Finite Group Databasebeta

← Group #12252249

Character table — Group #12252249

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size1122222444448888224444488888161616162244444888881616161655101010101020202020204040404011222224444488882244444888881616161622444448888816161616551010101010202020202040404040
order12244888161616162288510102020404040808080801010404051010202040404080808080101040402224488816161616228822244888161616162288101010202040404080808080101040401010102020404040808080801010404022244888161616162288
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1
χ311111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-1
χ411111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111
χ511-11-1-1-11ii−i−i1-1i−i11-11-1-1-11ii−i−i1-1i−i11-11-1-1-11ii−i−i1-1i−i11-11-1-1-11ii−i−i1-1i−i11-11-1-1-11ii−i−i1-1i−i11-11-1-1-11ii−i−i1-1i−i11-11-1-1-11ii−i−i1-1i−i11-11-1-1-11ii−i−i1-1i−i
χ611-11-1-1-11ii−i−i-11−ii11-11-1-1-11ii−i−i-11−ii11-11-1-1-11ii−i−i-11−ii11-11-1-1-11ii−i−i-11−ii11-11-1-1-11ii−i−i-11−ii11-11-1-1-11ii−i−i-11−ii11-11-1-1-11ii−i−i-11−ii11-11-1-1-11ii−i−i-11−ii
χ711-11-1-1-11−i−iii1-1−ii11-11-1-1-11−i−iii1-1−ii11-11-1-1-11−i−iii1-1−ii11-11-1-1-11−i−iii1-1−ii11-11-1-1-11−i−iii1-1−ii11-11-1-1-11−i−iii1-1−ii11-11-1-1-11−i−iii1-1−ii11-11-1-1-11−i−iii1-1−ii
χ811-11-1-1-11−i−iii-11i−i11-11-1-1-11−i−iii-11i−i11-11-1-1-11−i−iii-11i−i11-11-1-1-11−i−iii-11i−i11-11-1-1-11−i−iii-11i−i11-11-1-1-11−i−iii-11i−i11-11-1-1-11−i−iii-11i−i11-11-1-1-11−i−iii-11i−i
χ922222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-20000000022222-2-2-200000000
χ10222-2-2000i2−i2i2−i20000222-2-2000i2−i2i2−i20000222-2-2000i2−i2i2−i20000222-2-2000i2−i2i2−i20000222-2-2000i2−i2i2−i20000222-2-2000i2−i2i2−i20000222-2-2000i2−i2i2−i20000222-2-2000i2−i2i2−i20000
χ11222-2-2000−i2i2−i2i20000222-2-2000−i2i2−i2i20000222-2-2000−i2i2−i2i20000222-2-2000−i2i2−i2i20000222-2-2000−i2i2−i2i20000222-2-2000−i2i2−i2i20000222-2-2000−i2i2−i2i20000222-2-2000−i2i2−i2i20000
χ1222-22-222-20000000022-22-222-20000000022-22-222-20000000022-22-222-20000000022-22-222-20000000022-22-222-20000000022-22-222-20000000022-22-222-200000000
χ1322-2-220002−2−22000022-2-220002−2−22000022-2-220002−2−22000022-2-220002−2−22000022-2-220002−2−22000022-2-220002−2−22000022-2-220002−2−22000022-2-220002−2−220000
χ1422-2-22000−222−2000022-2-22000−222−2000022-2-22000−222−2000022-2-22000−222−2000022-2-22000−222−2000022-2-22000−222−2000022-2-22000−222−2000022-2-22000−222−20000
χ154-400022−220000000004-400022−220000000004-400022−220000000004-400022−220000000004-400022−220000000004-400022−220000000004-400022−220000000004-400022−22000000000
χ164-4000−22220000000004-4000−22220000000004-4000−22220000000004-4000−22220000000004-4000−22220000000004-4000−22220000000004-4000−22220000000004-4000−2222000000000
χ17111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ18111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ1911111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-111111111-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ2011111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-11111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1
χ2111-11-1-1-11ii−i−i1-1i−i11-11-1-1-11ii−i−i1-1i−i11-11-1-1-11ii−i−i1-1i−i-1-11-1111-1−i−iii-11−ii11-11-1-1-11ii−i−i1-1i−i11-11-1-1-11ii−i−i1-1i−i11-11-1-1-11ii−i−i1-1i−i-1-11-1111-1−i−iii-11−ii
χ2211-11-1-1-11ii−i−i-11−ii11-11-1-1-11ii−i−i-11−ii11-11-1-1-11ii−i−i-11−ii-1-11-1111-1−i−iii1-1i−i11-11-1-1-11ii−i−i-11−ii11-11-1-1-11ii−i−i-11−ii11-11-1-1-11ii−i−i-11−ii-1-11-1111-1−i−iii1-1i−i
