Finite Group Databasebeta

← Group #12074607

Character table — Group #12074607

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222222244444488888888888888881616161616161616161616161616161616161616161616161616161616202020204040404040404040808080
order1222225510101010101044101010102444448810101010202020202481010101020202020202020202020202020204040404040404040224424444488448
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1
χ411111111111111111111111111-1-111111111-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ51111111111111111111111-1-1-1-11111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-11-11-1-111-1-11
χ61111111111111111111111-1-1-1-11111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-11-111-1-111-1
χ71111111111111111111111-1-1-1-1-1-11111111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-11-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-11111111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-11
χ911111111111111111111-1-111-1-111-1-1-1-111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-1-1111-1-1
χ1011111111111111111111-1-111-1-111-1-1-1-111111-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111-1-1-111
χ1111111111111111111111-1-111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111-11-1-1-1-1-1-111
χ1211111111111111111111-1-111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-1111111-1-1
χ1311111111111111111111-1-1-1-11111-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-11-1
χ1411111111111111111111-1-1-1-11111-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11
χ1511111111111111111111-1-1-1-111-1-1-1-1-1-111111-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11-11
χ1611111111111111111111-1-1-1-111-1-1-1-1-1-111111-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-11-1
χ1722222222222222-2-222222-20000002222-2-2-2-20000000-2-20000000000000000000022-2-20-2020000000
χ1822222222222222-2-222222-20000002222-2-2-2-20000000-2-200000000000000000000-2-222020-20000000
χ1922222222222222-2-22222-22000000-2-2-2-2-2-2-2-20000000220000000000000000000022-2-2020-20000000
χ2022222222222222-2-22222-22000000-2-2-2-2-2-2-2-200000002200000000000000000000-2-2220-2020000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−5222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52222−1+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+52−1−52−1−52000000000000000
χ22222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52222222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-21−521−521+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+521−521−521+521+521−521−521+521+52000000000000000
χ23222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−5222-2-2-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-221−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000
χ24222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−5222-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000000000
χ25222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52-2-222-2-2221−521−521+521+52−1+52−1+52−1−52−1−522-2-2−1+52−1+52−1−52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000
χ26222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52-2-222-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52-2221−521−521+521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000
χ27222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52-2-2-2-222221−521−521+521+52−1+52−1+52−1−52−1−52-22-21−521−521+521+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+52−1−52−1−521−521−521+521+52000000000000000
χ28222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52-2-2-2-222-2-21−521−521+521+52−1+52−1+52−1−52−1−522-22−1+52−1+52−1−52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000
χ29222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+5222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222−1−52−1−52−1+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+52000000000000000
χ30222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52222222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-21+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+521−521−521+521+521−521−52000000000000000
χ31222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+5222-2-2-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-221+521+521−521−52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000
χ32222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+5222-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000000
χ33222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52-2-222-2-2221+521+521−521−52−1−52−1−52−1+52−1+522-2-2−1−52−1−52−1+52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000
χ34222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52-2-222-2-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52-2221+521+521−521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000
χ35222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52-2-2-2-222221+521+521−521−52−1−52−1−52−1+52−1+52-22-21+521+521−521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000
χ36222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52-2-2-2-222-2-21+521+521−521−52−1−52−1−52−1+52−1+522-22−1−52−1−52−1+52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000
χ372222-2-2222222222-2-2-2-2-200002-20000002-22-200000000000002-22-20000000000002-22-200002-200000
χ382222-2-2222222222-2-2-2-2-200002-20000002-22-200000000000002-22-2000000000000-22-220000-2200000
χ392222-2-2222222222-2-2-2-2-20000-220000002-22-20000000000000-22-220000000000002-22-20000-2200000
χ402222-2-2222222222-2-2-2-2-20000-220000002-22-20000000000000-22-22000000000000-22-2200002-200000
χ412222-2-222222222-22-2-2-2-2002-200000000-22-220000000002-22-200000000000000002-2-2220-200000000
χ422222-2-222222222-22-2-2-2-2002-200000000-22-220000000002-22-20000000000000000-222-2-20200000000
