Finite Group Databasebeta

← Group #495692

Character table — Group #495692

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order122222224444444444444444444488888888224488888888888822224444444444441616161616161616161616161616161622444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ611111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ711111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ811111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ91111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ121111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1
χ1711-11-11-1-11-1ii−i−i11-1-1ii−i−iii−i−i1-11111-1-1-1-11-1i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i1-11-1i−ii−i
χ1811-11-11-1-11-1ii−i−i11-1-1ii−i−iii−i−i1-11111-1-1-1-11-1i−iii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii-11-11−ii−ii
χ1911-11-11-1-11-1ii−i−i11-1-1ii−i−iii−i−i1-11111-1-1-1-11-1i−iii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-11-11−ii−ii
χ2011-11-11-1-11-1ii−i−i11-1-1ii−i−iii−i−i1-11111-1-1-1-11-1i−iii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii-1-111−i−iii-1-111−i−iii1-11-1i−ii−i
χ2111-11-11-1-11-1ii−i−i-1-111ii−i−i−i−iii1-11111-1-1-1-1-11−iiii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii1-1-11−iii−i
χ2211-11-11-1-11-1ii−i−i-1-111ii−i−i−i−iii1-11111-1-1-1-1-11−iiii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i-111-1i−i−ii
χ2311-11-11-1-11-1ii−i−i-1-111ii−i−i−i−iii1-11111-1-1-1-1-11−iiii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-111-1i−i−ii
χ2411-11-11-1-11-1ii−i−i-1-111ii−i−i−i−iii1-11111-1-1-1-1-11−iiii−i−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i1-1-11−iii−i
χ2511-11-11-1-11-1−i−iii11-1-1−i−iii−i−iii1-11111-1-1-1-11-1−ii−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii1-11-1−ii−ii
χ2611-11-11-1-11-1−i−iii11-1-1−i−iii−i−iii1-11111-1-1-1-11-1−ii−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i-11-11i−ii−i
χ2711-11-11-1-11-1−i−iii11-1-1−i−iii−i−iii1-11111-1-1-1-11-1−ii−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-11-11i−ii−i
χ2811-11-11-1-11-1−i−iii11-1-1−i−iii−i−iii1-11111-1-1-1-11-1−ii−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i1-11-1−ii−ii
χ2911-11-11-1-11-1−i−iii-1-111−i−iiiii−i−i1-11111-1-1-1-1-11i−i−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i1-1-11i−i−ii
χ3011-11-11-1-11-1−i−iii-1-111−i−iiiii−i−i1-11111-1-1-1-1-11i−i−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii-111-1−iii−i
χ3111-11-11-1-11-1−i−iii-1-111−i−iiiii−i−i1-11111-1-1-1-1-11i−i−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-111-1−iii−i
χ3211-11-11-1-11-1−i−iii-1-111−i−iiiii−i−i1-11111-1-1-1-1-11i−i−i−iii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii1-1-11i−i−ii
χ332222222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ3422222222222222-2-2-2-22222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ352222222222-2-2-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ362222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-20000000000000000000000000000000000000000
χ3722222222-2-222222222-2-2-2-22222-2-200000000-2-2-2-200000000000000000000000000002−22−22−22−22−22−22−22−200000000
χ3822222222-2-222222222-2-2-2-22222-2-200000000-2-2-2-20000000000000000000000000000−22−22−22−22−22−22−22−2200000000
χ3922222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000000000000000000000002−22−22−22−2−22−22−22−2200000000
