Finite Group Databasebeta

← Group #494266

Character table — Group #494266

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order122244442222222222444444444488888888224488888888888844444444444444441616161616161616161616161616161688888888
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
χ51111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111-1-1-111-1-1-11-1-111-1-11-1-1111111111-11-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i
χ101111111111-1-1-111-1-1-11-1-111-1-11-1-1111111111-11-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111−i−iii−i−iii
χ111111111111-1-1-111-1-1-11-1-111-1-11-1-1111111111-11-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii
χ121111111111-1-1-111-1-1-11-1-111-1-11-1-1111111111-11-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111ii−i−iii−i−i
χ131111111111-1-1-1-1-111-11-1-1-1-1111-1-111111111-11-11-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ141111111111-1-1-1-1-111-11-1-1-1-1111-1-111111111-11-11-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i
χ151111111111-1-1-1-1-111-11-1-1-1-1111-1-111111111-11-11-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ161111111111-1-1-1-1-111-11-1-1-1-1111-1-111111111-11-11-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii
χ171111-1-1-1-1-1-111-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-111-1-1i−ii−ii−ii−i
χ181111-1-1-1-1-1-111-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-111-1-111-1-111-1-111−ii−ii−ii−ii
χ191111-1-1-1-1-1-111-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-111-1-1−ii−ii−ii−ii
χ201111-1-1-1-1-1-111-111-1-1-1111-1-1111-1-1-1-1-1-11111-111-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii-1-111-1-111-1-111-1-111i−ii−ii−ii−i
χ211111-1-1-1-1-1-111-1-1-111-111111-1-11-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii11-1-111-1-1-1-111-1-111i−ii−i−ii−ii
χ221111-1-1-1-1-1-111-1-1-111-111111-1-11-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-111-1-11111-1-111-1-1−ii−iii−ii−i
χ231111-1-1-1-1-1-111-1-1-111-111111-1-11-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i11-1-111-1-1-1-111-1-111−ii−iii−ii−i
χ241111-1-1-1-1-1-111-1-1-111-111111-1-11-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-111-1-11111-1-111-1-1i−ii−i−ii−ii
χ251111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111-1-111-1-11
χ261111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-111-1-111-1
χ271111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-11111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-111-1-111-1
χ281111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-11111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-1-111-1-11
χ291111-1-1-1-1-1-1-1-11-1-1-1-111-1-11111111-1-1-1-1111111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-11-1-11-111-1
χ301111-1-1-1-1-1-1-1-11-1-1-1-111-1-11111111-1-1-1-1111111-1-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-111-11-1-11
χ311111-1-1-1-1-1-1-1-11-1-1-1-111-1-11111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-111-11-1-11
χ321111-1-1-1-1-1-1-1-11-1-1-1-111-1-11111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-11111-1-111-1-1-1-1111-1-11-111-1
χ332222222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ342222222222222-2-2-2-22222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ352222222222-2-2-222-2-2-22-2-222-2-22-2-2-2-2-2-2-2-2-2-22-22-22222-2-2-2-222220000000000000000000000000000000000000000
χ362222222222-2-2-2-2-222-22-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-22-2222222222-2-2-2-20000000000000000000000000000000000000000
χ3722222222-2-222-222-2-2-2-2-2-222-2-2-22200000000-22-220000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ3822222222-2-222-222-2-2-2-2-2-222-2-2-22200000000-22-220000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ3922222222-2-222-2-2-222-2-2-2-2-2-222-222000000002-22-20000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ4022222222-2-222-2-2-222-2-2-2-2-2-222-222000000002-22-20000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ4122222222-2-2-2-2222222-2222222-2-2-200000000-2-2-2-20000000000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ4222222222-2-2-2-2222222-2222222-2-2-200000000-2-2-2-20000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ4322222222-2-2-2-22-2-2-2-22-222-2-2-2-2-2-2-20000000022220000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ4422222222-2-2-2-22-2-2-2-22-222-2-2-2-2-2-2-20000000022220000000000000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ452222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000000022-2-20000000000000000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ462222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000000022-2-20000000000000000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ472222-2-2-2-222222-2-2-2-22-2-2-22222-2-2-200000000-2-2220000000000000000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ482222-2-2-2-222222-2-2-2-22-2-2-22222-2-2-200000000-2-2220000000000000000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ492222-2-2-2-222-2-2-222-2-2-2-222-2-222-222000000002-2-220000000000000000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ502222-2-2-2-222-2-2-222-2-2-2-222-2-222-222000000002-2-220000000000000000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ512222-2-2-2-222-2-2-2-2-222-2-22222-2-2-22200000000-222-20000000000000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ522222-2-2-2-222-2-2-2-2-222-2-22222-2-2-22200000000-222-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ532222-2-2-2-2-2-222-222-2-2-2222-2-2222-2-22222-2-2-2-2-222-2-2-222-2-222-2-2220000000000000000000000000000000000000000
