Finite Group Databasebeta

← Group #72342475

Character table — Group #72342475

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size1111222222222222444444444444444444444444444888888888888888888888888888161616161616161616161616161616161616323232323232323232323232
order12222244444488882244444888888888888161616161616161624444488888888816161616161616161616161624444444881616161616161616224444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111-1-11111-1-1-1-1-1-1-1-111111111111-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11111-1-1-1-11-11-111-1-1-1-1-1-1
χ61111111111111111111-1-11111-1-1-1-1-1-1-1-111111111111-1-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-11-11-1-1111111
χ71111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-1-1-1-111111-11-1-1-111-1-111
χ81111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-1-1-1-1-11111-11-1111-1-111-1-1
χ91111111111111111-1-11111111-1-1-1-1-1-1-1-11111111111-1111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-1-1-11111-11-11-1-111-1-1-1-1
χ101111111111111111-1-11111111-1-1-1-1-1-1-1-11111111111-1111-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-11-111-1-11111
χ111111111111111111-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111111-1-1-1-1-11-1111-1-1-1-111
χ121111111111111111-1-11111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-111111-1-1-1-11-11-1-1-11111-1-1
χ131111111111111111-1-11-1-11111111111111111111111-1-1-1-1-1-11-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ141111111111111111-1-11-1-11111111111111111111111-1-1-1-1-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ151111111111111111-1-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ161111111111111111-1-11-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-111
χ171111-1-1-1-11111-1-1-1-111-1111-1111111-1-1-1-1-1-1iiii−i−i−i−i-11-1-11-11-1-1-1-1-1-111ii−i−iiiii−i−i−i−i11-1-1i−ii−i11ii−i−iii−i−i11-1-1i−ii−i1-1i−i
χ181111-1-1-1-11111-1-1-1-111-1111-1111111-1-1-1-1-1-1iiii−i−i−i−i-11-1-11-11-1-1-1-1-1-111ii−i−iiiii−i−i−i−i-1-111−ii−ii11ii−i−iii−i−i-1-111−ii−ii-11−ii
χ191111-1-1-1-11111-1-1-1-111-1111-1111111-1-1-1-1-1-1−i−i−i−iiiii-11-1-11-11-1-1-1-1-1-111−i−iii−i−i−i−iiiii11-1-1−ii−ii11−i−iii−i−iii11-1-1−ii−ii1-1−ii
χ201111-1-1-1-11111-1-1-1-111-1111-1111111-1-1-1-1-1-1−i−i−i−iiiii-11-1-11-11-1-1-1-1-1-111−i−iii−i−i−i−iiiii-1-111i−ii−i11−i−iii−i−iii-1-111i−ii−i-11i−i
χ211111-1-1-1-11111-1-1-1-111-1-1-11-111-1-1-1-11111-1-1iiii−i−i−i−i-1-1111-11-1-11111-1-1ii−i−i−i−i−i−iiiii11-1-1i−ii−i1-1ii−i−i−i−iii1-1-11i−i−ii-11−ii
χ221111-1-1-1-11111-1-1-1-111-1-1-11-111-1-1-1-11111-1-1iiii−i−i−i−i-1-1111-11-1-11111-1-1ii−i−i−i−i−i−iiiii-1-111−ii−ii1-1ii−i−i−i−iii-111-1−iii−i1-1i−i
χ231111-1-1-1-11111-1-1-1-111-1-1-11-111-1-1-1-11111-1-1−i−i−i−iiiii-1-1111-11-1-11111-1-1−i−iiiiiii−i−i−i−i11-1-1−ii−ii1-1−i−iiiii−i−i1-1-11−iii−i-11i−i
χ241111-1-1-1-11111-1-1-1-111-1-1-11-111-1-1-1-11111-1-1−i−i−i−iiiii-1-1111-11-1-11111-1-1−i−iiiiiii−i−i−i−i-1-111i−ii−i1-1−i−iiiii−i−i-111-1i−i−ii1-1−ii
χ251111-1-1-1-11111-1-1-1-1-1-1-1111-111-1-1-1-11111-1-1iiii−i−i−i−i11-1-1-11111-1-111-1-1ii−i−i−i−i−i−iiiii11-1-1i−ii−i-11−i−iiiii−i−i-111-1−iii−i-11−ii
χ261111-1-1-1-11111-1-1-1-1-1-1-1111-111-1-1-1-11111-1-1iiii−i−i−i−i11-1-1-11111-1-111-1-1ii−i−i−i−i−i−iiiii-1-111−ii−ii-11−i−iiiii−i−i1-1-11i−i−ii1-1i−i
