Finite Group Databasebeta

← Group #12075685

Character table — Group #12075685

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222224444444444444888888888888888888888888101016161616161616161616161616161616161616202020202020203232404040404040808080
order1222444455101010101010444442020202020202020444488202020202020202020204040404040404040442882020202020202020404040404040404024444441010222488488
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
χ5111111111111111111-1-11111111111-1-1-111-1-1-1-11111111111111111-1-11-1-111-1-1-1-11111-1-1-1-111-1-1111-1-11-1-1-111-1-11
χ6111111111111111111-1-11111111111-1-1-111-1-1-1-111111111111111-1-1-1-11-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111-1-111-1
χ7111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-111-1
χ8111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-111-111111-1-11
χ91111111111111111-1-111111111111-1-1-11111111-1-1-1-1111111111111-11-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1111-11-1
χ101111111111111111-1-111111111111-1-1-11111111-1-1-1-11111111111-1-1-11-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-1111-1-1-11-11
χ111111111111111111-1-111111111111-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111-1111-1-1-1-1-1-11111-1-1-1-111111-1-111-1-1-11-1-11-11
χ121111111111111111-1-111111111111-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111111-111-11-1
χ131111111111111111-1-1-1-1111111111-111-111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-1-111-111-1111-1-1
χ141111111111111111-1-1-1-1111111111-111-111-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111111-1-11-1-1-111
χ151111111111111111-1-1-1-1111111111-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-111-1-1-1-111111111111111-1-11-1-1-1-1-111-1-1-1-111
χ161111111111111111-1-1-1-1111111111-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-111-111-1-11-1-11111-1-1
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+52−1−522-2-2-2221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2-221−521+52−1+52−1−521−521−521+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+52−1−522-2-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+520022-21−521+52−1+52−1−521−521−521+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+52−1−52-2-2-2222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-22-2−1+52−1−521−521+521−521−521+521+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+52−1−52-2-2-22-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+52002-22−1+52−1−521−521+521−521−521+521+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+52−1−52-222-2221−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002-2-21−521+521−521+52−1+52−1+52−1−52−1−521−521−521+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+52−1−52-222-2-2-21−521−521+521+521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+5200-2221−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000001−521+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+522-2-2-2221+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+5200-2-221+521−52−1−52−1+521+521+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+522-2-2-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−520022-21+521−52−1−52−1+521+521+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+52-2-2-2222−1−52−1−52−1+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+5200-22-2−1−52−1+521+521−521+521+521−521−521+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+52-2-2-22-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−52002-22−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+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+52-222-2221+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+52002-2-21+521−521+521−52−1−52−1−52−1+52−1+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+52-222-2-2-21+521+521−521−521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−5200-2221+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+5200000001+521−52000000000
χ3322222-2-22222222220022-222-2-222-2-2000-20022220000-2-20000000022000-2-200000000000000-2222-20000000-200000
χ3422222-2-22222222220022-222-2-222-2-2000-20022220000-2-200000000-2-2000-2-2000000000000002-2-2-220000000200000
χ3522222-2-222222222200-2-2-222-2-222-2-2000200-2-2-2-20000-2-200000000220002200000000000000-22-2-2-20000000200000