χ542222-2-2-2-2-2-222-2-2-222-222222-2-22-2-22222-2-2-2-22-2-22-2-22222-2-222-2-20000000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-2-22-2-2-2-222-2-222222222222-2-2-2-222-2-222-2-222-2-2-2-2220000000000000000000000000000000000000000
χ572-2-2222-2-22-22-220000-2-22-2000022-222-2-222-2-200002-22-200000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ582-2-2222-2-22-22-220000-2-22-2000022-222-2-222-2-200002-22-20000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ592-2-2222-2-22-22-220000-2-22-2000022-2-2-222-2-2220000-22-22000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ602-2-2222-2-22-22-220000-2-22-2000022-2-2-222-2-2220000-22-2200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ612-2-2222-2-22-2-22-200002-2-2200002-2222-2-222-2-20000-22-2200000000000000002-22-2-22-22000000000000000000000000
χ622-2-2222-2-22-2-22-200002-2-2200002-2222-2-222-2-20000-22-220000000000000000-22-222-22-2000000000000000000000000
χ632-2-2222-2-22-2-22-200002-2-2200002-22-2-222-2-22200002-22-2000000002-22-2-22-2200000000000000000000000000000000
χ642-2-2222-2-22-2-22-200002-2-2200002-22-2-222-2-22200002-22-200000000-22-222-22-200000000000000000000000000000000
χ652-2-22-2-222-222-2-200002-22-200002-2222-2-2-2-2220000-222-2000000002-2-222-2-2200000000000000000000000000000000
χ662-2-22-2-222-222-2-200002-22-200002-2222-2-2-2-2220000-222-200000000-222-2-222-200000000000000000000000000000000
χ672-2-22-2-222-222-2-200002-22-200002-22-2-22222-2-200002-2-2200000000000000002-2-222-2-22000000000000000000000000
χ682-2-22-2-222-222-2-200002-22-200002-22-2-22222-2-200002-2-220000000000000000-222-2-222-2000000000000000000000000
χ692-2-22-2-222-22-2220000-2-2-22000022-222-2-2-2-22200002-2-22000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ702-2-22-2-222-22-2220000-2-2-22000022-222-2-2-2-22200002-2-2200000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ712-2-22-2-222-22-2220000-2-2-22000022-2-2-22222-2-20000-222-200000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ722-2-22-2-222-22-2220000-2-2-22000022-2-2-22222-2-20000-222-20000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ7344-4-44i−4i4i−4i00000004-40000004i−4i00022−2222−222i2−2i22i2−2i200000000000022−222i2−2i20000000000000000000000000000000000000000
χ7444-4-44i−4i4i−4i00000004-40000004i−4i000−2222−2222−2i22i2−2i22i2000000000000−2222−2i22i20000000000000000000000000000000000000000
χ7544-4-44i−4i4i−4i0000000-44000000−4i4i00022−2222−222i2−2i22i2−2i2000000000000−2222−2i22i20000000000000000000000000000000000000000
χ7644-4-44i−4i4i−4i0000000-44000000−4i4i000−2222−2222−2i22i2−2i22i200000000000022−222i2−2i20000000000000000000000000000000000000000
χ7744-4-4−4i4i−4i4i00000004-4000000−4i4i00022−2222−22−2i22i2−2i22i200000000000022−22−2i22i20000000000000000000000000000000000000000
χ7844-4-4−4i4i−4i4i00000004-4000000−4i4i000−2222−22222i2−2i22i2−2i2000000000000−22222i2−2i20000000000000000000000000000000000000000
χ7944-4-4−4i4i−4i4i0000000-440000004i−4i00022−2222−22−2i22i2−2i22i2000000000000−22222i2−2i20000000000000000000000000000000000000000
χ8044-4-4−4i4i−4i4i0000000-440000004i−4i000−2222−22222i2−2i22i2−2i200000000000022−22−2i22i20000000000000000000000000000000000000000
χ814-44-44i−4i−4i4i000004-40000004i−4i0000022−22−22222i2−2i2−2i22i2000000002i2−2i222−2200000000000000000000000000000000000000000000
χ824-44-44i−4i−4i4i000004-40000004i−4i00000−222222−22−2i22i22i2−2i200000000−2i22i2−222200000000000000000000000000000000000000000000
χ834-44-44i−4i−4i4i00000-44000000−4i4i0000022−22−22222i2−2i2−2i22i200000000−2i22i2−222200000000000000000000000000000000000000000000
χ844-44-44i−4i−4i4i00000-44000000−4i4i00000−222222−22−2i22i22i2−2i2000000002i2−2i222−2200000000000000000000000000000000000000000000
χ854-44-4−4i4i4i−4i000004-4000000−4i4i0000022−22−2222−2i22i22i2−2i200000000−2i22i222−2200000000000000000000000000000000000000000000
χ864-44-4−4i4i4i−4i000004-4000000−4i4i00000−222222−222i2−2i2−2i22i2000000002i2−2i2−222200000000000000000000000000000000000000000000
χ874-44-4−4i4i4i−4i00000-440000004i−4i0000022−22−2222−2i22i22i2−2i2000000002i2−2i2−222200000000000000000000000000000000000000000000
χ884-44-4−4i4i4i−4i00000-440000004i−4i00000−222222−222i2−2i2−2i22i200000000−2i22i222−2200000000000000000000000000000000000000000000
χ894-4-4444-4-4-444-4-4000044-440000-44-40000000000000000000000000000000000000000000000000000000000000000
χ904-4-4444-4-4-44-4440000-444-40000-4-440000000000000000000000000000000000000000000000000000000000000000
χ914-4-44-4-4444-44-440000-44-440000-4-440000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-4444-4-44-40000444-40000-44-40000000000000000000000000000000000000000000000000000000000000000

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