Finite Group Databasebeta

← Group #13018823

Character table — Group #13018823

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222444444444444444444444444444455558888888888888888888888881010101010102020202020202020202020208080808080808080
order12224444445888888888888101010202020202020202020202020444440404040404040404040404040404040404040404040404022444488888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iii
χ8111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i
χ911111111111-1-1-1-11111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11-11-11-11-1
χ1011111111111-1-1-1-11111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-11-11-11-11
χ1111111111111-1-1-1-11111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111i−ii−i−ii−ii
χ1211111111111-1-1-1-11111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111−ii−iii−ii−i
χ1311111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111-1-111-1-11
χ1411111111111-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-111-1-111-1
χ1511111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1i−i−ii−iii−i
χ1611111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1−iii−ii−i−ii
χ17222222-2-2-2-220000000022-2-22222222-2-2-2-2-2-2-2-2222200000000000000002222-2-2-2-222-2-2-2-20000000022-2-200000000
χ18222222-2-2-2-220000000022-2-22222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-2-2-2-2-2222200000000-2-22200000000
χ19222222-2-2-2-2200000000-2-2222222222-2-2-2-2-2-2-2-222220000000000000000-2-2-2-2222222-2-2-2-200000000-2-22200000000
χ20222222-2-2-2-2200000000-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222-2-222220000000022-2-200000000
χ212222-2-222-2-22000022-2-20000222-2-2-2-22222-2-2-2-22222000000002222-2-2-2-200000000-2-222-2-2000022-2-2000000000000
χ222222-2-222-2-22000022-2-20000222-2-2-2-22222-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000022-2-2220000-2-222000000000000
χ232222-2-222-2-220000-2-2220000222-2-2-2-22222-2-2-2-2222200000000-2-2-2-2222200000000-2-222-2-20000-2-222000000000000
χ242222-2-222-2-220000-2-2220000222-2-2-2-22222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000022-2-222000022-2-2000000000000
χ252222-2-2-2-222222-2-200000000222-2-2-2-2-2-2-2-2222222222222-2-2-2-20000000000000000-2-2-2-22222-2-20000000000000000
χ262222-2-2-2-222222-2-200000000222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000002222-2-2-2-2220000000000000000
χ272222-2-2-2-2222-2-22200000000222-2-2-2-2-2-2-2-222222222-2-2-2-222220000000000000000-2-2-2-222-2-2220000000000000000
χ282222-2-2-2-2222-2-22200000000222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000002222-2-222-2-20000000000000000
χ2922-2-22-200002i2−i2i2−i2i2−i2i2−i2002-22-2-222-2-20000000022-2-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000022-2-22-20000i2−i2i2−i2i2−i2i2−i2002-200000000
χ3022-2-22-200002i2−i2i2−i2i2−i2i2−i2002-22-2-222-2-200000000-2-222i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000022-2-2-220000−i2i2−i2i2−i2i2−i2i200-2200000000
χ3122-2-22-200002i2−i2i2−i2−i2i2−i2i200-222-2-222-2-20000000022-2-2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000-2-2222-20000i2−i2i2−i2−i2i2−i2i200-2200000000
χ3222-2-22-200002i2−i2i2−i2−i2i2−i2i200-222-2-222-2-200000000-2-222i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000-2-222-220000−i2i2−i2i2i2−i2i2−i2002-200000000
χ3322-2-22-200002−i2i2−i2i2i2−i2i2−i200-222-2-222-2-20000000022-2-2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000-2-2222-20000−i2i2−i2i2i2−i2i2−i200-2200000000
χ3422-2-22-200002−i2i2−i2i2i2−i2i2−i200-222-2-222-2-200000000-2-222−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000-2-222-220000i2−i2i2−i2−i2i2−i2i2002-200000000
χ3522-2-22-200002−i2i2−i2i2−i2i2−i2i2002-22-2-222-2-20000000022-2-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000022-2-22-20000−i2i2−i2i2−i2i2−i2i2002-200000000
χ3622-2-22-200002−i2i2−i2i2−i2i2−i2i2002-22-2-222-2-200000000-2-222−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000022-2-2-220000i2−i2i2−i2i2−i2i2−i200-2200000000
χ3722-2-2-2200002i2−i2−i2i2i2−i2−i2i22-2002-2-2-2-2220000000022-2-2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i222-2-20000-220000i2−i2−i2i2i2−i2−i2i22-20000000000
χ3822-2-2-2200002i2−i2−i2i2i2−i2−i2i22-2002-2-2-2-22200000000-2-222i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i222-2-200002-20000−i2i2i2−i2−i2i2i2−i2-220000000000