χ3622222-2-222222222200-2-2-222-2-222-2-2000200-2-2-2-20000-2-200000000-2-200022000000000000002-22220000000-200000
χ372222-222-2222222222200-2-2-222-2-222-20000000002222-2-2000000002200000-2-20000000000002-200-22200-200000000
χ382222-222-2222222222200-2-2-222-2-222-20000000002222-2-200000000-2-200000-2-2000000000000-22002-2-200200000000
χ392222-222-222222222-2-200-2-2-222-2-2222000000000-2-2-2-2-2-2000000002200000220000000000002-200-2-2-200200000000
χ402222-222-222222222-2-200-2-2-222-2-2222000000000-2-2-2-2-2-200000000-2-20000022000000000000-220022200-200000000
χ412222-2-2-2-22222222200002-2-2-2-2-2-2-2-202-20000000000022000000002200000002-22-200000000-2-2002000002-2000000
χ422222-2-2-2-22222222200002-2-2-2-2-2-2-2-202-2000000000002200000000-2-200000002-22-2000000002200-200000-22000000
χ432222-2-2-2-22222222200002-2-2-2-2-2-2-2-20-22000000000002200000000220000000-22-2200000000-2-200200000-22000000
χ442222-2-2-2-22222222200002-2-2-2-2-2-2-2-20-22000000000002200000000-2-20000000-22-22000000002200-2000002-2000000
χ4544444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−50044-4−1+5−1−51−51+5−1+5−1−51−51+5000-400−1+5−1+5−1−5−1−500001−51+500000000000001−51+500000000000000000000000000000000
χ4644444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-4-4-4−1+5−1−51−51+5−1+5−1−51−51+50004001−51−51+51+500001−51+50000000000000−1+5−1−500000000000000000000000000000000
χ4744444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+50044-4−1−5−1+51+51−5−1−5−1+51+51−5000-400−1−5−1−5−1+5−1+500001+51−500000000000001+51−500000000000000000000000000000000
χ4844444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-4-4-4−1−5−1+51+51−5−1−5−1+51+51−50004001+51+51−51−500001+51−50000000000000−1−5−1+500000000000000000000000000000000
χ494444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−54400-41−51+5−1+5−1−51−51+5−1+5−1−5-4000000000−1+5−1+5−1−5−1−51−51+50000000000000001−51+5000000000000000000000000000000
χ504444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-400-41−51+5−1+5−1−51−51+5−1+5−1−540000000001−51−51+51+51−51+5000000000000000−1+5−1−5000000000000000000000000000000
χ514444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+54400-41+51−5−1−5−1+51+51−5−1−5−1+5-4000000000−1−5−1−5−1+5−1+51+51−50000000000000001+51−5000000000000000000000000000000
χ524444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-400-41+51−5−1−5−1+51+51−5−1−5−1+540000000001+51+51−51−51+51−5000000000000000−1−5−1+5000000000000000000000000000000
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+504-400000000000−1+5−1−500000000000000000−1+51−5−1−51+500000000000000000000000000
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+50-4400000000000−1+5−1−5000000000000000001−5−1+51+5−1−500000000000000000000000000
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+51−504-400000000000−1−5−1+500000000000000000−1−51+5−1+51−500000000000000000000000000
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+51−50-4400000000000−1−5−1+5000000000000000001+5−1−51−5−1+500000000000000000000000000
χ5744-4-404-4044-4-4-4-4440000000-4-40044000000000000000000000000000000000000000000000000004i−4i00000000000
χ5844-4-404-4044-4-4-4-4440000000-4-4004400000000000000000000000000000000000000000000000000−4i4i00000000000
χ5944-4-40-44044-4-4-4-4444i−4i000004400-4-400000000004i−4i4i−4i0000000000000000000000000000000000000000000000000
χ6044-4-40-44044-4-4-4-444−4i4i000004400-4-40000000000−4i4i−4i4i0000000000000000000000000000000000000000000000000
χ6144-4-40-440−1+5−1−51−51+51−51+5−1+5−1−54i−4i00000−1+5−1−5001−51+50000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ390000000000000ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ390000000000000000000000
χ6244-4-40-440−1+5−1−51−51+51−51+5−1+5−1−54i−4i00000−1+5−1−5001−51+50000000000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ390000000000000−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ390000000000000000000000
χ6344-4-40-440−1+5−1−51−51+51−51+5−1+5−1−5−4i4i00000−1+5−1−5001−51+500000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ390000000000000−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ390000000000000000000000
χ6444-4-40-440−1+5−1−51−51+51−51+5−1+5−1−5−4i4i00000−1+5−1−5001−51+500000000002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ390000000000000ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ390000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.