χ432222-2-222222222-22-2-2-2-200-2200000000-22-22000000000-22-2200000000000000002-2-22-20200000000
χ442222-2-222222222-22-2-2-2-200-2200000000-22-22000000000-22-220000000000000000-222-220-200000000
χ45444444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-4-4−1+5−1−5−1+5−1−54-4000000−1+5−1+5−1−5−1−51−51−51+51+500000001−51+500000000000000000000000000000000000
χ46444444−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-4-4−1+5−1−5−1+5−1−5-440000001−51−51+51+51−51−51+51+50000000−1+5−1−500000000000000000000000000000000000
χ47444444−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-4-4−1−5−1+5−1−5−1+54-4000000−1−5−1−5−1+5−1+51+51+51−51−500000001+51−500000000000000000000000000000000000
χ48444444−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-4-4−1−5−1+5−1−5−1+5-440000001+51+51−51−51+51+51−51−50000000−1−5−1+500000000000000000000000000000000000
χ494444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−54-41−51+51−51+500004-4000000−1+51−5−1−51+50000000000000−1+51−5−1−51+5000000000000000000000000000
χ504444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−54-41−51+51−51+50000-44000000−1+51−5−1−51+500000000000001−5−1+51+5−1−5000000000000000000000000000
χ514444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-441−51+51−51+5004-4000000001−5−1+51+5−1−5000000000−1+51−5−1−51+50000000000000000000000000000000
χ524444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-441−51+51−51+500-44000000001−5−1+51+5−1−50000000001−5−1+51+5−1−50000000000000000000000000000000
χ534444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+54-41+51−51+51−500004-4000000−1−51+5−1+51−50000000000000−1−51+5−1+51−5000000000000000000000000000
χ544444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+54-41+51−51+51−50000-44000000−1−51+5−1+51−500000000000001+5−1−51−5−1+5000000000000000000000000000
χ554444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-441+51−51+51−5004-4000000001+5−1−51−5−1+5000000000−1−51+5−1+51−50000000000000000000000000000000
χ564444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-441+51−51+51−500-44000000001+5−1−51−5−1+50000000001+5−1−51−5−1+50000000000000000000000000000000
χ5744-4-44-44444-4-4-4-40044-4-4000000000000000000000000000000000000000000000000000000022−22000
χ5844-4-44-44444-4-4-4-40044-4-40000000000000000000000000000000000000000000000000000000−2222000
χ5944-4-4-444444-4-4-4-400-4-4440000002i2−2i2000000000000000000000000000002i2−2i22i2−2i20000000000000000000
χ6044-4-4-444444-4-4-4-400-4-444000000−2i22i200000000000000000000000000000−2i22i2−2i22i20000000000000000000
χ6144-4-4-44−1+5−1−5−1+5−1−51−51−51+51+5001−51+5−1+5−1−50000002i2−2i22ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ360000000000000000000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39000000000000000
χ6244-4-4-44−1+5−1−5−1+5−1−51−51−51+51+5001−51+5−1+5−1−50000002i2−2i2−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ360000000000000000000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39000000000000000
χ6344-4-4-44−1+5−1−5−1+5−1−51−51−51+51+5001−51+5−1+5−1−5000000−2i22i22ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ360000000000000000000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39000000000000000
χ6444-4-4-44−1+5−1−5−1+5−1−51−51−51+51+5001−51+5−1+5−1−5000000−2i22i2−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ360000000000000000000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39000000000000000
χ6544-4-4-44−1−5−1+5−1−5−1+51+51+51−51−5001+51−5−1−5−1+50000002i2−2i2−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ280000000000000000000000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37000000000000000
χ6644-4-4-44−1−5−1+5−1−5−1+51+51+51−51−5001+51−5−1−5−1+50000002i2−2i22ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ280000000000000000000000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37000000000000000
χ6744-4-4-44−1−5−1+5−1−5−1+51+51+51−51−5001+51−5−1−5−1+5000000−2i22i2−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ280000000000000000000000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37000000000000000
χ6844-4-4-44−1−5−1+5−1−5−1+51+51+51−51−5001+51−5−1−5−1+5000000−2i22i22ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ280000000000000000000000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37000000000000000
χ6988-8-88-8−2+25−2−25−2+25−2−252−252−252+252+2500−2+25−2−252−252+25000000000000000000000000000000000000000000000000000000000000
χ7088-8-88-8−2−25−2+25−2−25−2+252+252+252−252−2500−2−25−2+252+252−25000000000000000000000000000000000000000000000000000000000000
χ718-88-80088-8-88-88-8000000000000000000000000000000000000000000000000000000000000000000
χ728-88-800−2+25−2−252−252+25−2+252−25−2−252+2500000000000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ360000000000000000000000000000000000000
χ738-88-800−2+25−2−252−252+25−2+252−25−2−252+250000000000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ360000000000000000000000000000000000000
χ748-88-800−2−25−2+252+252−25−2−252+25−2+252−250000000000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ280000000000000000000000000000000000000
χ758-88-800−2−25−2+252+252−25−2−252+25−2+252−2500000000000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ280000000000000000000000000000000000000
χ768-8-880088-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000
χ778-8-8800−2+25−2−252−252+252−25−2+252+25−2−250000000000000000000000000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000
χ788-8-8800−2+25−2−252−252+252−25−2+252+25−2−25000000000000000000000000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000
χ798-8-8800−2−25−2+252+252−252+25−2−252−25−2+25000000000000000000000000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000
χ808-8-8800−2−25−2+252+252−252+25−2−252−25−2+250000000000000000000000000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000

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