Finite Group Databasebeta

← Group #138201

Character table — Group #138201

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888224444444488888888888816161616161616161616161616161616888888882444
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
χ5111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11
χ6111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ7111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1
χ8111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-11
χ911111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ1011111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ1111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ1211111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ1311111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-11-1
χ1411111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-11-11
χ1511111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-11-11
χ1611111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-11-1
χ172222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000
χ192222222222-2-2-2-2220000000022-2-222-2-2-2-200000000000022−2−222−2−222−2−222−2−2000000000000
χ202222222222-2-2-2-2220000000022-2-222-2-2-2-2000000000000−2−222−2−222−2−222−2−222000000000000
χ212222222222-2-2-2-22200000000-2-2-2-2-2-2222200000000000022−2−222−2−2−2−222−2−222000000000000
χ222222222222-2-2-2-22200000000-2-2-2-2-2-22222000000000000−2−222−2−22222−2−222−2−2000000000000
χ2322222222-2-22222-2-22222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-22222-2-222222222-2-2-2-22222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-222-2-2000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-222-2-2000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2722222222-2-2-2-2-2-2-2-200000000-2-22222-2-222000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2822222222-2-2-2-2-2-2-2-200000000-2-22222-2-222000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ2922-22-22-2-22i−2i00002i−2ii2i2−i2−i2i2i2−i2−i22-2002i−2i000022−2−222−2−2i2i2−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+ζ3000000000000
χ3022-22-22-2-22i−2i00002i−2ii2i2−i2−i2i2i2−i2−i22-2002i−2i000022−2−222−2−2i2i2−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−ζ3000000000000
χ3122-22-22-2-22i−2i00002i−2ii2i2−i2−i2i2i2−i2−i2-2200−2i2i000022−2−2−2−222−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−ζ3000000000000
χ3222-22-22-2-22i−2i00002i−2ii2i2−i2−i2i2i2−i2−i2-2200−2i2i000022−2−2−2−222−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+ζ3000000000000
χ3322-22-22-2-22i−2i00002i−2i−i2−i2i2i2−i2−i2i2i22-2002i−2i0000−2−222−2−222−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−ζ7000000000000
χ3422-22-22-2-22i−2i00002i−2i−i2−i2i2i2−i2−i2i2i22-2002i−2i0000−2−222−2−222−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+ζ7000000000000
χ3522-22-22-2-22i−2i00002i−2i−i2−i2i2i2−i2−i2i2i2-2200−2i2i0000−2−22222−2−2i2i2−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+ζ7000000000000
χ3622-22-22-2-22i−2i00002i−2i−i2−i2i2i2−i2−i2i2i2-2200−2i2i0000−2−22222−2−2i2i2−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−ζ7000000000000
χ3722-22-22-2-2−2i2i0000−2i2ii2i2−i2−i2i2i2−i2−i22-200−2i2i0000−2−222−2−222i2i2−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+ζ3000000000000
χ3822-22-22-2-2−2i2i0000−2i2ii2i2−i2−i2i2i2−i2−i22-200−2i2i0000−2−222−2−222i2i2−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−ζ3000000000000
χ3922-22-22-2-2−2i2i0000−2i2ii2i2−i2−i2i2i2−i2−i2-22002i−2i0000−2−22222−2−2−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−ζ3000000000000
χ4022-22-22-2-2−2i2i0000−2i2ii2i2−i2−i2i2i2−i2−i2-22002i−2i0000−2−22222−2−2−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+ζ3000000000000
