Finite Group Databasebeta

← Group #12089950

Character table — Group #12089950

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222222222444444444448888888888888888888888888881616161616161616161616161616161616162020202020202020202032324040404040808080
order1222444455101010101010224202020202020202044488888810101010202020202020404040404040404024202020202020202040404040404040404444888888101044888448
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11-111-1-11-1
χ4111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-11-1-111-11
χ51111111111111111111111111111-1-111-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111
χ61111111111111111111111111111-1-111-1-1111111-1-1-1-11111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-11111-1-1-1
χ71111111111111111111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-11-11-1
χ81111111111111111111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-11-11
χ91111111111111111-1-1111111111-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-11-1-1
χ101111111111111111-1-1111111111-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1111-111
χ111111111111111111-1-1111111111-111-1-11111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-11-1-1-11-1-11
χ121111111111111111-1-1111111111-111-1-11111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1111-111-1
χ131111111111111111-1-1111111111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-111111111111111-1-1-1-111-1-1-1-11-11111-1-1
χ141111111111111111-1-1111111111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-11111-1-111-1-1-11-1-1-1-111
χ151111111111111111-1-1111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-11
χ161111111111111111-1-1111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111-1
χ1722222222−1+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+52−1−52222222222−1+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+52−1−52−1−52−1−52−1−5222−1+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+52−1−52−1−520000000000−1+52−1−5200000000
χ1822222222−1+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+52−1−52222-2-2-2-2-2-2−1+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+52-22−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200000000001−521+5200000000
χ1922222222−1+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+52−1−522-2-222-2-222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000001−521+5200000000
χ2022222222−1+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+52−1−522-2-2-2-222-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+522-2−1+52−1−521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000000000−1+52−1−5200000000
χ2122222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-22222-2-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+522-21−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000000000−1+52−1−5200000000
χ2222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-222-2-222221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000001−521+5200000000
χ2322222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-22222-2-21−521−521+521+521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+52-221−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000001−521+5200000000
χ2422222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-2-2-2-2221−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52221−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000000−1+52−1−5200000000
χ2522222222−1−52−1+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+52222222222−1−52−1−52−1+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+5222−1−52−1+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+520000000000−1−52−1+5200000000
χ2622222222−1−52−1+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+52222-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-22−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000000001+521−5200000000
χ2722222222−1−52−1+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+522-2-222-2-222−1−52−1−52−1+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+52-2-2−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000001+521−5200000000
χ2822222222−1−52−1+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+522-2-2-2-222-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−522-2−1−52−1+521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000000000−1−52−1+5200000000
χ2922222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-22222-2-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−522-21+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000000000−1−52−1+5200000000
χ3022222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-222-2-222221+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+52-2-21+521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000001+521−5200000000
χ3122222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-22222-2-21+521+521−521−521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−52-221+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+5200000000001+521−5200000000
χ3222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-2-2-2-2221+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+52221+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000000−1−52−1+5200000000
