Finite Group Databasebeta

← Group #138162

Character table — Group #138162

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222222222222222222222444444444444444444448888888888888888161616161616161632323232
order12222222444444888888888888244444444488888888881616161616161616161616161616161616161616161616162444
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
χ511111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111
χ711111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111
χ811111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1
χ911111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ1011111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ1111111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ1211111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ1311111-1-1111-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ1411111-1-1111-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ1511111-1-1111-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ1611111-1-1111-1-111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-222-2-20000000000000000000000000000
χ1822222222222222-2-2-2-2-2-22222-2-222-2-2-2-2-2-2-2-2-2-22222-2-2220000000000000000000000000000
χ1922222-2-2222-2-2222222-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2220000000000000000000000000000
χ2022222-2-2222-2-222-2-2-2-222-2-2-2-222-2-2-2-2-2-22222-2-2222222-2-20000000000000000000000000000
χ212222-222-22-2222-2222222000022-2-200000000-2-20000-2-20000000000000000002−22−22−22−20000
χ222222-222-22-2222-2222222000022-2-200000000-2-20000-2-2000000000000000000−22−22−22−220000
χ232222-222-22-2222-2-2-2-2-2-2-20000-2-2-2-20000000022000022000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ242222-222-22-2222-2-2-2-2-2-2-20000-2-2-2-20000000022000022000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ252222-222-2-22-2-2-22000000222200-22000000000022-2-200-2-222−2−222−2−222−2−222−2−2000000000000
χ262222-222-2-22-2-2-22000000222200-22000000000022-2-200-2-2−2−222−2−222−2−222−2−222000000000000
χ272222-222-2-22-2-2-22000000-2-2-2-200-220000000000-2-2220022i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000000000
χ282222-222-2-22-2-2-22000000-2-2-2-200-220000000000-2-2220022−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000000000
χ292222-2-2-2-22-2-2-22-22222-2-20000-2-22200000000-2-2000022000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ302222-2-2-2-22-2-2-22-22222-2-20000-2-22200000000-2-2000022000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ312222-2-2-2-22-2-2-22-2-2-2-2-2220000222200000000220000-2-20000000000000000002−2−22−222−20000
χ322222-2-2-2-22-2-2-22-2-2-2-2-2220000222200000000220000-2-2000000000000000000−222−22−2−220000
χ332222-2-2-2-2-2222-220000002222002-20000000000-2-22200-2-222−2−2−2−222−2−22222−2−2000000000000
χ342222-2-2-2-2-2222-220000002222002-20000000000-2-22200-2-2−2−22222−2−222−2−2−2−222000000000000
χ352222-2-2-2-2-2222-22000000-2-2-2-2002-2000000000022-2-20022i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ362222-2-2-2-2-2222-22000000-2-2-2-2002-2000000000022-2-20022−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ372-2-22200-22-200-222i2i−2i−2i0022-2-2000000002i2i−2i−2i2i−2i0000002-2i2−i2i2−i22−22−22−22−2i2−i2i2−i2000000000000
χ382-2-22200-22-200-222i2i−2i−2i0022-2-2000000002i2i−2i−2i2i−2i0000002-2−i2i2−i2i2−22−22−22−22−i2i2−i2i2000000000000
χ392-2-22200-22-200-222i2i−2i−2i00-2-22200000000−2i−2i2i2i2i−2i000000-222−22−2i2−i2i2−i2−i2i2−i2i2−22−22000000000000
χ402-2-22200-22-200-222i2i−2i−2i00-2-22200000000−2i−2i2i2i2i−2i000000-22−22−22−i2i2−i2i2i2−i2i2−i22−22−2000000000000
χ412-2-22200-22-200-22−2i−2i2i2i0022-2-200000000−2i−2i2i2i−2i2i0000002-2i2−i2i2−i2−22−22−22−22i2−i2i2−i2000000000000