χ3922-2-2-2200002i2−i2−i2i2−i2i2i2−i2-22002-2-2-2-2220000000022-2-2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2-2-2220000-220000i2−i2−i2i2−i2i2i2−i2-220000000000
χ4022-2-2-2200002i2−i2−i2i2−i2i2i2−i2-22002-2-2-2-22200000000-2-222i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2-2-22200002-20000−i2i2i2−i2i2−i2−i2i22-20000000000
χ4122-2-2-2200002−i2i2i2−i2i2−i2−i2i2-22002-2-2-2-2220000000022-2-2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2-2-2220000-220000−i2i2i2−i2i2−i2−i2i2-220000000000
χ4222-2-2-2200002−i2i2i2−i2i2−i2−i2i2-22002-2-2-2-22200000000-2-222−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2-2-22200002-20000i2−i2−i2i2−i2i2i2−i22-20000000000
χ4322-2-2-2200002−i2i2i2−i2−i2i2i2−i22-2002-2-2-2-2220000000022-2-2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i222-2-20000-220000−i2i2i2−i2−i2i2i2−i22-20000000000
χ4422-2-2-2200002−i2i2i2−i2−i2i2i2−i22-2002-2-2-2-22200000000-2-222−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i222-2-200002-20000i2−i2−i2i2i2−i2−i2i2-220000000000
χ454444444444-1444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ464444444444-14444-4-4-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1111111111111111100000000000000000000000000
χ474444444444-1-4-4-4-44444-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000011111111-1-1-1-1-1-1-1-11111111100000000000000000000000000
χ484444444444-1-4-4-4-4-4-4-4-44444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111111111111111-1-1-1-1-1-1-1-100000000000000000000000000
χ49444444-4-4-4-4-10000000044-4-4-1-1-1-1-1-1-1111111110000i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5-1-1-1-1111100000000000000000000000000
χ50444444-4-4-4-4-10000000044-4-4-1-1-1-1-1-1-1111111110000−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5-1-1-1-1111100000000000000000000000000
χ51444444-4-4-4-4-100000000-4-444-1-1-1-1-1-1-1111111110000i5−i5i5−i5i5−i5i5−i5−i5i5−i5i5−i5i5−i5i51111-1-1-1-100000000000000000000000000
χ52444444-4-4-4-4-100000000-4-444-1-1-1-1-1-1-1111111110000−i5i5−i5i5−i5i5−i5i5i5−i5i5−i5i5−i5i5−i51111-1-1-1-100000000000000000000000000
χ534444-4-444-4-4-1000044-4-40000-1-1-11111-1-1-1-111110000i5−i5i5−i5−i5i5−i5i5-1-1-1-11111i5−i5i5−i5i5−i5i5−i500000000000000000000000000
χ544444-4-444-4-4-1000044-4-40000-1-1-11111-1-1-1-111110000−i5i5−i5i5i5−i5i5−i5-1-1-1-11111−i5i5−i5i5−i5i5−i5i500000000000000000000000000
χ554444-4-444-4-4-10000-4-4440000-1-1-11111-1-1-1-111110000i5−i5i5−i5−i5i5−i5i51111-1-1-1-1−i5i5−i5i5−i5i5−i5i500000000000000000000000000
χ564444-4-444-4-4-10000-4-4440000-1-1-11111-1-1-1-111110000−i5i5−i5i5i5−i5i5−i51111-1-1-1-1i5−i5i5−i5i5−i5i5−i500000000000000000000000000
χ574444-4-4-4-444-144-4-400000000-1-1-111111111-1-1-1-10000-1-1-1-11111i5−i5i5−i5−i5i5−i5i5−i5i5−i5i5i5−i5i5−i500000000000000000000000000
χ584444-4-4-4-444-144-4-400000000-1-1-111111111-1-1-1-10000-1-1-1-11111−i5i5−i5i5i5−i5i5−i5i5−i5i5−i5−i5i5−i5i500000000000000000000000000
χ594444-4-4-4-444-1-4-44400000000-1-1-111111111-1-1-1-100001111-1-1-1-1i5−i5i5−i5−i5i5−i5i5i5−i5i5−i5−i5i5−i5i500000000000000000000000000
χ604444-4-4-4-444-1-4-44400000000-1-1-111111111-1-1-1-100001111-1-1-1-1−i5i5−i5i5i5−i5i5−i5−i5i5−i5i5i5−i5i5−i500000000000000000000000000
χ6144-4-44-40000-12i2−2i22i2−2i22i2−2i22i2−2i2004-4-111-1-111i5i5−i5−i5i5i5−i5−i50000ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29i5−i5−i5i5-1-11100000000000000000000000000
χ6244-4-44-40000-12i2−2i22i2−2i22i2−2i22i2−2i2004-4-111-1-111−i5−i5i5i5−i5−i5i5i50000ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−i5i5i5−i5-1-11100000000000000000000000000
χ6344-4-44-40000-12i2−2i22i2−2i2−2i22i2−2i22i200-44-111-1-111i5i5−i5−i5i5i5−i5−i50000ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−i5i5i5−i511-1-100000000000000000000000000
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χ6644-4-44-40000-1−2i22i2−2i22i22i2−2i22i2−2i200-44-111-1-111−i5−i5i5i5−i5−i5i5i50000−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39i5−i5−i5i511-1-100000000000000000000000000
χ6744-4-44-40000-1−2i22i2−2i22i2−2i22i2−2i22i2004-4-111-1-111i5i5−i5−i5i5i5−i5−i50000−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29i5−i5−i5i5-1-11100000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.