Finite Group Databasebeta

← Group #72342486

Character table — Group #72342486

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94
size11112222222222224444444444444448888888888888888888888888888816161616161616161616161616161616161616161616161632323232323232323232
order122222444444888822444448888888822244444448888888888816161616161616164444448888881616161616161616161616162444444488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111111-1-11111111111111111111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-111111-1-111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111-1-11111-1-1-1-11111111-1-1-111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ61111111111111111111-1-11111-1-1-1-11111111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ71111111111111111111-1-11111-1-1-1-1111-1-111-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-111-1-11111
χ81111111111111111111-1-11111-1-1-1-1111-1-111-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-111111111-1-11111-1-1-1-1
χ91111111111111111-1-11111111-1-1-1-111-111-1-1111111-1-111-1-1-1-1-1-111111111111111-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1
χ101111111111111111-1-11111111-1-1-1-111-111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-11111-1-111
χ111111111111111111-1-11111111-1-1-1-111-1-1-1-1-1111-1-11-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111-1-111-1-111
χ121111111111111111-1-11111111-1-1-1-111-1-1-1-1-1111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111111111-1-1-1-1111111-1-1-1-111-1-1
χ131111111111111111-1-11-1-11111111111-111-1-1-1-1-1111-1-1-1-111111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ141111111111111111-1-11-1-11111111111-111-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ151111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ161111111111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ171111-1-1-1-11111-1-1-1-111-1111-11111-1-1-1-1-1111-11-1-1-1-11-1-1-1-11-111-1-1ii−i−iii−i−i1-1i−ii−i1111-1-1ii−i−iii−i−iii−i−i1-11-1i−ii−ii−i
χ181111-1-1-1-11111-1-1-1-111-1111-11111-1-1-1-1-1111-11-1-1-1-11-1-1-1-11-111-1-1−i−iii−i−iii1-1−ii−ii1111-1-1−i−iii−i−iii−i−iii1-11-1−ii−ii−ii
χ191111-1-1-1-11111-1-1-1-111-1111-11111-1-1-1-1-1-1-11-11-1-1111-1-1-1-11-111-1-1ii−i−iii−i−i-11−ii−ii11-1-111ii−i−iii−i−iii−i−i-11-11−ii−ii−ii
χ201111-1-1-1-11111-1-1-1-111-1111-11111-1-1-1-1-1-1-11-11-1-1111-1-1-1-11-111-1-1−i−iii−i−iii-11i−ii−i11-1-111−i−iii−i−iii−i−iii-11-11i−ii−ii−i
χ211111-1-1-1-11111-1-1-1-111-1-1-11-111-1-111-1-1-1111-1-111-1-11-1-111-11-1-111ii−i−iii−i−i1-1i−ii−i1-1-1-111ii−i−i−i−iii−i−iii1-1-11i−i−ii−ii
χ221111-1-1-1-11111-1-1-1-111-1-1-11-111-1-111-1-1-1111-1-111-1-11-1-111-11-1-111−i−iii−i−iii1-1−ii−ii1-1-1-111−i−iiiii−i−iii−i−i1-1-11−iii−ii−i
χ231111-1-1-1-11111-1-1-1-111-1-1-11-111-1-111-1-1-1-1-11-1-111111-1-111-11-1-111ii−i−iii−i−i-11−ii−ii1-111-1-1ii−i−i−i−iii−i−iii-111-1−iii−ii−i
χ241111-1-1-1-11111-1-1-1-111-1-1-11-111-1-111-1-1-1-1-11-1-111111-1-111-11-1-111−i−iii−i−iii-11i−ii−i1-111-1-1−i−iiiii−i−iii−i−i-111-1i−i−ii−ii
χ251111-1-1-1-11111-1-1-1-1-1-1-1111-111-1-111-1-1111-111-1-1-1-1111-1-1-11-1-111ii−i−iii−i−i1-1i−ii−i-11-1-111−i−iiiii−i−i−i−iii-111-1−iii−i−ii
χ261111-1-1-1-11111-1-1-1-1-1-1-1111-111-1-111-1-1111-111-1-1-1-1111-1-1-11-1-111−i−iii−i−iii1-1−ii−ii-11-1-111ii−i−i−i−iiiii−i−i-111-1i−i−iii−i
χ271111-1-1-1-11111-1-1-1-1-1-1-1111-111-1-111-1-11-1-1-111-1-111111-1-1-11-1-111ii−i−iii−i−i-11−ii−ii-1111-1-1−i−iiiii−i−i−i−iii1-1-11i−i−iii−i
χ281111-1-1-1-11111-1-1-1-1-1-1-1111-111-1-111-1-11-1-1-111-1-111111-1-1-11-1-111−i−iii−i−iii-11i−ii−i-1111-1-1ii−i−i−i−iiiii−i−i1-1-11−iii−i−ii
χ291111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11111-1-1-1-1111-11-111-1-1111111-111-1-1ii−i−iii−i−i1-1i−ii−i-1-111-1-1−i−iii−i−iiiii−i−i-11-11−ii−iii−i
χ301111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11111-1-1-1-1111-11-111-1-1111111-111-1-1−i−iii−i−iii1-1−ii−ii-1-111-1-1ii−i−iii−i−i−i−iii-11-11i−ii−i−ii
