Finite Group Databasebeta

← Group #13030063

Character table — Group #13030063

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222444444444555588888888888888810101010101010101010101010101010161616161616161616202020202020202020202020202020202020202020404040404040404040
order12224444444444444510101044442222020202020202020202020202222224488888888101010101010202020224448888888888888888444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1
χ3111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i111111111-1-1-1-1-1ii−i−iiiiiii−i−i−i−i−i−i-1-1-1iii−i−i−i
χ4111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii111111111-1-1-1-1-1−i−iii−i−i−i−i−i−iiiiiii-1-1-1−i−i−iiii
χ5111111111111111-1-111111111-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1111-1-1111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ6111111111111111-1-111111111-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-111111-1-1-1−i−iiiiiiiii−i−i−i−i−i−i111−i−i−iiii
χ8111111111111111-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-111111-1-1-1ii−i−i−i−i−i−i−i−iiiiiii111iii−i−i−i
χ911111111-1-1-1-11-1-111111111111-1-11111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-11-1-1111-1-1111111-1-1-1-111-1-1-1-11-1-11-1-11-1-1
χ1011111111-1-1-1-11-1-111111111111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11-1-1111-1-1-1-1-1-1-1-11111-1-111111-1-1-111-111
χ1111111111-1-1-1-11-1-1111111-1-1-1-11-1-11111-1-1-1-11111-1-11111-1-1iiii−i−i−i−i11-1-1-1-11-1-1-1-1-111ii−i−iii−i−i−i−i−i−iiiii-111i−i−i−iii
χ1211111111-1-1-1-11-1-1111111-1-1-1-11-1-11111-1-1-1-11111-1-11111-1-1−i−i−i−iiiii11-1-1-1-11-1-1-1-1-111−i−iii−i−iiiiiii−i−i−i−i-111−iiii−i−i
χ1311111111-1-1-1-11-1-1-1-111111111-1111111-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111-1-1-1-1-111-111-111
χ1411111111-1-1-1-11-1-1-1-111111111-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-1-11-1-11111-1-11111-1-11111-1111-1-11-1-1
χ1511111111-1-1-1-11-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-111111-1-111-111−i−iiiii−i−i−i−i−i−iiiii1-1-1−iiii−i−i
χ1611111111-1-1-1-11-1-1-1-11111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-111111-1-111-111ii−i−i−i−iiiiiii−i−i−i−i1-1-1i−i−i−iii
χ17111111-1-111-1-1-11-11111111111-11-111-1-111-1-11111-1-111-1-11111111111-1-111-1-1-11-111-11-11111-1-111-1-1-1-111-1-1-11-1-11-1-11-1
χ18111111-1-111-1-1-11-11111111111-11-111-1-111-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-11-111-11-1-1-1-1-111-1-11111-1-111-11-11-111-11
χ19111111-1-111-1-1-11-1111111-1-1-1-1-11-111-1-111-1-1111111-1-111-1-1iiii−i−i−i−i-1-111-1-1-11-1-1-11-11ii−i−i−i−iii−i−iii−i−iii1-11−ii−ii−ii
χ20111111-1-111-1-1-11-1111111-1-1-1-1-11-111-1-111-1-1111111-1-111-1-1−i−i−i−iiiii-1-111-1-1-11-1-1-11-11−i−iiiii−i−iii−i−iii−i−i1-11i−ii−ii−i
χ21111111-1-111-1-1-11-1-1-1111111111-1111-1-111-1-1-1-1-1-1-1-111-1-1111111111111-1-111-11-1-1-1-11-1-1-1-1-1-1-111-1-1-1-111-1-11-111-111-11
χ22111111-1-111-1-1-11-1-1-1111111111-1111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-111-11-1-1-1-11-1111111-1-11111-1-1111-11-11-1-11-1
χ23111111-1-111-1-1-11-1-1-11111-1-1-1-11-1111-1-111-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i11-1-111-11-1111-11−i−iii−i−iii−i−iii−i−iii-11-1i−ii−ii−i
χ24111111-1-111-1-1-11-1-1-11111-1-1-1-11-1111-1-111-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii11-1-111-11-1111-11ii−i−iii−i−iii−i−iii−i−i-11-1−ii−ii−ii
χ25111111-1-1-1-111-1-111111111111-1-1111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-111-1-1111-1-111111-1-1-1-111-1-1-1-111-1-11-1-11-1-11
