Finite Group Databasebeta

← Group #12090330

Character table — Group #12090330

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222222222444444444448888888888888888888888888881616161616161616161616161616161616162020202020202020202032324040404040808080
order1222444455101010101010444202020202020202024488888820202020202020202020404040404040404024101020202020202040404040404040404444888888101024888228
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-1-1-111-11
χ4111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1111-1-11-1
χ51111111111111111111111111111-1-111-1-111-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-11-1111-1-1-1
χ61111111111111111111111111111-1-111-1-111-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1111
χ71111111111111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-11-11-1
χ81111111111111111111111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111-11-11
χ91111111111111111-1-1111111111-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-1-11111-1-111111111-1-1-11-1-1
χ101111111111111111-1-1111111111-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1111-111
χ111111111111111111-1-1111111111-111-1-111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-111-111-1
χ121111111111111111-1-1111111111-111-1-111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111111111-1-1-11-1-11-1-11
χ131111111111111111-1-1111111111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-111111111111111-1-1-1-11111-1-11-1-1-1-1-111
χ141111111111111111-1-1111111111-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-111111-1-1
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+52−1−52−1−522-2-222-2-2221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2−1+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+52−1−52−1−522-2-2-2-222-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+522-2−1+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+52−1−52−1−52-22222-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+522-21−521+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+52−1−52−1−52-222-2-22222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-21−521+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+522-2-222-2-2221+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+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+522-2-2-2-222-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−522-2−1−52−1+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+52-22222-2-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−522-21+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+52-222-2-22222−1−52−1−52−1+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+52-2-21+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
χ3322222-2-222222222222-22-22-22-22-2-20000000000002222-2-20000000000-2-200000000000000220022000000-2000-2000
χ3422222-2-222222222222-22-22-22-22-2-20000000000002222-2-20000000000-2-200000000000000-2-200-2-200000020002000
χ3522222-2-2222222222-2-2-22-22-22-22-22000000000000-2-2-2-2-2-2000000000022000000000000002200-2-2000000-20002000
χ3622222-2-2222222222-2-2-22-22-22-22-22000000000000-2-2-2-2-2-200000000002200000000000000-2-200220000002000-2000
χ372222-222-22222222200-2-22-22-22-2202-200000022220000-2-2000000000000-2-2000000000000002200-2-222000-2000000
χ382222-222-22222222200-2-22-22-22-2202-200000022220000-2-2000000000000-2-200000000000000-2-20022-2-20002000000
χ392222-222-22222222200-2-22-22-22-220-22000000-2-2-2-20000-2-20000000000002200000000000000220022-2-2000-2000000
χ402222-222-22222222200-2-22-22-22-220-22000000-2-2-2-20000-2-20000000000002200000000000000-2-200-2-2220002000000
χ4122-2-2200-222-2-22-22-22i−2i02020-20-20000i2−i2002−200002i−2i2i−2i0022−2−222−2−20000000000i2−i2i2−i200002i−2i002-22−22−20000i2−i20000
χ4222-2-2200-222-2-22-22-22i−2i02020-20-20000i2−i2002−200002i−2i2i−2i0022−2−222−2−20000000000i2−i2i2−i20000−2i2i00-22−22−220000−i2i20000
χ4322-2-2200-222-2-22-22-22i−2i02020-20-20000−i2i200−2200002i−2i2i−2i00−2−222−2−2220000000000−i2i2−i2i200002i−2i002-2−22−220000−i2i20000
χ4422-2-2200-222-2-22-22-22i−2i02020-20-20000−i2i200−2200002i−2i2i−2i00−2−222−2−2220000000000−i2i2−i2i20000−2i2i00-222−22−20000i2−i20000
χ4522-2-2200-222-2-22-22-2−2i2i02020-20-20000i2−i200−220000−2i2i−2i2i00−2−222−2−2220000000000i2−i2i2−i200002i−2i00-222−22−20000−i2i20000
χ4622-2-2200-222-2-22-22-2−2i2i02020-20-20000i2−i200−220000−2i2i−2i2i00−2−222−2−2220000000000i2−i2i2−i20000−2i2i002-2−22−220000i2−i20000
χ4722-2-2200-222-2-22-22-2−2i2i02020-20-20000−i2i2002−20000−2i2i−2i2i0022−2−222−2−20000000000−i2i2−i2i200002i−2i00-22−22−220000i2−i20000
χ4822-2-2200-222-2-22-22-2−2i2i02020-20-20000−i2i2002−20000−2i2i−2i2i0022−2−222−2−20000000000−i2i2−i2i20000−2i2i002-22−22−20000−i2i20000
χ4944444-4-44−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−544-4−1+51−5−1−51+5−1+51−5−1−51+5-4000000000000−1+5−1+5−1−5−1−51−51+500000000001−51+50000000000000000000000000000000000
χ5044444-4-44−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-4-4-4−1+51−5−1−51+5−1+51−5−1−51+540000000000001−51−51+51+51−51+50000000000−1+5−1−50000000000000000000000000000000000
χ5144444-4-44−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+544-4−1−51+5−1+51−5−1−51+5−1+51−5-4000000000000−1−5−1−5−1+5−1+51+51−500000000001+51−50000000000000000000000000000000000
χ5244444-4-44−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-4-4-4−1−51+5−1+51−5−1−51+5−1+51−540000000000001+51+51−51−51+51−50000000000−1−5−1+50000000000000000000000000000000000
χ534444-444-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−500-41−5−1+51+5−1−51−5−1+51+5−1−504-4000000−1+5−1+5−1−5−1−500001−51+50000000000001−51+500000000000000000000000000000000
χ544444-444-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−500-41−5−1+51+5−1−51−5−1+51+5−1−50-440000001−51−51+51+500001−51+5000000000000−1+5−1−500000000000000000000000000000000
χ554444-444-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500-41+5−1−51−5−1+51+5−1−51−5−1+504-4000000−1−5−1−5−1+5−1+500001+51−50000000000001+51−500000000000000000000000000000000
χ564444-444-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500-41+5−1−51−5−1+51+5−1−51−5−1+50-440000001+51+51−51−500001+51−5000000000000−1−5−1+500000000000000000000000000000000
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
χ6244-4-4400-4−1+5−1−51−51+5−1+51−5−1−51+54i−4i0−1+50−1−501−501+500002i2−2i20022−220000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ390000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39000000000000000000000000
χ6344-4-4400-4−1+5−1−51−51+5−1+51−5−1−51+54i−4i0−1+50−1−501−501+50000−2i22i200−22220000−2ζ22−2ζ382ζ22+2ζ38−2ζ6−2ζ142ζ6+2ζ1400ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ390000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39000000000000000000000000
χ6444-4-4400-4−1+5−1−51−51+5−1+51−5−1−51+5−4i4i0−1+50−1−501−501+500002i2−2i200−222200002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ390000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39000000000000000000000000
χ6544-4-4400-4−1+5−1−51−51+5−1+51−5−1−51+5−4i4i0−1+50−1−501−501+50000−2i22i20022−2200002ζ22+2ζ38−2ζ22−2ζ382ζ6+2ζ14−2ζ6−2ζ1400−ζ7+ζ13−ζ23+ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ21−ζ29+ζ31+ζ390000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.