Finite Group Databasebeta

← Group #12077337

Character table — Group #12077337

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222224444444444444888888888888888888888888101016161616161616161616161616161616161616202020202020203232404040404040808080
order1222444455101010101010488882020202020202020224444101010102020202020204040404040404040444881010202020202020404040404040404024488882020244444288
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-11-1-1-11111-1-1-1-1111111111111-11-1-1-111-1-1-1-11111-1-1-1-11111111-1-1-11-11-1-1-11-1
χ4111111111111111111111111111111-11-1-1-11111-1-1-1-11111111111-1-1-11-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-11
χ511111111111111111111111111111-11-11-1-1-1-1-1-11111111111111111-1-1111-1-1-1-1-1-1-1-1-1-111111111111-1-11-11-1-1-1-1-11
χ611111111111111111111111111111-11-11-1-1-1-1-1-111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-111111-1
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111
χ911111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1
χ1011111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111
χ1111111111111111111-1-1-1-1111111111-11-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111-11-1-111-1-1-1-1-1-1-1-11111111-1-1-1-111-11-11-1-11-11
χ1211111111111111111-1-1-1-1111111111-11-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-11111-1-1-11111111-11-111-11-1
χ1311111111111111111-1-1-1-111111111-11-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111-11-1-1-111-1
χ1411111111111111111-1-1-1-111111111-11-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-1-1-1-1-1-1111111-11-1111-1-11
χ1511111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-111-111
χ1611111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-11111-1-11111-1-11-1-1
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+52−1−52−1−522-22-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-22-21−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000001−521+52000000000
χ1922222222−1+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+52−1−52−1−52-22-22-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2-22−1+52−1−521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200000001−521+52000000000
χ2022222222−1+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+52−1−52−1−52-2-2-2-2221−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002-2-21−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000−1+52−1−52000000000
χ2122222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-2-2-2−1+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+52−1−521−521−521−521−521+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
χ2222222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-22-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+52002-221−521+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
χ2322222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-22-22-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+520022-2−1+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
χ2422222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2221−521−521+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+522-22-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-22-21+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000001+521−52000000000
χ2722222222−1−52−1+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+52-22-22-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2-22−1−52−1+521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+5200000001+521−52000000000
χ2822222222−1−52−1+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+52-2-2-2-2221+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+52002-2-21+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000−1−52−1+52000000000
χ2922222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-2-2-2−1−52−1−52−1+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+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
χ3022222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-22-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−52002-221+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
χ3122222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-22-22-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−520022-2−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000000−1−52−1+52000000000
χ3222222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2221+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
χ3322222-2-2222222222-200002-22-22-22-220-200022220000-2-2000000002200000-2-2000000000000-2-22000000020-200000
χ3422222-2-2222222222-200002-22-22-22-220-200022220000-2-200000000-2-200000-2-200000000000022-20000000-20200000
χ3522222-2-2222222222-200002-22-22-22-2-202000-2-2-2-20000-2-200000000220000022000000000000-2-220000000-20200000
χ3622222-2-2222222222-200002-22-22-22-2-202000-2-2-2-20000-2-200000000-2-2000002200000000000022-2000000020-200000
χ372222-222-222222222-20000-22-22-22-22020-2000000-2-2-2-2-2-2000000002200022000000000000002-2-2000000-202000000
χ382222-222-222222222-20000-22-22-22-22020-2000000-2-2-2-2-2-200000000-2-20002200000000000000-22200000020-2000000
χ392222-222-222222222-20000-22-22-22-220-2020000002222-2-20000000022000-2-2000000000000002-2-200000020-2000000
χ402222-222-222222222-20000-22-22-22-220-2020000002222-2-200000000-2-2000-2-200000000000000-222000000-202000000