χ2311-11-1-1-11−i−iii1-1−ii11-11-1-1-11−i−iii1-1−ii11-11-1-1-11−i−iii1-1−ii-1-11-1111-1ii−i−i-11i−i11-11-1-1-11−i−iii1-1−ii11-11-1-1-11−i−iii1-1−ii11-11-1-1-11−i−iii1-1−ii-1-11-1111-1ii−i−i-11i−i
χ2411-11-1-1-11−i−iii-11i−i11-11-1-1-11−i−iii-11i−i11-11-1-1-11−i−iii-11i−i-1-11-1111-1ii−i−i1-1−ii11-11-1-1-11−i−iii-11i−i11-11-1-1-11−i−iii-11i−i11-11-1-1-11−i−iii-11i−i-1-11-1111-1ii−i−i1-1−ii
χ2522222-2-2-20000000022222-2-2-20000000022222-2-2-200000000-2-2-2-2-22220000000022222-2-2-20000000022222-2-2-20000000022222-2-2-200000000-2-2-2-2-222200000000
χ26222-2-2000i2−i2i2−i20000222-2-2000i2−i2i2−i20000222-2-2000i2−i2i2−i20000-2-2-222000−i2i2−i2i20000222-2-2000i2−i2i2−i20000222-2-2000i2−i2i2−i20000222-2-2000i2−i2i2−i20000-2-2-222000−i2i2−i2i20000
χ27222-2-2000−i2i2−i2i20000222-2-2000−i2i2−i2i20000222-2-2000−i2i2−i2i20000-2-2-222000i2−i2i2−i20000222-2-2000−i2i2−i2i20000222-2-2000−i2i2−i2i20000222-2-2000−i2i2−i2i20000-2-2-222000i2−i2i2−i20000
χ2822-22-222-20000000022-22-222-20000000022-22-222-200000000-2-22-22-2-220000000022-22-222-20000000022-22-222-20000000022-22-222-200000000-2-22-22-2-2200000000
χ2922-2-220002−2−22000022-2-220002−2−22000022-2-220002−2−220000-2-222-2000−222−2000022-2-220002−2−22000022-2-220002−2−22000022-2-220002−2−220000-2-222-2000−222−20000
χ3022-2-22000−222−2000022-2-22000−222−2000022-2-22000−222−20000-2-222-20002−2−22000022-2-22000−222−2000022-2-22000−222−2000022-2-22000−222−20000-2-222-20002−2−220000
χ314-400022−220000000004-400022−220000000004-400022−22000000000-44000−22220000000004-400022−220000000004-400022−220000000004-400022−22000000000-44000−2222000000000
χ324-4000−22220000000004-4000−22220000000004-4000−2222000000000-4400022−220000000004-4000−22220000000004-4000−22220000000004-4000−2222000000000-4400022−22000000000
χ332222222222222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−5200000000000000002222222222222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−520000000000000000
χ34222222222222-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+520000000000000000222222222222-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+520000000000000000
χ3522222222-2-2-2-222-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−521+521+52000000000000000022222222-2-2-2-222-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−521+521+520000000000000000
χ3622222222-2-2-2-2-2-222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−521−52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+52−1−52−1−52000000000000000022222222-2-2-2-2-2-222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−521−52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+52−1−52−1−520000000000000000
χ3722-22-2-2-222i2i−2i−2i2-22i−2i−1+52−1+521−52−1+521−521−521−52−1+52−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ38−1+521−52−ζ22−ζ38ζ22+ζ38−1−52−1−521+52−1−521+521+521+52−1−52−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ14−1−521+52−ζ6−ζ14ζ6+ζ14000000000000000022-22-2-2-222i2i−2i−2i2-22i−2i−1+52−1+521−52−1+521−521−521−52−1+52−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ38−1+521−52−ζ22−ζ38ζ22+ζ38−1−52−1−521+52−1−521+521+521+52−1−52−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ14−1−521+52−ζ6−ζ14ζ6+ζ140000000000000000
χ3822-22-2-2-222i2i−2i−2i-22−2i2i−1+52−1+521−52−1+521−521−521−52−1+52−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ381−52−1+52ζ22+ζ38−ζ22−ζ38−1−52−1−521+52−1−521+521+521+52−1−52−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ141+52−1−52ζ6+ζ14−ζ6−ζ14000000000000000022-22-2-2-222i2i−2i−2i-22−2i2i−1+52−1+521−52−1+521−521−521−52−1+52−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ381−52−1+52ζ22+ζ38−ζ22−ζ38−1−52−1−521+52−1−521+521+521+52−1−52−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ141+52−1−52ζ6+ζ14−ζ6−ζ140000000000000000