χ271111-1-1-1-11111-1-1-1-1-1-1-1111-111-1-1-1-11111-1-1−i−i−i−iiiii11-1-1-11111-1-111-1-1−i−iiiiiii−i−i−i−i11-1-1−ii−ii-11ii−i−i−i−iii-111-1i−i−ii-11i−i
χ281111-1-1-1-11111-1-1-1-1-1-1-1111-111-1-1-1-11111-1-1−i−i−i−iiiii11-1-1-11111-1-111-1-1−i−iiiiiii−i−i−i−i-1-111i−ii−i-11ii−i−i−i−iii1-1-11−iii−i1-1−ii
χ291111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111111-1-1-1-1-1-1iiii−i−i−i−i1-111-1111111-1-111ii−i−iiiii−i−i−i−i11-1-1i−ii−i-1-1−i−iii−i−iii-1-111−ii−ii1-1i−i
χ301111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111111-1-1-1-1-1-1iiii−i−i−i−i1-111-1111111-1-111ii−i−iiiii−i−i−i−i-1-111−ii−ii-1-1−i−iii−i−iii11-1-1i−ii−i-11−ii
χ311111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111111-1-1-1-1-1-1−i−i−i−iiiii1-111-1111111-1-111−i−iii−i−i−i−iiiii11-1-1−ii−ii-1-1ii−i−iii−i−i-1-111i−ii−i1-1−ii
χ321111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111111-1-1-1-1-1-1−i−i−i−iiiii1-111-1111111-1-111−i−iii−i−i−i−iiiii-1-111i−ii−i-1-1ii−i−iii−i−i11-1-1−ii−ii-11i−i
χ33222222222222-2-2-2-22222222-2-22222-2-2-2-2-2-200000000222222-2-2-2-2-222-2-200000000000000000000-2-200000000000000000000
χ34222222222222-2-2-2-2222-2-222-2-2-2-2-2-22222-2-2000000002-2-2-222-2-2-222-2-22200000000000000000000-2200000000000000000000
χ35222222222222-2-2-2-2-2-222222-2-2-2-2-2-22222-2-200000000-2222-2-2-222-2-2-2-222000000000000000000002-200000000000000000000
χ36222222222222-2-2-2-2-2-22-2-222-2-22222-2-2-2-2-2-200000000-2-2-2-2-2-2-2222222-2-2000000000000000000002200000000000000000000
χ3722222222-2-222222200-200-2-22200000000-2-222222222000000-200000000-2-2-2-2000000002-2-22-2-2220000000000000000000000
χ3822222222-2-222222200-200-2-22200000000-2-222222222000000-200000000-2-2-2-200000000-222-222-2-20000000000000000000000
χ3922222222-2-222222200-200-2-22200000000-2-2-2-2-2-2-2-2-2-2000000-2000000002222000000002-2-2222-2-20000000000000000000000
χ4022222222-2-222222200-200-2-22200000000-2-2-2-2-2-2-2-2-2-2000000-200000000222200000000-222-2-2-2220000000000000000000000
χ41222222-2-222-2-2000022-222-220022-2-200000022−2−222−2−22-22-2-2-2000002-2002−22−222−2−222−2−200000000002−22−22−22−2000000000000
χ42222222-2-222-2-2000022-222-220022-2-2000000−2−222−2−2222-22-2-2-2000002-200−22−22−2−222−2−2220000000000−22−22−22−22000000000000
χ43222222-2-222-2-2000022-2-2-2-2200-2-22200000022−2−222−2−222-22-2-200000-22002−22−2−2−222−2−22200000000002−22−2−22−22000000000000
χ44222222-2-222-2-2000022-2-2-2-2200-2-222000000−2−222−2−22222-22-2-200000-2200−22−2222−2−222−2−20000000000−22−222−22−2000000000000
χ45222222-2-222-2-20000-2-2-222-2200-2-22200000022−2−222−2−2-2-22-22200000-22002−22−2−2−222−2−2220000000000−22−222−22−2000000000000
χ46222222-2-222-2-20000-2-2-222-2200-2-222000000−2−222−2−222-2-22-22200000-2200−22−2222−2−222−2−200000000002−22−2−22−22000000000000
χ47222222-2-222-2-20000-2-2-2-2-2-220022-2-200000022−2−222−2−2-22-2222000002-2002−22−222−2−222−2−20000000000−22−22−22−22000000000000
χ48222222-2-222-2-20000-2-2-2-2-2-220022-2-2000000−2−222−2−222-22-2222000002-200−22−22−2−222−2−22200000000002−22−22−22−2000000000000