χ26111111-1-1-1-111-1-111111111111-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-11-1-1-1-11111-1-11111-1-1-1-1111-111-1
χ27111111-1-1-1-111-1-11111111-1-1-1-1-1-1111-1-1-1-11111111111-1-1-1-1iiii−i−i−i−i-1-1-1-111-1-11-1-111-1ii−i−i−i−i−i−iiiiiii−i−i11-1−i−iiii−i
χ28111111-1-1-1-111-1-11111111-1-1-1-1-1-1111-1-1-1-11111111111-1-1-1-1−i−i−i−iiiii-1-1-1-111-1-11-1-111-1−i−iiiiiii−i−i−i−i−i−iii11-1ii−i−i−ii
χ29111111-1-1-1-111-1-11-1-11111111111-111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-111-111-1
χ30111111-1-1-1-111-1-11-1-11111111111-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-1111111111-1-11111-1-111-1-1-11-1-11
χ31111111-1-1-1-111-1-11-1-11111-1-1-1-111-111-1-1-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-111111-1−i−iii−i−i−i−iiiiiii−i−i-1-11ii−i−i−ii
χ32111111-1-1-1-111-1-11-1-11111-1-1-1-111-111-1-1-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-111111-1ii−i−iiiii−i−i−i−i−i−iii-1-11−i−iiii−i
χ332222-2-2222222-2-2-20022222222000-2-22222220000222222-2-200000000000000-2-2-200-2-2-20000000000000000000000000
χ342222-2-2222222-2-2-2002222-2-2-2-2000-2-22222220000-2-2-2-2-2-22200000000000000-2-2-2002220000000000000000000000000
χ352222-2-222-2-2-2-2-2220022222222000-2-222-2-2-2-2000022-2-2-2-2-2-200000000000000-22200-2220000000000000000000000000
χ362222-2-222-2-2-2-2-222002222-2-2-2-2000-2-222-2-2-2-20000-2-222222200000000000000-222002-2-20000000000000000000000000
χ372222-2-2-2-222-2-22-220022222222000-2-2-2-222-2-20000-2-222-2-2-2-2000000000000002-22002-220000000000000000000000000
χ382222-2-2-2-222-2-22-22002222-2-2-2-2000-2-2-2-222-2-2000022-2-22222000000000000002-2200-22-20000000000000000000000000
χ392222-2-2-2-2-2-22222-20022222222000-2-2-2-2-2-2220000-2-2-2-222-2-20000000000000022-20022-20000000000000000000000000
χ402222-2-2-2-2-2-22222-2002222-2-2-2-2000-2-2-2-2-2-22200002222-2-2220000000000000022-200-2-220000000000000000000000000
χ412-22-22-20000000002i−2i22-2-22i−2i2i−2i0002-20000002i2i−2i−2i0000002i−2i−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ390000000002-2000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
χ422-22-22-20000000002i−2i22-2-22i−2i2i−2i0002-20000002i2i−2i−2i0000002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000002-20002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
χ432-22-22-20000000002i−2i22-2-2−2i2i−2i2i0002-20000002i2i−2i−2i000000−2i2i−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000-220002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ442-22-22-20000000002i−2i22-2-2−2i2i−2i2i0002-20000002i2i−2i−2i000000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000-22000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ452-22-22-2000000000−2i2i22-2-22i−2i2i−2i0002-2000000−2i−2i2i2i0000002i−2i−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000-220002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000
χ462-22-22-2000000000−2i2i22-2-22i−2i2i−2i0002-2000000−2i−2i2i2i0000002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000-22000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000
χ472-22-22-2000000000−2i2i22-2-2−2i2i−2i2i0002-2000000−2i−2i2i2i000000−2i2i−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ370000000002-2000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000
χ482-22-22-2000000000−2i2i22-2-2−2i2i−2i2i0002-2000000−2i−2i2i2i000000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000002-20002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000