χ311111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11111-1-1-1-11-1-1-11-11111111111-111-1-1ii−i−iii−i−i-11−ii−ii-1-1-1-111−i−iii−i−iiiii−i−i1-11-1i−ii−i−ii
χ321111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11111-1-1-1-11-1-1-11-11111111111-111-1-1−i−iii−i−iii-11i−ii−i-1-1-1-111ii−i−iii−i−i−i−iii1-11-1−ii−iii−i
χ33222222222222-2-2-2-22222222-2-22222-2-22002222200-2-2-2-2-222-2-2-2-200000000000000-2-200000000000000000000000000
χ34222222222222-2-2-2-2222-2-222-2-2-2-2-2-2-2-220022-2-2-200-2-2-222-2-2222200000000000000-2200000000000000000000000000
χ35222222222222-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-200-2-222200-222-2-2-2-22222000000000000002-200000000000000000000000000
χ36222222222222-2-2-2-2-2-22-2-222-2-22222-2-2-200-2-2-2-2-200-2222222-2-2-2-2000000000000002200000000000000000000000000
χ372222222222-2-2222200-200-2-2220000-2-20220000022-200000000002222-2-2-2-2-2-222-2-20000000000000000000000000000
χ382222222222-2-2222200-200-2-2220000-2-20220000022-20000000000-2-2-2-22222-2-2-2-2220000000000000000000000000000
χ392222222222-2-2222200-200-2-2220000-2-20-2-200000-2-2-200000000002222-2-2-2-222-2-2220000000000000000000000000000
χ402222222222-2-2222200-200-2-2220000-2-20-2-200000-2-2-20000000000-2-2-2-222222222-2-20000000000000000000000000000
χ41222222-2-2-2-222000022-222-220022-2-200200-2-2-22-20000000-2200002−22−22−22−20000000000002−22−22−22−22−22−20000000000
χ42222222-2-2-2-222000022-222-220022-2-200200-2-2-22-20000000-220000−22−22−22−22000000000000−22−22−22−22−22−220000000000
χ43222222-2-2-2-222000022-2-2-2-2200-2-22200200-2-22-2200000002-200002−22−22−22−20000000000002−22−2−22−22−22−220000000000
χ44222222-2-2-2-222000022-2-2-2-2200-2-22200200-2-22-2200000002-20000−22−22−22−22000000000000−22−222−22−22−22−20000000000
χ45222222-2-2-2-2220000-2-2-222-2200-2-22200-20022-22-200000002-200002−22−22−22−2000000000000−22−222−22−2−22−220000000000
χ46222222-2-2-2-2220000-2-2-222-2200-2-22200-20022-22-200000002-20000−22−22−22−220000000000002−22−2−22−222−22−20000000000
χ47222222-2-2-2-2220000-2-2-2-2-2-220022-2-200-200222-220000000-2200002−22−22−22−2000000000000−22−22−22−222−22−20000000000
χ48222222-2-2-2-2220000-2-2-2-2-2-220022-2-200-200222-220000000-220000−22−22−22−220000000000002−22−22−22−2−22−220000000000
χ492222-2-222-2-222000022222-2-200222200-200-22-2-220000000-2-20000i2−i2−i2i2i2−i2−i2i2000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000
χ502222-2-222-2-222000022222-2-200222200-200-22-2-220000000-2-20000−i2i2i2−i2−i2i2i2−i2000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000
χ512222-2-222-2-2220000222-2-2-2-200-2-2-2-200-200-2222-20000000220000i2−i2−i2i2i2−i2−i2i2000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i20000000000
χ522222-2-222-2-2220000222-2-2-2-200-2-2-2-200-200-2222-20000000220000−i2i2i2−i2−i2i2i2−i2000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i20000000000
χ532222-2-222-2-2220000-2-2222-2-200-2-2-2-2002002-2-2-220000000220000i2−i2−i2i2i2−i2−i2i2000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000
χ542222-2-222-2-2220000-2-2222-2-200-2-2-2-2002002-2-2-220000000220000−i2i2i2−i2−i2i2i2−i2000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000
χ552222-2-222-2-2220000-2-22-2-2-2-2002222002002-222-20000000-2-20000i2−i2−i2i2i2−i2−i2i2000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000
χ562222-2-222-2-2220000-2-22-2-2-2-2002222002002-222-20000000-2-20000−i2i2i2−i2−i2i2i2−i2000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000
χ572222-2-2-2-22222222222-2222-2-2-222-2-222-2002-22-2-200-222222-2-2-22200000000000000-2-200000000000000000000000000
χ582222-2-2-2-22222222222-2-2-22-2-2-2-2-22222-2002-2-22200-222-2-2-2222-2-200000000000000-2200000000000000000000000000
χ592222-2-2-2-222222222-2-2-2222-2-2-2-2-22222200-222-2-200-2-2-222-2222-2-2000000000000002-200000000000000000000000000
χ602222-2-2-2-222222222-2-2-2-2-22-2-2-222-2-222200-22-22200-2-2-2-2-22-2-2-222000000000000002200000000000000000000000000
