Finite Group Databasebeta

← Group #12075689

Character table — Group #12075689

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222224444444444444888888888888888888888888101016161616161616161616161616161616161616202020202020203232404040404040808080
order1222444455101010101010444442020202020202020224488202020202020202020204040404040404040444881010101020202020404040404040404024444442020244488288
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1-1
χ4111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111-1-1111111111-1-11-1111111-1-1-1-1111111111111-1-11-1-1-1-111-1-11111-1-1-1-111111-1-1-1-11-1-1-111-1-11
χ6111111111111111111-1-1111111111-1-11-1111111-1-1-1-11111111111-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-1-1111-1-111-1
χ7111111111111111111-1-1111111111-1-11-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1111111111-1-1111-1-1-1-1-111-1
χ8111111111111111111-1-1111111111-1-11-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11111-111111-1-11
χ91111111111111111-1-111111111111-1-1-1111-1-1-1-11111111111111111-11-1-1-1-1-1-1-111-1-1-1-11111111-1-111-1-1-11-1-111-11-1
χ101111111111111111-1-111111111111-1-1-1111-1-1-1-111111111111111-1-1-11-1-1-1-1-1-1-111-1-1-1-11111-1-1-111-1-1-1-11-111-1-11-11
χ111111111111111111-1-111111111111-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-11-1-1-1-1-1-1111111-1-1-1-1111-1-11111-11-1-1-1-11-11
χ121111111111111111-1-111111111111-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1111-11111-11-1
χ131111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111111-1-1
χ141111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-11111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111
χ151111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1111111-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-111
χ161111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-11111-1-111-1-1111-1-1
χ1722222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222222−1+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+52−1−52−1−52−1−52−1−5200222−1+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+52−1−52−1−520000000−1+52−1−52000000000
χ1822222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522222-2-2−1+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+5200-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+5200000001−521+52000000000
χ1922222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22-222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2-221−521−521+521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+5200000001−521+52000000000
χ2022222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+520022-21−521−521+521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−520000000−1+52−1−52000000000
χ2122222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-22221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-22-21−521−521+521+521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200000001−521+52000000000
χ2222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-22-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+52002-221−521−521+521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000000−1+52−1−52000000000
χ2322222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-2-2221−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002-2-2−1+52−1+52−1−52−1−521−521+521−521+521−521−521+521+521−521−521+521+520000000−1+52−1−52000000000
χ2422222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-2-2-2-21−521−521+521+521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+5200-222−1+52−1+52−1−52−1−521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000001−521+52000000000
χ2522222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222222−1−52−1−52−1+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+5200222−1−52−1−52−1+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+520000000−1−52−1+52000000000
χ2622222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−5200000001+521−52000000000
χ2722222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22-222−1−52−1−52−1+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+5200-2-221+521+521−521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−5200000001+521−52000000000
χ2822222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−520022-21+521+521−521−52−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+520000000−1−52−1+52000000000
χ2922222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-22221+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+52−1+52−1+5200-22-21+521+521−521−521+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200000001+521−52000000000
χ3022222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-22-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52002-221+521+521−521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000000−1−52−1+52000000000
χ3122222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-2-2221+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+52002-2-2−1−52−1−52−1+52−1+521+521−521+521−521+521+521−521−521+521+521−521−520000000−1−52−1+52000000000
χ3222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-2-2-2-21+521+521−521−521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−5200-222−1−52−1−52−1+52−1+521+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000001+521−52000000000
χ3322222-2-22222222220022-2-2-222-2-222000-20000002222-2-20000000022000000000-2-200000000-22-20022000-20000000
χ3422222-2-22222222220022-2-2-222-2-222000-20000002222-2-200000000-2-2000000000-2-2000000002-2200-2-200020000000
χ3522222-2-222222222200-2-2-2-2-222-2-2220002000000-2-2-2-2-2-200000000220000000002200000000-22-200-2-200020000000
χ3622222-2-222222222200-2-2-2-2-222-2-2220002000000-2-2-2-2-2-200000000-2-200000000022000000002-220022000-20000000
