Finite Group Databasebeta

← Group #12073661

Character table — Group #12073661

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222222222444444448888888888888161616161616161616161616161616161616161616161616161616161616202020202020404040404080808080
order1222225510101010101022441010101022444101010102020202024881010101010101010202020202020202020204040404040404040224444244444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-1111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1111111-1-1
χ911111111111111-1-11111111-11-1-1-1-1-1-111111-11-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-111-1-11-11-1
χ1011111111111111-1-11111111-11-1-1-1-1-1-111111-11-111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-111-11-11
χ1111111111111111-1-11111111-11-1-1-1-1-1-11111-11-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-111-1-1-11-11
χ1211111111111111-1-11111111-11-1-1-1-1-1-11111-11-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111-1-1111-11-1
χ1311111111111111-1-1111111-11-11-1-1-1-1-111111-1-11-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-11
χ1411111111111111-1-1111111-11-11-1-1-1-1-111111-1-11-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-111-1
χ1511111111111111-1-1111111-11-11-1-1-1-1-11111-111-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-111-111-1
χ1611111111111111-1-1111111-11-11-1-1-1-1-11111-111-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-11-1-11
χ172222222222222222-2-222220000-22222-2-2-2-2000000000000-2-2000000000000000022-2-2-2-2200000000
χ182222222222222222-2-222220000-22222-2-2-2-2000000000000-2-20000000000000000-2-22222-200000000
χ1922222222222222-2-2-2-2222200002-2-2-2-2-2-2-2-200000000000022000000000000000022-2-222-200000000
χ2022222222222222-2-2-2-2222200002-2-2-2-2-2-2-2-2000000000000220000000000000000-2-222-2-2200000000
χ21222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1−52−1+52−1−5222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522222−1+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+52−1−522222−1+52−1−52−1+52−1−5222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2−1+52−1−52−1+52−1−521−521−521+521+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+52−1−522222−1+52−1−52−1+52−1−52-2-2-2-22−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-21−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000000000
χ24222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52-2-2-2-22−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2221−521+521−521+521−521−521+521+52−1+52−1−521−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000
χ25222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−522-22-2-21−521−521+521+52−1+52−1+52−1−52−1−522-22-2−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−521−521+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+52−1−52-2-222−1+52−1−52−1+52−1−522-22-2-21−521−521+521+52−1+52−1+52−1−52−1−52-22-22−1+52−1−521−521+521−521−521+521+521−521+52−1+52−1−521−521+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+52−1−52-2-222−1+52−1−52−1+52−1−52-22-22-21−521−521+521+52−1+52−1+52−1−52−1−522-2-221−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521+521−521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000
χ28222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−52-22-22-21−521−521+521+52−1+52−1+52−1−52−1−52-222-21−521+52−1+52−1−521−521−521+521+521−521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000
χ29222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+52−1−52−1+5222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522222−1−52−1+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+522222−1−52−1+52−1−52−1+5222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+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+522222−1−52−1+52−1−52−1+52-2-2-2-22−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-21+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000000
χ32222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52-2-2-2-22−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2221+521−521+521−521+521+521−521−52−1−52−1+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
χ33222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+522-22-2-21+521+521−521−52−1−52−1−52−1+52−1+522-22-2−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+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+52-2-222−1−52−1+52−1−52−1+522-22-2-21+521+521−521−52−1−52−1−52−1+52−1+52-22-22−1−52−1+521+521−521+521+521−521−521+521−52−1−52−1+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+52-2-222−1−52−1+52−1−52−1+52-22-22-21+521+521−521−52−1−52−1−52−1+52−1+522-2-221+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521−521+521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000
χ36222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+52-22-22-21+521+521−521−52−1−52−1−52−1+52−1+52-222-21+521−52−1−52−1+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+521+521+521−521−52000000000000000
χ372222-2-222222222002-2-2-2-2-2020-2000002-22-20000002200000000-2-20000000000002-22-2000002-20000
χ382222-2-222222222002-2-2-2-2-2020-2000002-22-20000002200000000-2-2000000000000-22-2200000-220000
χ392222-2-222222222002-2-2-2-2-20-202000002-22-2000000-2-200000000220000000000002-22-200000-220000
χ402222-2-222222222002-2-2-2-2-20-202000002-22-2000000-2-20000000022000000000000-22-22000002-20000
χ412222-2-22222222200-22-2-2-2-220-2000000-22-2200002200000000-2-2000000000000002-2-220002-2000000