χ4022222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000000−22−22−22−222−22−22−22−200000000
χ4122222222-2-2-2-2-2-222222222-2-2-2-2-2-200000000-2-22200000000000000000000000000002−22−2−22−222−22−2−22−2200000000
χ4222222222-2-2-2-2-2-222222222-2-2-2-2-2-200000000-2-2220000000000000000000000000000−22−222−22−2−22−222−22−200000000
χ4322222222-2-2-2-2-2-2-2-2-2-222222222-2-20000000022-2-200000000000000000000000000002−22−2−22−22−22−222−22−200000000
χ4422222222-2-2-2-2-2-2-2-2-2-222222222-2-20000000022-2-20000000000000000000000000000−22−222−22−22−22−2−22−2200000000
χ4522-22-22-2-22-22i2i−2i−2i22-2-22i2i−2i−2i2i2i−2i−2i2-2-2-2-2-222222-22i−2i−2i−2i2i2i-2-222−2i−2i2i2i0000000000000000000000000000000000000000
χ4622-22-22-2-22-22i2i−2i−2i-2-2222i2i−2i−2i−2i−2i2i2i2-2-2-2-2-22222-22−2i2i−2i−2i2i2i22-2-22i2i−2i−2i0000000000000000000000000000000000000000
χ4722-22-22-2-22-2−2i−2i2i2i22-2-2−2i−2i2i2i−2i−2i2i2i2-2-2-2-2-222222-2−2i2i2i2i−2i−2i-2-2222i2i−2i−2i0000000000000000000000000000000000000000
χ4822-22-22-2-22-2−2i−2i2i2i-2-222−2i−2i2i2i2i2i−2i−2i2-2-2-2-2-22222-222i−2i2i2i−2i−2i22-2-2−2i−2i2i2i0000000000000000000000000000000000000000
χ4922-22-22-2-2-222i2i−2i−2i22-2-2−2i−2i2i2i2i2i−2i−2i-2200000000-22−2i2i00000000000000000000000000002−2−22i2−i2−i2i22−2−22i2−i2−i2i200000000
χ5022-22-22-2-2-222i2i−2i−2i22-2-2−2i−2i2i2i2i2i−2i−2i-2200000000-22−2i2i0000000000000000000000000000−222−2−i2i2i2−i2−222−2−i2i2i2−i200000000
χ5122-22-22-2-2-222i2i−2i−2i-2-222−2i−2i2i2i−2i−2i2i2i-22000000002-22i−2i00000000000000000000000000002−2−22i2−i2−i2i2−222−2−i2i2i2−i200000000
χ5222-22-22-2-2-222i2i−2i−2i-2-222−2i−2i2i2i−2i−2i2i2i-22000000002-22i−2i0000000000000000000000000000−222−2−i2i2i2−i22−2−22i2−i2−i2i200000000
χ5322-22-22-2-2-22−2i−2i2i2i22-2-22i2i−2i−2i−2i−2i2i2i-2200000000-222i−2i00000000000000000000000000002−2−22−i2i2i2−i22−2−22−i2i2i2−i200000000
χ5422-22-22-2-2-22−2i−2i2i2i22-2-22i2i−2i−2i−2i−2i2i2i-2200000000-222i−2i0000000000000000000000000000−222−2i2−i2−i2i2−222−2i2−i2−i2i200000000
χ5522-22-22-2-2-22−2i−2i2i2i-2-2222i2i−2i−2i2i2i−2i−2i-22000000002-2−2i2i00000000000000000000000000002−2−22−i2i2i2−i2−222−2i2−i2−i2i200000000
χ5622-22-22-2-2-22−2i−2i2i2i-2-2222i2i−2i−2i2i2i−2i−2i-22000000002-2−2i2i0000000000000000000000000000−222−2i2−i2−i2i22−2−22−i2i2i2−i200000000
χ572-22-222-2-2-222i−2i2i−2i00002i−2i2i−2i00002-222-2-222-2-200002i−2i2i−2i00000000000000002-22-22i−2i2i−2i000000000000000000000000
χ582-22-222-2-2-222i−2i2i−2i00002i−2i2i−2i00002-222-2-222-2-200002i−2i2i−2i0000000000000000-22-22−2i2i−2i2i000000000000000000000000
χ592-22-222-2-2-222i−2i2i−2i00002i−2i2i−2i00002-2-2-222-2-2220000−2i2i−2i2i000000002-22-22i−2i2i−2i00000000000000000000000000000000
χ602-22-222-2-2-222i−2i2i−2i00002i−2i2i−2i00002-2-2-222-2-2220000−2i2i−2i2i00000000-22-22−2i2i−2i2i00000000000000000000000000000000
χ612-22-222-2-2-22−2i2i−2i2i0000−2i2i−2i2i00002-222-2-222-2-20000−2i2i−2i2i00000000000000002-22-2−2i2i−2i2i000000000000000000000000
χ622-22-222-2-2-22−2i2i−2i2i0000−2i2i−2i2i00002-222-2-222-2-20000−2i2i−2i2i0000000000000000-22-222i−2i2i−2i000000000000000000000000
χ632-22-222-2-2-22−2i2i−2i2i0000−2i2i−2i2i00002-2-2-222-2-22200002i−2i2i−2i000000002-22-2−2i2i−2i2i00000000000000000000000000000000
χ642-22-222-2-2-22−2i2i−2i2i0000−2i2i−2i2i00002-2-2-222-2-22200002i−2i2i−2i00000000-22-222i−2i2i−2i00000000000000000000000000000000