χ412222-2-2-2-22222222220000-2-2-2-2-2-2-2-200002-20000000022000000002200000002-22-200000000-22-200000000002-2000
χ422222-2-2-2-22222222220000-2-2-2-2-2-2-2-200002-2000000002200000000-2-200000002-22-2000000002-220000000000-22000
χ432222-2-2-2-22222222220000-2-2-2-2-2-2-2-20000-22000000002200000000220000000-22-2200000000-22-20000000000-22000
χ442222-2-2-2-22222222220000-2-2-2-2-2-2-2-20000-22000000002200000000-2-20000000-22-22000000002-2200000000002-2000
χ4544444-4-44−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-40000−1+51−5−1−51+5−1+51−5−1−51+540-4000−1+5−1+5−1−5−1−500001−51+50000000000000001−51+5000000000000000000000000000000
χ4644444-4-44−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-40000−1+51−5−1−51+5−1+51−5−1−51+5-4040001−51−51+51+500001−51+5000000000000000−1+5−1−5000000000000000000000000000000
χ4744444-4-44−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-40000−1−51+5−1+51−5−1−51+5−1+51−540-4000−1−5−1−5−1+5−1+500001+51−50000000000000001+51−5000000000000000000000000000000
χ4844444-4-44−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-40000−1−51+5−1+51−5−1−51+5−1+51−5-4040001+51+51−51−500001+51−5000000000000000−1−5−1+5000000000000000000000000000000
χ494444-444-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-400001−5−1+51+5−1−51−5−1+51+5−1−5040-40000001−51−51+51+51−51+50000000000000−1+5−1−500000000000000000000000000000000
χ504444-444-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-400001−5−1+51+5−1−51−5−1+51+5−1−50-404000000−1+5−1+5−1−5−1−51−51+500000000000001−51+500000000000000000000000000000000
χ514444-444-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-400001+5−1−51−5−1+51+5−1−51−5−1+5040-40000001+51+51−51−51+51−50000000000000−1−5−1+500000000000000000000000000000000
χ524444-444-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-400001+5−1−51−5−1+51+5−1−51−5−1+50-404000000−1−5−1−5−1+5−1+51+51−500000000000001+51−500000000000000000000000000000000
χ534444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5400001−51−51+51+51−51−51+51+500004-400000000−1+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+5−1−5−1−5400001−51−51+51+51−51−51+51+50000-4400000000−1+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+5400001+51+51−51−51+51+51−51−500004-400000000−1−5−1+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+5400001+51+51−51−51+51+51−51−50000-4400000000−1−5−1+5000000000000000001+5−1−51−5−1+500000000000000000000000000
χ5744-4-404-4044-4-44-44-4000000-40-404040000000000000000000000000000000000000000000000002i22i2−2i2−2i200000000000
χ5844-4-404-4044-4-44-44-4000000-40-40404000000000000000000000000000000000000000000000000−2i2−2i22i22i200000000000
χ5944-4-40-44044-4-44-44-402i22i2−2i2−2i204040-40-400000000000000002i22i2−2i2−2i22i22i2−2i2−2i2000000000000000000000000000000000000000
χ6044-4-40-44044-4-44-44-40−2i2−2i22i22i204040-40-40000000000000000−2i2−2i22i22i2−2i2−2i22i22i2000000000000000000000000000000000000000
χ6144-4-40-440−1+5−1−51−51+5−1+51−5−1−51+502i22i2−2i2−2i20−1+50−1−501−501+50000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+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−ζ3900000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000000
χ6244-4-40-440−1+5−1−51−51+5−1+51−5−1−51+502i22i2−2i2−2i20−1+50−1−501−501+500000000002ζ22−2ζ38−2ζ22+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−ζ3900000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000000
χ6344-4-40-440−1+5−1−51−51+5−1+51−5−1−51+50−2i2−2i22i22i20−1+50−1−501−501+50000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+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+ζ3900000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000000
χ6444-4-40-440−1+5−1−51−51+5−1+51−5−1−51+50−2i2−2i22i22i20−1+50−1−501−501+500000000002ζ22−2ζ38−2ζ22+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+ζ3900000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000000
χ6544-4-40-440−1−5−1+51+51−5−1−51+5−1+51−502i22i2−2i2−2i20−1−50−1+501+501−500000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ3800ζ21+ζ29+ζ31+ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37−ζ7−ζ13−ζ23−ζ3700000000000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37000000000000000000
χ6644-4-40-440−1−5−1+51+51−5−1−51+5−1+51−502i22i2−2i2−2i20−1−50−1+501+501−50000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ3800ζ21+ζ29+ζ31+ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37−ζ7−ζ13−ζ23−ζ3700000000000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37000000000000000000
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χ764-44-4400-4−1−5−1+51+51−51+5−1−51−5−1+502i2−2i22i2−2i2−1−50−1+501+501−500000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ370000000000000−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ370000000000000000000000
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χ814-4-4400004444-4-4-4-402-2-220000000000000000000000002-2-222-2-224i−4i00000000000000000000002i−2i−2i2i00000000000
χ824-4-4400004444-4-4-4-402-2-220000000000000000000000002-2-222-2-22−4i4i0000000000000000000000−2i2i2i−2i00000000000
χ834-4-4400004444-4-4-4-40-222-2000000000000000000000000-222-2-222-24i−4i0000000000000000000000−2i2i2i−2i00000000000
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χ928-8-880000−2−25−2+25−2−25−2+252+252+252−252−250-444-40000000000000000000000001+5−1−5−1−51+51−5−1+5−1+51−5000000000000000000000000000000000000000

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