χ492-2-22002-22-22-2000002-2-2222-2-2000002-22-22-200002-22-22-200i2−i2i2−i2i2−i2i2−i2000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000
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χ522-2-22002-22-22-2000002-2-22-2-222000002-22-22-20000-22-22-2200−22−222−22−2000000000000000000−22−22−222−22−22−2000000000
χ532-2-22002-2-22-22000002-2-2222-2-2000002-2-22-2200002-2-22-2200i2−i2i2−i2i2−i2i2−i2000000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2−i2i2000000000
χ542-2-22002-2-22-22000002-2-2222-2-2000002-2-22-2200002-2-22-2200−i2i2−i2i2−i2i2−i2i2000000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2i2−i2000000000
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χ562-2-22002-2-22-22000002-2-22-2-222000002-2-22-220000-222-22-200−22−222−22−2000000000000000000−222−22−22−2−22−22000000000
χ572-2-2200-222-2-22000002-2-2222-2-200000-222-2-220000-222-2-2200i2−i2i2−i2i2−i2i2−i2000000000000000000−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2000000000
χ582-2-2200-222-2-22000002-2-2222-2-200000-222-2-220000-222-2-2200−i2i2−i2i2−i2i2−i2i2000000000000000000i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2000000000
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χ602-2-2200-222-2-22000002-2-22-2-22200000-222-2-2200002-2-222-200−22−222−22−20000000000000000002−2−222−2−222−2−22000000000
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χ642-2-2200-22-222-2000002-2-22-2-22200000-22-222-200002-22-2-2200−22−222−22−20000000000000000002−22−2−22−22−222−2000000000
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χ66444444444444444-4-4-1-1-1-10000-4-4-4-1-1-1-1-1-1-1-111110000000000000000111111-1-1-1000000000000000000000000000000
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χ8244-4-400000000000004-44-44i−4i−4i4i00000000000000000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000000
χ8344-4-400000000000004-44-4−4i4i4i−4i000000000000000000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000000000000000000000000000000000000000
χ8444-4-400000000000004-44-4−4i4i4i−4i00000000000000000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000000
χ854-44-4-440000000000044-4-44i−4i4i−4i000-440000000000000000−4i4i00000000000000000000000000000000000000000000000
χ864-44-4-440000000000044-4-4−4i4i−4i4i000-4400000000000000004i−4i00000000000000000000000000000000000000000000000
χ878-88-88-80000000008i−8i-2-2220000000-22000000−2i−2i2i2i0000000000000000000000000000000000000000000000000000000
χ888-88-88-8000000000−8i8i-2-2220000000-220000002i2i−2i−2i0000000000000000000000000000000000000000000000000000000
χ898-88-8-8800000000000-2-22200000002-20000002i5−2i5−2i52i50000000000000000000000000000000000000000000000000000000
χ908-88-8-8800000000000-2-22200000002-2000000−2i52i52i5−2i50000000000000000000000000000000000000000000000000000000
χ918-8-88008-88-88-800000-222-2000000000-22-22-2200000000000000000000000000000000000000000000000000000000000
χ928-8-88008-8-88-8800000-222-2000000000-222-22-200000000000000000000000000000000000000000000000000000000000
χ938-8-8800-888-8-8800000-222-20000000002-2-222-200000000000000000000000000000000000000000000000000000000000
χ948-8-8800-88-888-800000-222-20000000002-22-2-2200000000000000000000000000000000000000000000000000000000000
χ951616-16-160000000000000-44-4400000000000000000000000000000000000000000000000000000000000000000000000000

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