2-2-22222-22-200002−22−22−22−2000000-22-222−22−2−2−222−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ402-2-2-2-22222-22-200002−22−22−22−2000000-22-222−22−2−2−222−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ412-2-2-2-22222-22-20000−22−22−22−220000002-22-2−22−22−2−222−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ422-2-2-2-22222-22-20000−22−22−22−220000002-22-2−22−22−2−222−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ432-2-2-2-22222-22-20000−22−22−22−22000000-22-22−22−2222−2−222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ442-2-2-2-22222-22-20000−22−22−22−22000000-22-22−22−2222−2−222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ452-2-2-2-2222-22-2200002−22−22−22−20000002-2-22−22−2222−2−2−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ462-2-2-2-2222-22-2200002−22−22−22−20000002-2-22−22−2222−2−2−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ472-2-2-2-2222-22-2200002−22−22−22−2000000-222-2−22−22−2−22222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ482-2-2-2-2222-22-2200002−22−22−22−2000000-222-2−22−22−2−22222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ492-2-2-2-2222-22-220000−22−22−22−220000002-2-222−22−2−2−22222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ502-2-2-2-2222-22-220000−22−22−22−220000002-2-222−22−2−2−22222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ512-2-2-2-2222-22-220000−22−22−22−22000000-222-22−22−222−2−2−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ522-2-2-2-2222-22-220000−22−22−22−22000000-222-22−22−222−2−2−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ53444-4-4-44-44i4i−4i−4i-4-44400000000−4i4i000000000000000000000000000000000000000000000000
χ54444-4-4-44-4−4i−4i4i4i-4-444000000004i−4i000000000000000000000000000000000000000000000000
χ5544-44-44-4-40000000022−22−2222−222222−22004-4000000000022−2222−2200000000000000000000000000000000
χ5644-44-44-4-40000000022−22−2222−222222−2200-440000000000−2222−222200000000000000000000000000000000
χ5744-44-44-4-400000000−222222−2222−22−2222004-40000000000−2222−222200000000000000000000000000000000
χ5844-44-44-4-400000000−222222−2222−22−222200-44000000000022−2222−2200000000000000000000000000000000
χ5944-4-44-4-440000000022−2222−22−2222−222200004i−4i0000000000002i2−2i22i2−2i20000000000000000000000000000
χ6044-4-44-4-440000000022−2222−22−2222−22220000−4i4i000000000000−2i22i2−2i22i20000000000000000000000000000
χ6144-4-44-4-4400000000−2222−222222−2222−2200004i−4i000000000000−2i22i2−2i22i20000000000000000000000000000
χ6244-4-44-4-4400000000−2222−222222−2222−220000−4i4i0000000000002i2−2i22i2−2i20000000000000000000000000000
χ634-444-4-4-4400004-44-4000000000000000000000000004i−4i−4i4i0000000000000000000000000000
χ644-444-4-4-4400004-44-400000000000000000000000000−4i4i4i−4i0000000000000000000000000000
χ654-444-4-4-440000-44-444444-4-4-4-400000000000000000000000000000000000000000000000000
χ664-444-4-4-440000-44-44-4-4-4-4444400000000000000000000000000000000000000000000000000
χ674-44-444-4-400004-4-4400000000000000000000004-4-4400000000000000000000000000000000
χ684-44-444-4-400004-4-440000000000000000000000-444-400000000000000000000000000000000
χ694-44-444-4-40000-444-444-4-4-4-44400000000000000000000000000000000000000000000000000
χ704-44-444-4-40000-444-4-4-44444-4-400000000000000000000000000000000000000000000000000
χ714-4-444-44-44i−4i−4i4i000022−22−222222−22−222200000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ724-4-444-44-44i−4i−4i4i0000−222222−22−222222−220000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ734-4-444-44-4−4i4i4i−4i000022−22−222222−22−22220000000000−2i22i22i2−2i2000000000000000000000000000000000000
χ744-4-444-44-4−4i4i4i−4i0000−222222−22−222222−2200000000002i2−2i2−2i22i2000000000000000000000000000000000000

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