χ3322222-22-22222222200-2-2-222-2-22202-20000000000-2-2-2-2-2-20000000000002200000000000022002200-2-200-20000000
χ3422222-22-22222222200-2-2-222-2-22202-20000000000-2-2-2-2-2-200000000000022000000000000-2-200-2-200220020000000
χ3522222-22-22222222200-2-2-222-2-2220-2200000000002222-2-2000000000000-2-20000000000002200-2-2002200-20000000
χ3622222-22-22222222200-2-2-222-2-2220-2200000000002222-2-2000000000000-2-2000000000000-2-2002200-2-20020000000
χ372222-22-222222222222-222-2-222-2-2-20000000022220000-2-20000000000-2-2000000000000000022002200000-200-2000
χ382222-22-222222222222-222-2-222-2-2-20000000022220000-2-20000000000-2-20000000000000000-2-200-2-2000002002000
χ392222-22-2222222222-2-2-222-2-222-2-2200000000-2-2-2-20000-2-200000000002200000000000000002200-2-200000-2002000
χ402222-22-2222222222-2-2-222-2-222-2-2200000000-2-2-2-20000-2-20000000000220000000000000000-2-2002200000200-2000
χ412-22-20-2022222-2-2-2-22-20-2-2002200000i2−i200i2−i22-22-2000000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i20000002i−2i2−22i−2i2−200002−20000
χ422-22-20-2022222-2-2-2-22-20-2-2002200000i2−i200i2−i22-22-2000000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i2000000−2i2i−22−2i2i−220000−220000
χ432-22-20-2022222-2-2-2-22-20-2-2002200000−i2i200−i2i22-22-2000000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i20000002i−2i−222i−2i−220000−220000
χ442-22-20-2022222-2-2-2-22-20-2-2002200000−i2i200−i2i22-22-2000000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i2000000−2i2i2−2−2i2i2−200002−20000
χ452-22-20-2022222-2-2-2-2-220-2-2002200000i2−i200−i2i2-22-22000000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i20000002i−2i2−2−2i2i2−20000−220000
χ462-22-20-2022222-2-2-2-2-220-2-2002200000i2−i200−i2i2-22-22000000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i2000000−2i2i−222i−2i−2200002−20000
χ472-22-20-2022222-2-2-2-2-220-2-2002200000−i2i200i2−i2-22-22000000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i20000002i−2i−22−2i2i−2200002−20000
χ482-22-20-2022222-2-2-2-2-220-2-2002200000−i2i200i2−i2-22-22000000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i2000000−2i2i2−22i−2i2−20000−220000
χ4944444-44-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-41−51+5−1+5−1−51−51+5−1+5−1−504-400000000001−51−51+51+51−51+5000000000000−1+5−1−500000000000000000000000000000000
χ5044444-44-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-41−51+5−1+5−1−51−51+5−1+5−1−50-440000000000−1+5−1+5−1−5−1−51−51+50000000000001−51+500000000000000000000000000000000
χ5144444-44-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-41+51−5−1−5−1+51+51−5−1−5−1+504-400000000001+51+51−51−51+51−5000000000000−1−5−1+500000000000000000000000000000000
χ5244444-44-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-41+51−5−1−5−1+51+51−5−1−5−1+50-440000000000−1−5−1−5−1+5−1+51+51−50000000000001+51−500000000000000000000000000000000
χ534444-44-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−544-4−1+5−1−51−51+5−1+5−1−51−51+5-400000000−1+5−1+5−1−5−1−500001−51+500000000001−51+50000000000000000000000000000000000
χ544444-44-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4-4−1+5−1−51−51+5−1+5−1−51−51+54000000001−51−51+51+500001−51+50000000000−1+5−1−50000000000000000000000000000000000
χ554444-44-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+544-4−1−5−1+51+51−5−1−5−1+51+51−5-400000000−1−5−1−5−1+5−1+500001+51−500000000001+51−50000000000000000000000000000000000
χ564444-44-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-4-4−1−5−1+51+51−5−1−5−1+51+51−54000000001+51+51−51−500001+51−50000000000−1−5−1+50000000000000000000000000000000000
χ574444-4-4-4-444444444004-4-4-4-4-4-4-4-400000000000000000440000000000000000000000000000000000000000000000
χ584444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−50041−51+51−51+51−51+51−51+500000000000000000−1+5−1−5000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ360000000000000000000000000000
χ594444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−50041−51+51−51+51−51+51−51+500000000000000000−1+5−1−500000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ360000000000000000000000000000
χ604444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+50041+51−51+51−51+51−51+51−500000000000000000−1−5−1+500000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ280000000000000000000000000000
χ614444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+50041+51−51+51−51+51−51+51−500000000000000000−1−5−1+5000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ280000000000000000000000000000
χ6244-4-440-4044-4-444-4-4000004400-4-40000022−22000000000000000000000000000000000022−2222−2200000000000000000000
χ6344-4-440-4044-4-444-4-4000004400-4-400000−22220000000000000000000000000000000000−2222−222200000000000000000000
χ6444-4-440-40−1+5−1−51−51+5−1+5−1−51−51+500000−1+5−1−5001−51+50000022−22000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ1400ζ7−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−ζ3900000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ3900000000000000000000
χ6544-4-440-40−1+5−1−51−51+5−1+5−1−51−51+500000−1+5−1−5001−51+50000022−220000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ1400−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+ζ3900000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ3900000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.