χ422222-2-22222222200-22-2-2-2-220-2000000-22-2200002200000000-2-200000000000000-222-2000-22000000
χ432222-2-22222222200-22-2-2-2-2-202000000-22-220000-2-20000000022000000000000002-2-22000-22000000
χ442222-2-22222222200-22-2-2-2-2-202000000-22-220000-2-2000000002200000000000000-222-20002-2000000
χ45444444−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−544-4-4−1+5−1−5−1+5−1−50000-4−1+5−1+5−1−5−1−51−51−51+51+50000000000001−51+50000000000000000000000000000000
χ46444444−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4-4-4-4−1+5−1−5−1+5−1−5000041−51−51+51+51−51−51+51+5000000000000−1+5−1−50000000000000000000000000000000
χ47444444−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+544-4-4−1−5−1+5−1−5−1+50000-4−1−5−1−5−1+5−1+51+51+51−51−50000000000001+51−50000000000000000000000000000000
χ48444444−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4-4-4-4−1−5−1+5−1−5−1+5000041+51+51−51−51+51+51−51−5000000000000−1−5−1+50000000000000000000000000000000
χ494444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5004-41−51+51−51+5040-400000−1+51−5−1−51+5000000−1+5−1−5000000001−51+5000000000000000000000000000
χ504444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5004-41−51+51−51+50-40400000−1+51−5−1−51+50000001−51+500000000−1+5−1−5000000000000000000000000000
χ514444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−500-441−51+51−51+540-40000001−5−1+51+5−1−50000−1+5−1−5000000001−51+500000000000000000000000000000
χ524444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−500-441−51+51−51+5-4040000001−5−1+51+5−1−500001−51+500000000−1+5−1−500000000000000000000000000000
χ534444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5004-41+51−51+51−5040-400000−1−51+5−1+51−5000000−1−5−1+5000000001+51−5000000000000000000000000000
χ544444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5004-41+51−51+51−50-40400000−1−51+5−1+51−50000001+51−500000000−1−5−1+5000000000000000000000000000
χ554444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+500-441+51−51+51−540-40000001+5−1−51−5−1+50000−1−5−1+5000000001+51−500000000000000000000000000000
χ564444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+500-441+51−51+51−5-4040000001+5−1−51−5−1+500001+51−500000000−1−5−1+500000000000000000000000000000
χ5744-4-44-444-4-4-4-444000044-4-4000000000000000000000000000000000000000000000004i−4i000000000
χ5844-4-44-444-4-4-4-444000044-4-400000000000000000000000000000000000000000000000−4i4i000000000
χ5944-4-4-4444-4-4-4-4444-400-4-444000004-44-40000000000000000000000000000000000000000000000000
χ6044-4-4-4444-4-4-4-444-4400-4-44400000-44-440000000000000000000000000000000000000000000000000
χ6144-4-4-44−1+5−1−51−51−51+51+5−1+5−1−54-4001−51+5−1+5−1−500000−1+51−5−1−51+500000000000000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000
χ6244-4-4-44−1+5−1−51−51−51+51+5−1+5−1−54-4001−51+5−1+5−1−500000−1+51−5−1−51+500000000000000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000
χ6344-4-4-44−1+5−1−51−51−51+51+5−1+5−1−5-44001−51+5−1+5−1−5000001−5−1+51+5−1−500000000000000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000
χ6444-4-4-44−1+5−1−51−51−51+51+5−1+5−1−5-44001−51+5−1+5−1−5000001−5−1+51+5−1−500000000000000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000
χ6544-4-4-44−1−5−1+51+51+51−51−5−1−5−1+54-4001+51−5−1−5−1+500000−1−51+5−1+51−500000000000000000000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37000000000000000
χ6644-4-4-44−1−5−1+51+51+51−51−5−1−5−1+54-4001+51−5−1−5−1+500000−1−51+5−1+51−500000000000000000000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37000000000000000
χ6744-4-4-44−1−5−1+51+51+51−51−5−1−5−1+5-44001+51−5−1−5−1+5000001+5−1−51−5−1+500000000000000000000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37000000000000000
χ6844-4-4-44−1−5−1+51+51+51−51−5−1−5−1+5-44001+51−5−1−5−1+5000001+5−1−51−5−1+500000000000000000000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37000000000000000
χ6988-8-88-8−2+25−2−252−252−252+252+25−2+25−2−250000−2+25−2−252−252+250000000000000000000000000000000000000000000000000000000000
χ7088-8-88-8−2−25−2+252+252+252−252−25−2−25−2+250000−2−25−2+252+252−250000000000000000000000000000000000000000000000000000000000
χ718-88-800888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000
χ728-88-800−2+25−2−25−2+252−25−2−252+252−252+25000000000000000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000000000000000000
χ738-88-800−2+25−2−25−2+252−25−2−252+252−252+2500000000000000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000000000000000000
χ748-88-800−2−25−2+25−2−252+25−2+252−252+252−2500000000000000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000000000000000000
χ758-88-800−2−25−2+25−2−252+25−2+252−252+252−25000000000000000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000000000000
χ768-8-880088-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000
χ778-8-8800−2+25−2−252−25−2+252+25−2−252−252+250000000000000000000000000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000
χ788-8-8800−2+25−2−252−25−2+252+25−2−252−252+25000000000000000000000000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000
χ798-8-8800−2−25−2+252+25−2−252−25−2+252+252−25000000000000000000000000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000
χ808-8-8800−2−25−2+252+25−2−252−25−2+252+252−250000000000000000000000000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000

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