χ422-2-22200-22-200-22−2i−2i2i2i0022-2-200000000−2i−2i2i2i−2i2i0000002-2−i2i2−i2i22−22−22−22−2−i2i2−i2i2000000000000
χ432-2-22200-22-200-22−2i−2i2i2i00-2-222000000002i2i−2i−2i−2i2i000000-222−22−2−i2i2−i2i2i2−i2i2−i2−22−22000000000000
χ442-2-22200-22-200-22−2i−2i2i2i00-2-222000000002i2i−2i−2i−2i2i000000-22−22−22i2−i2i2−i2−i2i2−i2i22−22−2000000000000
χ452-2-22-2002-2-2002200002222-2-2-2-20022-2-200000000002-2-222i−2i−2i2i000000002i−2i−2i2i000000000000
χ462-2-22-2002-2-2002200002222-2-2-2-20022-2-200000000002-2-22−2i2i2i−2i00000000−2i2i2i−2i000000000000
χ472-2-22-2002-2-20022000022-2-222-2-200-2-22200000000002-22-200002i−2i−2i2i−2i2i2i−2i0000000000000000
χ482-2-22-2002-2-20022000022-2-222-2-200-2-22200000000002-22-20000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ492-2-22-2002-2-200220000-2-222-2-22200-2-2220000000000-22-2200002-2-222-2-220000000000000000
χ502-2-22-2002-2-200220000-2-222-2-22200-2-2220000000000-22-220000-222-2-222-20000000000000000
χ512-2-22-2002-2-200220000-2-2-2-222220022-2-20000000000-222-22-2-2200000000-222-2000000000000
χ522-2-22-2002-2-200220000-2-2-2-222220022-2-20000000000-222-2-222-2000000002-2-22000000000000
χ5344444444-4-4-4-4-4-40000000000004-40000000000000000000000000000000000000000000000
χ5444444-4-44-4-444-4-4000000000000-440000000000000000000000000000000000000000000000
χ5544-4-40000004i−4i0022−2222−222i2−2i22i2−2i22i2−2i22i2−2i2002-22-22i−2i2i−2i000022−2200000000000000000000000000000000
χ5644-4-40000004i−4i0022−2222−222i2−2i2−2i22i2−2i22i22i2−2i200-22-22−2i2i−2i2i0000−222200000000000000000000000000000000
χ5744-4-40000004i−4i00−2222−2222−2i22i22i2−2i22i2−2i2−2i22i200-22-22−2i2i−2i2i000022−2200000000000000000000000000000000
χ5844-4-40000004i−4i00−2222−2222−2i22i2−2i22i2−2i22i2−2i22i2002-22-22i−2i2i−2i0000−222200000000000000000000000000000000
χ5944-4-4000000−4i4i0022−2222−22−2i22i22i2−2i22i2−2i2−2i22i200-22-222i−2i2i−2i0000−222200000000000000000000000000000000
χ6044-4-4000000−4i4i0022−2222−22−2i22i2−2i22i2−2i22i2−2i22i2002-22-2−2i2i−2i2i000022−2200000000000000000000000000000000
χ6144-4-4000000−4i4i00−2222−22222i2−2i22i2−2i22i2−2i22i2−2i2002-22-2−2i2i−2i2i0000−222200000000000000000000000000000000
χ6244-4-4000000−4i4i00−2222−22222i2−2i2−2i22i2−2i22i22i2−2i200-22-222i−2i2i−2i000022−2200000000000000000000000000000000
χ634-44-404-400000002i2−2i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i2002-2-22-222-2002i2−2i20000000000000000000000000000000000
χ644-44-404-400000002i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i200-222-22-2-2200−2i22i20000000000000000000000000000000000
χ654-44-404-40000000−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i200-222-22-2-22002i2−2i20000000000000000000000000000000000
χ664-44-404-40000000−2i22i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2002-2-22-222-200−2i22i20000000000000000000000000000000000
χ674-44-40-4400000002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i200-222-2-222-200−2i22i20000000000000000000000000000000000
χ684-44-40-4400000002i2−2i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i2002-2-222-2-22002i2−2i20000000000000000000000000000000000
χ694-44-40-440000000−2i22i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i2002-2-222-2-2200−2i22i20000000000000000000000000000000000
χ704-44-40-440000000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i200-222-2-222-2002i2−2i20000000000000000000000000000000000
χ714-4-44400-4-44004-40000440000-4-40000000000000000-44000000000000000000000000000000
χ724-4-44400-4-44004-40000-4-400004400000000000000004-4000000000000000000000000000000
χ734-4-44-40044400-4-44i4i−4i−4i000000000000000000−4i4i000000000000000000000000000000000000
χ744-4-44-40044400-4-4−4i−4i4i4i0000000000000000004i−4i000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).