Finite Group Databasebeta

← Group #72242604

Character table — Group #72242604

Order 3200.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size1111224444444444444444444444444444448888888888888888888888888888888888881616161616161616161616161616161616161616161616162525252550505050505050505050100100100100100100100100100100100100100100100100100100
order12224422445555558810101010101010101010101010101010101020202020202020202020202040404040404040404040404040404040404040404040404010101010101010101010101020202020202020202020202022224444444444224444444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1ii−i−iii−i−i-1-1-1-1-1ii−i−iii−i−i-1-1ii−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1−i−iii−i−iii-1-1-1-1-1−i−iii−i−iii-1-1−i−iii
χ511111111-1-1111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ611111111-1-1111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-11111
χ711111111-1-1111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1-111−i−iiiii−i−i11−i−iii
χ811111111-1-1111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii-1-1-111ii−i−i−i−iii11ii−i−i
χ9111111-1-111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ10111111-1-111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-11111-1-11111
χ11111111-1-111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1ii−i−iii−i−i-111-1-1ii−i−i−i−iii11−i−iii
χ12111111-1-111111111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1−i−iii−i−iii-111-1-1−i−iiiii−i−i11ii−i−i
χ13111111-1-1-1-111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ14111111-1-1-1-111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1
χ15111111-1-1-1-111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i-11111−i−iii−i−iii-1-1ii−i−i
χ16111111-1-1-1-111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii-11111ii−i−iii−i−i-1-1−i−iii
χ171-11-11-11-1i−i111111i−i-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-11-1-1i−ii−ii−ii−i11-1i−i1-11-1i−ii−ii−i1-11-1
χ181-11-11-11-1i−i111111i−i-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-11-1-1−ii−ii−ii−ii11-1i−i-11-11−ii−iii−i-11-11
χ191-11-11-11-1i−i111111i−i-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-11-1111-1-111-1-11-1-11−ii−iii−i1-1-11−ii−iii−i
χ201-11-11-11-1i−i111111i−i-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-11-111-111-1-111-1-1-11−iii−i−ii-111-1−iii−i−ii
χ211-11-11-11-1−ii111111−ii-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii1-11-1-1i−ii−ii−ii−i11-1−ii-11-11i−ii−i−ii-11-11
χ221-11-11-11-1−ii111111−ii-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii1-11-1-1−ii−ii−ii−ii11-1−ii1-11-1−ii−ii−ii1-11-1
χ231-11-11-11-1−ii111111−ii-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-11-1111-1-111-1-11-1-11i−ii−i−ii1-1-11i−ii−i−ii
χ241-11-11-11-1−ii111111−ii-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-11-111-111-1-111-1-1-11i−i−iii−i-111-1i−i−iii−i
χ251-11-11-1-11i−i111111−ii-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i1-11-1-1i−ii−ii−ii−i1-11i−i1-11-1−ii−ii−ii-11-11
χ261-11-11-1-11i−i111111−ii-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i1-11-1-1−ii−ii−ii−ii1-11i−i-11-11i−ii−i−ii1-11-1
χ271-11-11-1-11i−i111111−ii-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i-11-1111-1-111-1-11-11-1−ii−iii−i-111-1i−ii−i−ii
χ281-11-11-1-11i−i111111−ii-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i-11-111-111-1-111-1-11-1−iii−i−ii1-1-11i−i−iii−i
χ291-11-11-1-11−ii111111i−i-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii1-11-1-1i−ii−ii−ii−i1-11−ii-11-11−ii−iii−i1-11-1
χ301-11-11-1-11−ii111111i−i-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii1-11-1-1−ii−ii−ii−ii1-11−ii1-11-1i−ii−ii−i-11-11
χ311-11-11-1-11−ii111111i−i-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii-11-1111-1-111-1-11-11-1i−ii−i−ii-111-1−ii−iii−i
χ321-11-11-1-11−ii111111i−i-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii-11-111-111-1-111-1-11-1i−i−iii−i1-1-11−iii−i−ii
χ332222-2-2000022222200222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002222-22222-2-2-2-2-2000000000000000000
χ342222-2-2000022222200222222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000002222-2-2-2-2-22222-2000000000000000000
χ352222-2-2000022222200222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000-2-2-2-222i2i−2i−2i−2i−2i2i2i2000000000000000000
χ362222-2-2000022222200222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000-2-2-2-22−2i−2i2i2i2i2i−2i−2i2000000000000000000
χ372-22-2-22000022222200-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000000000000000000000000000002-22-222i−2i2i−2i−2i2i−2i2i-2000000000000000000
χ382-22-2-22000022222200-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-22222220000000000000000000000000000000000000000000000002-22-22−2i2i−2i2i2i−2i2i−2i-2000000000000000000
χ392-22-2-22000022222200-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000000000000000-22-22-22-2-22-222-22000000000000000000