χ612222-2-2-2-222-2-2-2-2-2-200200-222200002202200000-2-2-200000000002i2i−2i−2i−2i−2i2i2i-222i−2i−2i2i0000000000000000000000000000
χ622222-2-2-2-222-2-2-2-2-2-200200-222200002202200000-2-2-20000000000−2i−2i2i2i2i2i−2i−2i-22−2i2i2i−2i0000000000000000000000000000
χ632222-2-2-2-222-2-2-2-2-2-200200-22220000220-2-20000022-200000000002i2i−2i−2i−2i−2i2i2i2-2−2i2i2i−2i0000000000000000000000000000
χ642222-2-2-2-222-2-2-2-2-2-200200-22220000220-2-20000022-20000000000−2i−2i2i2i2i2i−2i−2i2-22i−2i−2i2i0000000000000000000000000000
χ654444444444-4-4-4-4-4-400-400-4-4-4-4000044000000000040000000000000000000000000000000000000000000000000000
χ66444444-4-4-4-4-4-40000004004-40000000000000000000000000000022−2222−22−2222−22220000000000000000000000000000000000
χ67444444-4-4-4-4-4-40000004004-400000000000000000000000000000−2222−222222−2222−220000000000000000000000000000000000
χ684444-4-444-4-4-4-4000000-40044000000000000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000
χ694444-4-444-4-4-4-4000000-4004400000000000000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000
χ704444-4-4-4-444-4-4444400400-44-4-40000-4-4000000000040000000000000000000000000000000000000000000000000000
χ7144-4-40000004-42i2−2i22i2−2i24-404-400004-4002i2−2i2000000000002i2−2i22i2−2i200002i2−2i2000000000000000000000000000000000000000000
χ7244-4-40000004-42i2−2i22i2−2i24-40-440000-44002i2−2i2000000000002i2−2i2−2i22i20000−2i22i2000000000000000000000000000000000000000000
χ7344-4-40000004-42i2−2i22i2−2i2-4404-40000-44002i2−2i200000000000−2i22i22i2−2i20000−2i22i2000000000000000000000000000000000000000000
χ7444-4-40000004-42i2−2i22i2−2i2-440-4400004-4002i2−2i200000000000−2i22i2−2i22i200002i2−2i2000000000000000000000000000000000000000000
χ7544-4-40000004-4−2i22i2−2i22i24-404-400004-400−2i22i200000000000−2i22i2−2i22i20000−2i22i2000000000000000000000000000000000000000000
χ7644-4-40000004-4−2i22i2−2i22i24-40-440000-4400−2i22i200000000000−2i22i22i2−2i200002i2−2i2000000000000000000000000000000000000000000
χ7744-4-40000004-4−2i22i2−2i22i2-4404-40000-4400−2i22i2000000000002i2−2i2−2i22i200002i2−2i2000000000000000000000000000000000000000000
χ7844-4-40000004-4−2i22i2−2i22i2-440-4400004-400−2i22i2000000000002i2−2i22i2−2i20000−2i22i2000000000000000000000000000000000000000000
χ794-44-44-44-44-40044-4-400000004-400000004-4000004-400000000000000000000000000000000000000000000000000000
χ804-44-44-44-44-40044-4-400000004-40000000-4400000-4400000000000000000000000000000000000000000000000000000
χ814-44-44-44-44-400-4-4440000000-4400000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000000000
χ824-44-44-44-44-400-4-4440000000-440000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000000000
χ834-44-4-44-444-40044-4-40000000-4400000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000000000
χ844-44-4-44-444-40044-4-40000000-440000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000000000
χ854-44-4-44-444-400-4-44400000004-400000004-400000-4400000000000000000000000000000000000000000000000000000
χ864-44-4-44-444-400-4-44400000004-40000000-44000004-400000000000000000000000000000000000000000000000000000
χ8788-8-8000000-884i2−4i24i2−4i20000000000000−4i24i2000000000000000000000000000000000000000000000000000000000000000
χ8888-8-8000000-88−4i24i2−4i24i200000000000004i2−4i2000000000000000000000000000000000000000000000000000000000000000
χ898-88-88-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-88000000004i2−4i2−4i24i20000000000042−4200000000000000000004i−4i00000000000000000000000000000000000000000000
χ928-8-88000000004i2−4i2−4i24i200000000000−42420000000000000000000−4i4i00000000000000000000000000000000000000000000
χ938-8-8800000000−4i24i24i2−4i20000000000042−420000000000000000000−4i4i00000000000000000000000000000000000000000000
χ948-8-8800000000−4i24i24i2−4i200000000000−424200000000000000000004i−4i00000000000000000000000000000000000000000000

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