χ492222-2-22222-2-2000022222-2-20022-2-2000000i2i2−i2−i2−i2−i2i2i2-2-2-22-2200000-2200i2−i2−i2i2i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ502222-2-22222-2-2000022222-2-20022-2-2000000−i2−i2i2i2i2i2−i2−i2-2-2-22-2200000-2200−i2i2i2−i2−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ512222-2-22222-2-20000222-2-2-2-200-2-222000000i2i2−i2−i2−i2−i2i2i2-222-2-22000002-200i2−i2−i2i2−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ522222-2-22222-2-20000222-2-2-2-200-2-222000000−i2−i2i2i2i2i2−i2−i2-222-2-22000002-200−i2i2i2−i2i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ532222-2-22222-2-20000-2-2222-2-200-2-222000000i2i2−i2−i2−i2−i2i2i22-2-222-2000002-200i2−i2−i2i2−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i2i2−i2−i2i2000000000000
χ542222-2-22222-2-20000-2-2222-2-200-2-222000000−i2−i2i2i2i2i2−i2−i22-2-222-2000002-200−i2i2i2−i2i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i2−i2i2i2−i2000000000000
χ552222-2-22222-2-20000-2-22-2-2-2-20022-2-2000000i2i2−i2−i2−i2−i2i2i2222-22-200000-2200i2−i2−i2i2i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i2−i2i2i2−i2000000000000
χ562222-2-22222-2-20000-2-22-2-2-2-20022-2-2000000−i2−i2i2i2i2i2−i2−i2222-22-200000-2200−i2i2i2−i2−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i2i2−i2−i2i2000000000000
χ572222-2-2-2-22222222222-2222-2-2-2222222222200000000-22-2-22-2-22222-2-2-2-200000000000000000000-2-200000000000000000000
χ582222-2-2-2-22222222222-2-2-22-2-2-2-2-2-2-2-2-2-2-22200000000-2-2222-2-222-2-2222200000000000000000000-2200000000000000000000
χ592222-2-2-2-222222222-2-2-2222-2-2-2-2-2-2-2-2-2-2-2220000000022-2-2-22-2-2-2222222000000000000000000002-200000000000000000000
χ602222-2-2-2-222222222-2-2-2-2-22-2-2-22222222222000000002-222-22-2-2-2-2-2-2-2-2-2000000000000000000002200000000000000000000
χ612222-2-2-2-2-2-222-2-2-2-200200-222200000000222i2i2i2i−2i−2i−2i−2i000000-200000000−2i−2i2i2i000000002-22-2−2i2i2i−2i0000000000000000000000
χ622222-2-2-2-2-2-222-2-2-2-200200-222200000000222i2i2i2i−2i−2i−2i−2i000000-200000000−2i−2i2i2i00000000-22-222i−2i−2i2i0000000000000000000000
χ632222-2-2-2-2-2-222-2-2-2-200200-22220000000022−2i−2i−2i−2i2i2i2i2i000000-2000000002i2i−2i−2i000000002-22-22i−2i−2i2i0000000000000000000000
χ642222-2-2-2-2-2-222-2-2-2-200200-22220000000022−2i−2i−2i−2i2i2i2i2i000000-2000000002i2i−2i−2i00000000-22-22−2i2i2i−2i0000000000000000000000
χ6544444444-4-444-4-4-4-400-400-4-4-4-4000000004400000000000000400000000000000000000000000000000000000000000000000
χ66444444-4-4-4-4-4-40000004004-40000000000002222−22−222222−22−22000000000000000−2222−222200000000000000000000000000000000000000
χ67444444-4-4-4-4-4-40000004004-4000000000000−22−222222−22−22222200000000000000022−2222−2200000000000000000000000000000000000000
χ684444-4-444-4-4-4-4000000-400440000000000002i22i2−2i2−2i2−2i2−2i22i22i2000000000000000−2i22i22i2−2i200000000000000000000000000000000000000
χ694444-4-444-4-4-4-4000000-40044000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000002i2−2i2−2i22i200000000000000000000000000000000000000
χ704444-4-4-4-4-4-444444400400-44-4-400000000-4-400000000000000400000000000000000000000000000000000000000000000000
χ7144-4-400004-4002i22i2−2i2−2i24-404-400004-4002i22i2−2i2−2i22i2−2i20000000000000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ7244-4-400004-4002i22i2−2i2−2i24-40-440000-4400−2i2−2i22i22i22i2−2i20000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ7344-4-400004-4002i22i2−2i2−2i2-4404-40000-4400−2i2−2i22i22i22i2−2i2000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ7444-4-400004-4002i22i2−2i2−2i2-440-4400004-4002i22i2−2i2−2i22i2−2i2000000000000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ7544-4-400004-400−2i2−2i22i22i24-404-400004-400−2i2−2i22i22i2−2i22i2000000000000000−2i22i2−2i22i20000000000000000000000000000000000000000000000