χ402-22-2-22000022222200-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000000000000000000000-22-22-2-222-22-2-222000000000000000000
χ4144444444444-1-1-1-1-1444-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-144-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-100000000000000000000000000000000
χ424444444444-14-1-1-1-144-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-144-1-1-1-1-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-100000000000000000000000000000000
χ434444444444-1-1−1+53−523+52−1−544-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1-1-1−1+5−1+53−523−523+523+52−1−5−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−500000000000000000000000000000000
χ444444444444-1-13−52−1−5−1+53+5244-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-1-1-13−523−52−1−5−1−5−1+5−1+53+523+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+5200000000000000000000000000000000
χ454444444444-1-13+52−1+5−1−53−5244-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-1-1-13+523+52−1+5−1+5−1−5−1−53−523−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−5200000000000000000000000000000000
χ464444444444-1-1−1−53+523−52−1+544-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-1-1-1-1−1−5−1−53+523+523−523−52−1+5−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+500000000000000000000000000000000
χ4744444444-4-44-1-1-1-1-1-4-44-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-4-41111111111-4-411111111114-1-1-1-1-14-1-1-1-1-1-411111-41111100000000000000000000000000000000
χ4844444444-4-4-14-1-1-1-1-4-4-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-111-4-41111111111-4-411111111-14-1-1-1-1-14-1-1-1-11-411111-4111100000000000000000000000000000000
χ4944444444-4-4-1-1−1+53−523+52−1−5-4-4-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−511111−51−5−3+52−3+52−3−52−3−521+51+511111−51−5−3+52−3+52−3−52−3−521+51+5-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−5111−5−3+52−3−521+5111−5−3+52−3−521+500000000000000000000000000000000
χ5044444444-4-4-1-13−52−1−5−1+53+52-4-4-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+521111−3+52−3+521+51+51−51−5−3−52−3−521111−3+52−3+521+51+51−51−5−3−52−3−52-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+5211−3+521+51−5−3−5211−3+521+51−5−3−5200000000000000000000000000000000
χ5144444444-4-4-1-13+52−1+5−1−53−52-4-4-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−521111−3−52−3−521−51−51+51+5−3+52−3+521111−3−52−3−521−51−51+51+5−3+52−3+52-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−5211−3−521−51+5−3+5211−3−521−51+5−3+5200000000000000000000000000000000
χ5244444444-4-4-1-1−1−53+523−52−1+5-4-4-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+511111+51+5−3−52−3−52−3+52−3+521−51−511111+51+5−3−52−3−52−3+52−3+521−51−5-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+5111+5−3−52−3+521−5111+5−3−52−3+521−500000000000000000000000000000000
χ53444444-4-4444-1-1-1-1-1-4-44-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-1-4-41111111111-4-41111111111-411111-4111114-1-1-1-1-14-1-1-1-1-100000000000000000000000000000000
χ54444444-4-444-14-1-1-1-1-4-4-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-1-14-1-1-1-111-4-41111111111-4-4111111111-411111-41111-14-1-1-1-1-14-1-1-1-100000000000000000000000000000000
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χ1268-8-88000000-2-23+5−2+25−2−253−50022−3−52−252+25−3+522−3−52−252+25−3+5-2-23+5−2+25−2−253−5000000000000−1010−1010−3ζ7+3ζ13+2ζ21−3ζ23+2ζ29−2ζ31+3ζ37−2ζ393ζ7−3ζ13−2ζ21+3ζ23−2ζ29+2ζ31−3ζ37+2ζ3900002ζ7−2ζ13−3ζ21+2ζ23−3ζ29+3ζ31−2ζ37+3ζ39−2ζ7+2ζ13+3ζ21−2ζ23+3ζ29−3ζ31+2ζ37−3ζ3910−1010−103ζ7−3ζ13−2ζ21+3ζ23−2ζ29+2ζ31−3ζ37+2ζ39−3ζ7+3ζ13+2ζ21−3ζ23+2ζ29−2ζ31+3ζ37−2ζ390000−2ζ7+2ζ13+3ζ21−2ζ23+3ζ29−3ζ31+2ζ37−3ζ392ζ7−2ζ13−3ζ21+2ζ23−3ζ29+3ζ31−2ζ37+3ζ3900000000000000000000000000000000000000000000000000000000
χ1278-8-88000000-2-2−2−253+53−5−2+2500222+25−3−5−3+52−25222+25−3−5−3+52−25-2-2−2−253+53−5−2+2500000000000010−10−101000−3ζ7+3ζ13+2ζ21−3ζ23+2ζ29−2ζ31+3ζ37−2ζ393ζ7−3ζ13−2ζ21+3ζ23−2ζ29+2ζ31−3ζ37+2ζ392ζ7−2ζ13−3ζ21+2ζ23−3ζ29+3ζ31−2ζ37+3ζ39−2ζ7+2ζ13+3ζ21−2ζ23+3ζ29−3ζ31+2ζ37−3ζ3900−101010−10003ζ7−3ζ13−2ζ21+3ζ23−2ζ29+2ζ31−3ζ37+2ζ39−3ζ7+3ζ13+2ζ21−3ζ23+2ζ29−2ζ31+3ζ37−2ζ39−2ζ7+2ζ13+3ζ21−2ζ23+3ζ29−3ζ31+2ζ37−3ζ392ζ7−2ζ13−3ζ21+2ζ23−3ζ29+3ζ31−2ζ37+3ζ390000000000000000000000000000000000000000000000000000000000
χ1288-8-88000000-2-2−2−253+53−5−2+2500222+25−3−5−3+52−25222+25−3−5−3+52−25-2-2−2−253+53−5−2+25000000000000−101010−10003ζ7−3ζ13−2ζ21+3ζ23−2ζ29+2ζ31−3ζ37+2ζ39−3ζ7+3ζ13+2ζ21−3ζ23+2ζ29−2ζ31+3ζ37−2ζ39−2ζ7+2ζ13+3ζ21−2ζ23+3ζ29−3ζ31+2ζ37−3ζ392ζ7−2ζ13−3ζ21+2ζ23−3ζ29+3ζ31−2ζ37+3ζ390010−10−101000−3ζ7+3ζ13+2ζ21−3ζ23+2ζ29−2ζ31+3ζ37−2ζ393ζ7−3ζ13−2ζ21+3ζ23−2ζ29+2ζ31−3ζ37+2ζ392ζ7−2ζ13−3ζ21+2ζ23−3ζ29+3ζ31−2ζ37+3ζ39−2ζ7+2ζ13+3ζ21−2ζ23+3ζ29−3ζ31+2ζ37−3ζ390000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.