Finite Group Databasebeta

← Group #142135

Character table — Group #142135

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order122222224444444488888888444444444488888888888816161616161616161616161616161616888888884444
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
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ1011111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ1211111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ1311111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ1411111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ1511111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ1611111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
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
χ192222222222-2-2-2-22200000000-2-22222-2-2-2-200000000000022−2−222−2−222−2−222−2−2000000000000
χ202222222222-2-2-2-22200000000-2-22222-2-2-2-2000000000000−2−222−2−222−2−222−2−222000000000000
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
χ2322222222-2-22222-2-222222222-2-222-2-222-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ2422222222-2-22222-2-222222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-2000000002222-2-2-2-222000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ2622222222-2-2-2-2-2-2-2-2000000002222-2-2-2-222000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2722222222-2-2-2-2-2-2-2-20000000022-2-22222-2-2000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ2822222222-2-2-2-2-2-2-2-20000000022-2-22222-2-2000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ292222-2-2-2-2220000-2-2222−2−2−22−2002-22-2000022−2−222−2−222−2−2ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ302222-2-2-2-2220000-2-2222−2−2−22−2002-22-2000022−2−222−2−222−2−2−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ312222-2-2-2-2220000-2-2222−2−2−22−200-22-22000022−2−2−2−222−2−222ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ322222-2-2-2-2220000-2-2222−2−2−22−200-22-22000022−2−2−2−222−2−222−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ332222-2-2-2-2220000-2-2−2−2−2222−22002-22-20000−2−222−2−222−2−222ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ342222-2-2-2-2220000-2-2−2−2−2222−22002-22-20000−2−222−2−222−2−222−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ352222-2-2-2-2220000-2-2−2−2−2222−2200-22-220000−2−22222−2−222−2−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7000000000000
χ362222-2-2-2-2220000-2-2−2−2−2222−2200-22-220000−2−22222−2−222−2−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7000000000000
χ372222-2-2-2-2-2-2000022222−2−2−22−2002-2-220000−2−222−2−22222−2−2ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ382222-2-2-2-2-2-2000022222−2−2−22−2002-2-220000−2−222−2−22222−2−2−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ392222-2-2-2-2-2-2000022222−2−2−22−200-222-20000−2−22222−2−2−2−222ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ402222-2-2-2-2-2-2000022222−2−2−22−200-222-20000−2−22222−2−2−2−222−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ412222-2-2-2-2-2-2000022−2−2−2222−22002-2-22000022−2−222−2−2−2−222ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ422222-2-2-2-2-2-2000022−2−2−2222−22002-2-22000022−2−222−2−2−2−222−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ432222-2-2-2-2-2-2000022−2−2−2222−2200-222-2000022−2−2−2−22222−2−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7000000000000
χ442222-2-2-2-2-2-2000022−2−2−2222−2200-222-2000022−2−2−2−22222−2−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7000000000000
χ4522-2-222-2-22-222-2-22-222-222-2-2-22-2000000002-22-200000000000000000000000000002-22-20000
χ4622-2-222-2-22-222-2-22-222-222-2-2-22-2000000002-22-20000000000000000000000000000-22-220000
χ4722-2-222-2-22-222-2-22-2-2-22-2-22222-200000000-22-220000000000000000000000002i−2i2i−2i00000000
χ4822-2-222-2-22-222-2-22-2-2-22-2-22222-200000000-22-22000000000000000000000000−2i2i−2i2i00000000
χ4922-2-222-2-2-2222-2-2-2222-222-2-2-2-2200000000-22-220000000000000000000000002-2-2200000000
χ5022-2-222-2-2-2222-2-2-2222-222-2-2-2-2200000000-22-22000000000000000000000000-222-200000000
χ5122-2-222-2-2-2222-2-2-22-2-22-2-2222-22000000002-22-200000000000000000000000000002i−2i−2i2i0000
χ5222-2-222-2-2-2222-2-2-22-2-22-2-2222-22000000002-22-20000000000000000000000000000−2i2i2i−2i0000
χ5344-4-444-4-44-4-4-4444-400000000-44000000000000000000000000000000000000000000000000
χ5444-4-444-4-4-44-4-444-44000000004-4000000000000000000000000000000000000000000000000
χ5544-4-4-4-4444-40000-442222−22−22−2222−2222000000000022−22−2222000000000000000000000000000000000000
χ5644-4-4-4-4444-40000-44−22−22222222−2222−220000000000−222222−22000000000000000000000000000000000000
χ5744-4-4-4-444-4400004-42222−22−22−2222−22220000000000−222222−22000000000000000000000000000000000000
χ5844-4-4-4-444-4400004-4−22−22222222−2222−22000000000022−22−2222000000000000000000000000000000000000
χ594-44-44-44-40000000022−222222−22−22−22220000004i−4i00000000002i2−2i22i2−2i20000000000000000000000000000
χ604-44-44-44-40000000022−222222−22−22−2222000000−4i4i0000000000−2i22i2−2i22i20000000000000000000000000000
χ614-44-44-44-400000000−2222−22−22222222−220000004i−4i0000000000−2i22i2−2i22i20000000000000000000000000000
χ624-44-44-44-400000000−2222−22−22222222−22000000−4i4i00000000002i2−2i22i2−2i20000000000000000000000000000
χ634-44-4-44-44004-44-400000000000000000000000000004i−4i−4i4i0000000000000000000000000000
χ644-44-4-44-44004-44-40000000000000000000000000000−4i4i4i−4i0000000000000000000000000000
χ654-44-4-44-4400-44-44004-44-444-4-400000000000000000000000000000000000000000000000000
χ664-44-4-44-4400-44-4400-44-44-4-44400000000000000000000000000000000000000000000000000
χ674-4-444-4-440000000022−22−2222−222222−22000000004i−4i00002i2−2i22i2−2i200000000000000000000000000000000
χ684-4-444-4-440000000022−22−2222−222222−2200000000−4i4i0000−2i22i2−2i22i200000000000000000000000000000000
χ694-4-444-4-4400000000−222222−2222−22−2222000000004i−4i0000−2i22i2−2i22i200000000000000000000000000000000
χ704-4-444-4-4400000000−222222−2222−22−222200000000−4i4i00002i2−2i22i2−2i200000000000000000000000000000000
χ714-4-44-444-4004-4-440000000000000000000000004i−4i−4i4i00000000000000000000000000000000
χ724-4-44-444-4004-4-44000000000000000000000000−4i4i4i−4i00000000000000000000000000000000
χ734-4-44-444-400-444-4004-4-4-44-44400000000000000000000000000000000000000000000000000
χ744-4-44-444-400-444-400-4444-44-4-400000000000000000000000000000000000000000000000000

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