χ7644-4-400004-400−2i2−2i22i22i24-40-440000-44002i22i2−2i2−2i2−2i22i2000000000000000−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ7744-4-400004-400−2i2−2i22i22i2-4404-40000-44002i22i2−2i2−2i2−2i22i20000000000000002i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ7844-4-400004-400−2i2−2i22i22i2-440-4400004-400−2i2−2i22i22i2−2i22i20000000000000002i2−2i22i2−2i20000000000000000000000000000000000000000000000
χ794-4-444-44-4004-40000000000000000022−2222−22002i2−2i22i2−2i22i2−2i22i2−2i2000000000000022−2200002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ804-4-444-44-4004-40000000000000000022−2222−2200−2i22i2−2i22i2−2i22i2−2i22i2000000000000022−220000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ814-4-444-44-4004-400000000000000000−2222−2222002i2−2i22i2−2i22i2−2i22i2−2i20000000000000−22220000−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000
χ824-4-444-44-4004-400000000000000000−2222−222200−2i22i2−2i22i2−2i22i2−2i22i20000000000000−222200002i−2i2i−2i2i−2i2i−2i000000000000000000000000000000
χ834-4-444-4-4400-444-44-400000004-400000000000000000000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000
χ844-4-444-4-4400-444-44-400000004-40000000000000000000000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000
χ854-4-444-4-4400-44-44-440000000-4400000000004i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000
χ864-4-444-4-4400-44-44-440000000-440000000000−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000
χ874-4-44-444-400-444-44-40000000-4400000000004-4-44-444-4000000000000000000000000000000000000000000000000000000000
χ884-4-44-444-400-444-44-40000000-440000000000-444-44-4-44000000000000000000000000000000000000000000000000000000000
χ894-4-44-444-400-44-44-4400000004-4000000000000000000000000000000000000022−22−2222−222222−22000000000000000000000000000000
χ904-4-44-444-400-44-44-4400000004-40000000000000000000000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ914-4-44-44-44004-40000000000000000022−2222−220022−2222−22−2222−22220000000000000−22220000-22-222-22-2000000000000000000000000000000
χ924-4-44-44-44004-40000000000000000022−2222−2200−2222−222222−2222−220000000000000−222200002-22-2-22-22000000000000000000000000000000
χ934-4-44-44-44004-400000000000000000−2222−22220022−2222−22−2222−2222000000000000022−2200002-22-2-22-22000000000000000000000000000000
χ944-4-44-44-44004-400000000000000000−2222−222200−2222−222222−2222−22000000000000022−220000-22-222-22-2000000000000000000000000000000
χ9588-8-80000-88004i24i2−4i2−4i200000000000000000−4i24i200000000000000000000000000000000000000000000000000000000000000000
χ9688-8-80000-8800−4i2−4i24i24i2000000000000000004i2−4i200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8000000004i2−4i2−4i24i20000000000042−424i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000
χ988-88-8000000004i2−4i2−4i24i200000000000−4242−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000
χ998-88-800000000−4i24i24i2−4i20000000000042−42−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-800000000−4i24i24i2−4i200000000000−42424i−4i−4i4i0000000000000000000000000000000000000000000000000000000000000000000

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