χ4122-22-22-2-2−2i2i0000−2i2i−i2−i2i2i2−i2−i2i2i22-200−2i2i000022−2−222−2−2−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−ζ7000000000000
χ4222-22-22-2-2−2i2i0000−2i2i−i2−i2i2i2−i2−i2i2i22-200−2i2i000022−2−222−2−2−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+ζ7000000000000
χ4322-22-22-2-2−2i2i0000−2i2i−i2−i2i2i2−i2−i2i2i2-22002i−2i000022−2−2−2−222i2i2−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+ζ7000000000000
χ4422-22-22-2-2−2i2i0000−2i2i−i2−i2i2i2−i2−i2i2i2-22002i−2i000022−2−2−2−222i2i2−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−ζ7000000000000
χ452-2-222-2-2222-2-222-2-22-22-22-22-2002-20000002-22-200000000000000000000000000002i−2i2i−2i0000
χ462-2-222-2-2222-2-222-2-22-22-22-22-2002-20000002-22-20000000000000000000000000000−2i2i−2i2i0000
χ472-2-222-2-2222-2-222-2-2-22-22-22-22002-2000000-22-220000000000000000000000002i−2i2i−2i00000000
χ482-2-222-2-2222-2-222-2-2-22-22-22-22002-2000000-22-22000000000000000000000000−2i2i−2i2i00000000
χ492-2-222-2-22-2-2-2-222222-22-22-22-200-22000000-22-220000000000000000000000002-2-2200000000
χ502-2-222-2-22-2-2-2-222222-22-22-22-200-22000000-22-22000000000000000000000000-222-200000000
χ512-2-222-2-22-2-2-2-22222-22-22-22-2200-220000002-22-200000000000000000000000000002-2-220000
χ522-2-222-2-22-2-2-2-22222-22-22-22-2200-220000002-22-20000000000000000000000000000-222-20000
χ53444-4-4-4-44004-44-400000000000000000000000000004i−4i4i−4i0000000000000000000000000000
χ54444-4-4-4-44004-44-40000000000000000000000000000−4i4i−4i4i0000000000000000000000000000
χ55444-4-4-4-4400-44-44004444-4-4-4-400000000000000000000000000000000000000000000000000
χ56444-4-4-4-4400-44-4400-4-4-4-4444400000000000000000000000000000000000000000000000000
χ5744-4-44-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i2000000004i−4i0000000022−22−22220000000000000000000000000000
χ5844-4-44-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000−4i4i00000000−222222−220000000000000000000000000000
χ5944-4-44-44-400000000−2i2−2i22i22i22i22i2−2i2−2i2000000004i−4i00000000−222222−220000000000000000000000000000
χ6044-4-44-44-400000000−2i2−2i22i22i22i22i2−2i2−2i200000000−4i4i0000000022−22−22220000000000000000000000000000
χ614-444-4-44-44i−4i0000−4i4i2i2−2i2−2i22i22i2−2i2−2i22i2000000000022−22−2222000000000000000000000000000000000000
χ624-444-4-44-44i−4i0000−4i4i−2i22i22i2−2i2−2i22i22i2−2i20000000000−222222−22000000000000000000000000000000000000
χ634-444-4-44-4−4i4i00004i−4i2i2−2i2−2i22i22i2−2i2−2i22i20000000000−222222−22000000000000000000000000000000000000
χ644-444-4-44-4−4i4i00004i−4i−2i22i22i2−2i2−2i22i22i2−2i2000000000022−22−2222000000000000000000000000000000000000
χ654-44-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i20000004i−4i00000022−2222−2200000000000000000000000000000000
χ664-44-444-4-4000000002i2−2i2−2i22i2−2i22i22i2−2i2000000−4i4i000000−2222−222200000000000000000000000000000000
χ674-44-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i20000004i−4i000000−2222−222200000000000000000000000000000000
χ684-44-444-4-400000000−2i22i22i2−2i22i2−2i2−2i22i2000000−4i4i00000022−2222−2200000000000000000000000000000000
χ694-4-444-4-444444-4-4-4-40000000000-440000000000000000000000000000000000000000000000
χ704-4-444-4-44-4-444-4-44400000000004-40000000000000000000000000000000000000000000000
χ714-4-4-4-4444004-4-44004-44-4-44-4400000000000000000000000000000000000000000000000000
χ724-4-4-4-4444004-4-4400-44-444-44-400000000000000000000000000000000000000000000000000
χ734-4-4-4-444400-444-40000000000000000000000004-4-4400000000000000000000000000000000
χ744-4-4-4-444400-444-4000000000000000000000000-444-400000000000000000000000000000000

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