χ3922-22-2-2-22−2i−2i2i2i2-2−2i2i−1+52−1+521−52−1+521−521−521−52−1+52ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ38−1+521−52ζ22+ζ38−ζ22−ζ38−1−52−1−521+52−1−521+521+521+52−1−52ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ14−1−521+52ζ6+ζ14−ζ6−ζ14000000000000000022-22-2-2-22−2i−2i2i2i2-2−2i2i−1+52−1+521−52−1+521−521−521−52−1+52ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ38−1+521−52ζ22+ζ38−ζ22−ζ38−1−52−1−521+52−1−521+521+521+52−1−52ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ14−1−521+52ζ6+ζ14−ζ6−ζ140000000000000000
χ4022-22-2-2-22−2i−2i2i2i-222i−2i−1+52−1+521−52−1+521−521−521−52−1+52ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ381−52−1+52−ζ22−ζ38ζ22+ζ38−1−52−1−521+52−1−521+521+521+52−1−52ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ141+52−1−52−ζ6−ζ14ζ6+ζ14000000000000000022-22-2-2-22−2i−2i2i2i-222i−2i−1+52−1+521−52−1+521−521−521−52−1+52ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ381−52−1+52−ζ22−ζ38ζ22+ζ38−1−52−1−521+52−1−521+521+521+52−1−52ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ141+52−1−52−ζ6−ζ14ζ6+ζ140000000000000000
χ4144444-4-4-400000000−1+5−1+5−1+5−1+5−1+51−51−51−500000000−1−5−1−5−1−5−1−5−1−51+51+51+500000000000000000000000044444-4-4-400000000−1+5−1+5−1+5−1+5−1+51−51−51−500000000−1−5−1−5−1−5−1−5−1−51+51+51+5000000000000000000000000
χ42444-4-40002i2−2i22i2−2i20000−1+5−1+5−1+51−51−5000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ370000−1−5−1−5−1−51+51+5000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ3900000000000000000000444-4-40002i2−2i22i2−2i20000−1+5−1+5−1+51−51−5000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ370000−1−5−1−5−1−51+51+5000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ3900000000000000000000
χ43444-4-4000−2i22i2−2i22i20000−1+5−1+5−1+51−51−5000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ370000−1−5−1−5−1−51+51+5000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ3900000000000000000000444-4-4000−2i22i2−2i22i20000−1+5−1+5−1+51−51−5000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ370000−1−5−1−5−1−51+51+5000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ3900000000000000000000
χ4444-44-444-400000000−1+5−1+51−5−1+51−5−1+5−1+51−500000000−1−5−1−51+5−1−51+5−1−5−1−51+500000000000000000000000044-44-444-400000000−1+5−1+51−5−1+51−5−1+5−1+51−500000000−1−5−1−51+5−1−51+5−1−5−1−51+5000000000000000000000000
χ4544-4-4400022−22−22220000−1+5−1+51−51−5−1+5000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ370000−1−5−1−51+51+5−1−5000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ390000000000000000000044-4-4400022−22−22220000−1+5−1+51−51−5−1+5000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ370000−1−5−1−51+51+5−1−5000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ3900000000000000000000
χ4644-4-44000−222222−220000−1+5−1+51−51−5−1+5000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ370000−1−5−1−51+51+5−1−5000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ390000000000000000000044-4-44000−222222−220000−1+5−1+51−51−5−1+5000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ370000−1−5−1−51+51+5−1−5000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ3900000000000000000000
χ478-800042−42000000000−2+252−25000−2ζ7+2ζ13−2ζ23+2ζ372ζ7−2ζ13+2ζ23−2ζ37000000000−2−252+250002ζ21+2ζ29−2ζ31−2ζ39−2ζ21−2ζ29+2ζ31+2ζ3900000000000000000000000008-800042−42000000000−2+252−25000−2ζ7+2ζ13−2ζ23+2ζ372ζ7−2ζ13+2ζ23−2ζ37000000000−2−252+250002ζ21+2ζ29−2ζ31−2ζ39−2ζ21−2ζ29+2ζ31+2ζ390000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.