χ372222-222-2222222222200-222-2-222-2-200-200022220000-2-200000000220000000-2-200000000002-2-2220000-200000000
χ382222-222-2222222222200-222-2-222-2-200-200022220000-2-200000000-2-20000000-2-20000000000-222-2-20000200000000
χ392222-222-222222222-2-200-222-2-222-2-2002000-2-2-2-20000-2-2000000002200000002200000000002-2-2-2-20000200000000
χ402222-222-222222222-2-200-222-2-222-2-2002000-2-2-2-20000-2-200000000-2-20000000220000000000-222220000-200000000
χ412222-2-2-2-22222222200002-2-2-2-2-2-2-2-22-20000000000002200000000220002-22-2000000000000-2-22000000002-200000
χ422222-2-2-2-22222222200002-2-2-2-2-2-2-2-22-20000000000002200000000-2-20002-22-200000000000022-200000000-2200000
χ432222-2-2-2-22222222200002-2-2-2-2-2-2-2-2-22000000000000220000000022000-22-22000000000000-2-2200000000-2200000
χ442222-2-2-2-22222222200002-2-2-2-2-2-2-2-2-220000000000002200000000-2-2000-22-2200000000000022-2000000002-200000
χ4544444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−50044-41−51+5−1+5−1−51−51+5−1+5−1−5000-4000000−1+5−1+5−1−5−1−51−51+500000000000000000001−51+500000000000000000000000000
χ4644444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-4-4-41−51+5−1+5−1−51−51+5−1+5−1−500040000001−51−51+51+51−51+50000000000000000000−1+5−1−500000000000000000000000000
χ4744444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+50044-41+51−5−1−5−1+51+51−5−1−5−1+5000-4000000−1−5−1−5−1+5−1+51+51−500000000000000000001+51−500000000000000000000000000
χ4844444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-4-4-41+51−5−1−5−1+51+51−5−1−5−1+500040000001+51+51−51−51+51−50000000000000000000−1−5−1+500000000000000000000000000
χ494444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−54400-4−1+5−1−51−51+5−1+5−1−51−51+500-4000−1+5−1+5−1−5−1−500001−51+5000000000000000001−51+50000000000000000000000000000
χ504444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-400-4−1+5−1−51−51+5−1+5−1−51−51+50040001−51−51+51+500001−51+500000000000000000−1+5−1−50000000000000000000000000000
χ514444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+54400-4−1−5−1+51+51−5−1−5−1+51+51−500-4000−1−5−1−5−1+5−1+500001+51−5000000000000000001+51−50000000000000000000000000000
χ524444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-400-4−1−5−1+51+51−5−1−5−1+51+51−50040001+51+51−51−500001+51−500000000000000000−1−5−1+50000000000000000000000000000
χ534444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5000041−51+51−51+51−51+51−51+54-4000000000000−1+5−1−50000000000000−1+51−5−1−51+5000000000000000000000000000000
χ544444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5000041−51+51−51+51−51+51−51+5-44000000000000−1+5−1−500000000000001−5−1+51+5−1−5000000000000000000000000000000
χ554444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5000041+51−51+51−51+51−51+51−54-4000000000000−1−5−1+50000000000000−1−51+5−1+51−5000000000000000000000000000000
χ564444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5000041+51−51+51−51+51−51+51−5-44000000000000−1−5−1+500000000000001+5−1−51−5−1+5000000000000000000000000000000
χ5744-4-4000044-4-444-4-4000000000000000002i−2i00000000002i2i−2i−2i2i2i−2i−2i4i−4i000000000000000000000000000000002-2000
χ5844-4-4000044-4-444-4-4000000000000000002i−2i00000000002i2i−2i−2i2i2i−2i−2i−4i4i00000000000000000000000000000000-22000
χ5944-4-4000044-4-444-4-400000000000000000−2i2i0000000000−2i−2i2i2i−2i−2i2i2i4i−4i00000000000000000000000000000000-22000
χ6044-4-4000044-4-444-4-400000000000000000−2i2i0000000000−2i−2i2i2i−2i−2i2i2i−4i4i000000000000000000000000000000002-2000
χ614-44-404-404444-4-4-4-44i−4i000-4-40044000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000
χ624-44-404-404444-4-4-4-4−4i4i000-4-4004400000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000
χ634-44-404-40−1+5−1−5−1+5−1−51−51+51−51+54i−4i0001−51+500−1+5−1−500000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14000000ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ390000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ390000000000000000000000
χ644-44-404-40−1+5−1−5−1+5−1−51−51+51−51+54i−4i0001−51+500−1+5−1−500000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ14000000−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ390000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ390000000000000000000000
χ654-44-404-40−1+5−1−5−1+5−1−51−51+51−51+5−4i4i0001−51+500−1+5−1−5000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14000000ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ390000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ390000000000000000000000
χ664-44-404-40−1+5−1−5−1+5−1−51−51+51−51+5−4i4i0001−51+500−1+5−1−5000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ14000000−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ390000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ390000000000000000000000
χ674-44-404-40−1−5−1+5−1−5−1+51+51−51+51−54i−4i0001+51−500−1−5−1+500000000−2ζ6−2ζ142ζ6+2ζ14−2ζ22−2ζ382ζ22+2ζ38000000−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ370000000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ370000000000000000000000
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χ898-88-80-880−2+25−2−25−2+25−2−252−252+252−252+2500000−2+25−2−25002−252+2500000000000000000000000000000000000000000000000000000000000000000
χ908-88-80-880−2−25−2+25−2−25−2+252+252−252+252−2500000−2−25−2+25002+252−2500000000000000000000000000000000000000000000000000000000000000000
χ918-8-88-8008−2+25−2−252−252+252−252+25−2+25−2−2500000002−252+2500−2+25−2−25000000000000000000000000000000000000000000000000000000000000000
χ928-8-88-8008−2−25−2+252+252−252+252−25−2−25−2+2500000002+252−2500−2−25−2+25000000000000000000000000000000000000000000000000000000000000000

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