χ652-2-2-2-2222-2-22-2-2200002-2-2200002222-2-2-2-22200002-2-2200000000000000002-2-222-2-22000000000000000000000000
χ662-2-2-2-2222-2-22-2-2200002-2-2200002222-2-2-2-22200002-2-220000000000000000-222-2-222-2000000000000000000000000
χ672-2-2-2-2222-2-22-2-2200002-2-22000022-2-22222-2-20000-222-2000000002-2-222-2-2200000000000000000000000000000000
χ682-2-2-2-2222-2-22-2-2200002-2-22000022-2-22222-2-20000-222-200000000-222-2-222-200000000000000000000000000000000
χ692-2-2-2-2222-2-2-222-20000-222-200002222-2-2-2-2220000-222-200000000000000002-2-22-222-2000000000000000000000000
χ702-2-2-2-2222-2-2-222-20000-222-200002222-2-2-2-2220000-222-20000000000000000-222-22-2-22000000000000000000000000
χ712-2-2-2-2222-2-2-222-20000-222-2000022-2-22222-2-200002-2-22000000002-2-22-222-200000000000000000000000000000000
χ722-2-2-2-2222-2-2-222-20000-222-2000022-2-22222-2-200002-2-2200000000-222-22-2-2200000000000000000000000000000000
χ73444-4-4-4-440000004i−4i4i−4i000000000022−2222−2222−2222−22000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ74444-4-4-4-440000004i−4i4i−4i0000000000−2222−2222−2222−222200000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ75444-4-4-4-44000000−4i4i−4i4i000000000022−2222−2222−2222−2200000000−2i22i2−2i22i200000000000000000000000000000000000000000000
χ76444-4-4-4-44000000−4i4i−4i4i0000000000−2222−2222−2222−2222000000002i2−2i22i2−2i200000000000000000000000000000000000000000000
χ7744-4-44-44-40000004i−4i−4i4i000000000022−2222−22−2222−2222000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ7844-4-44-44-40000004i−4i−4i4i0000000000−2222−222222−2222−2200000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ7944-4-44-44-4000000−4i4i4i−4i000000000022−2222−22−2222−222200000000−2i22i22i2−2i200000000000000000000000000000000000000000000
χ8044-4-44-44-4000000−4i4i4i−4i0000000000−2222−222222−2222−22000000002i2−2i2−2i22i200000000000000000000000000000000000000000000
χ814-444-4-44-4000000000000004i−4i4i−4i0022−22−222222−22−22220000000000002i2−2i22i2−2i20000000000000000000000000000000000000000
χ824-444-4-44-4000000000000004i−4i4i−4i00−222222−22−222222−22000000000000−2i22i2−2i22i20000000000000000000000000000000000000000
χ834-444-4-44-400000000000000−4i4i−4i4i0022−22−222222−22−2222000000000000−2i22i2−2i22i20000000000000000000000000000000000000000
χ844-444-4-44-400000000000000−4i4i−4i4i00−222222−22−222222−220000000000002i2−2i22i2−2i20000000000000000000000000000000000000000
χ854-44-444-4-44-44i−4i4i−4i0000−4i4i−4i4i0000-440000000000000000000000000000000000000000000000000000000000000000
χ864-44-444-4-44-4−4i4i−4i4i00004i−4i4i−4i0000-440000000000000000000000000000000000000000000000000000000000000000
χ874-4-444-4-44000000000000004-4-440022−22−2222−222222−2200000000000022−22−22220000000000000000000000000000000000000000
χ884-4-444-4-44000000000000004-4-4400−222222−2222−22−2222000000000000−222222−220000000000000000000000000000000000000000
χ894-4-444-4-4400000000000000-444-40022−22−2222−222222−22000000000000−222222−220000000000000000000000000000000000000000
χ904-4-444-4-4400000000000000-444-400−222222−2222−22−222200000000000022−22−22220000000000000000000000000000000000000000
χ914-4-4-4-4444444-4-440000-444-40000-4-40000000000000000000000000000000000000000000000000000000000000000
χ924-4-4-4-444444-444-400004-4-440000-4-40000000000000000000000000000000000000000000000000000000000000000

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