Finite Group Databasebeta

← Group #13034119

Character table — Group #13034119

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size1111111144444444444444555555558888888888882020202020202020202020202020202020202020202011111111444444444444445555555588888888888820202020202020202020202020202020202020202020
order12222222444444510101010101010444444442020202020202020202020202222228888888888888888222222224444441010101010101010444444442020202020202020202020202222228888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ41111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ51111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111-1-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111111111-1-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-11111111111-1-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii11111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i11111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1ii−i−i−i−iii−i−iiiii−i−i11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1−i−iiiii−i−iii−i−i−i−iii11111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222-2-2-2-20000002222-2-2-2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372222-2-2-2-20000002222-2-2-2-22i2i2i2i−2i−2i−2i−2i000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ182222-2-2-2-20000002222-2-2-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372222-2-2-2-20000002222-2-2-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ192222-2-2-2-20000002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392222-2-2-2-20000002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ202222-2-2-2-20000002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392222-2-2-2-20000002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ2122-2-222-2-200000022-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370022-2-222-2-200000022-2-222-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700
χ2222-2-222-2-200000022-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370022-2-222-2-200000022-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700
χ2322-2-222-2-200000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390022-2-222-2-200000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900
χ2422-2-222-2-200000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390022-2-222-2-200000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i00000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900
χ2522-2-2-2-2222-2000022-2-2-2-22222-2-2-2-22222-2-2000000002-20000000000000000000022-2-2-2-2222-2000022-2-2-2-22222-2-2-2-22222-2-2000000002-200000000000000000000
χ2622-2-2-2-2222-2000022-2-2-2-222-2-22222-2-222-2-200000000-220000000000000000000022-2-2-2-2222-2000022-2-2-2-222-2-22222-2-222-2-200000000-2200000000000000000000
χ2722-2-2-2-222-22000022-2-2-2-22222-2-2-2-222-2-22200000000-220000000000000000000022-2-2-2-222-22000022-2-2-2-22222-2-2-2-222-2-22200000000-2200000000000000000000
χ2822-2-2-2-222-22000022-2-2-2-222-2-22222-2-2-2-222000000002-20000000000000000000022-2-2-2-222-22000022-2-2-2-222-2-22222-2-2-2-222000000002-200000000000000000000
χ292-22-22-22-20000002-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700002-22-22-22-20000002-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ302-22-22-22-20000002-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002-22-22-22-20000002-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ312-22-22-22-20000002-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900002-22-22-22-20000002-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ322-22-22-22-20000002-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002-22-22-22-20000002-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ332-22-2-22-22002-2002-22-2-22-222-22-2-22-22000022-2-20000002-20000000000000000002-22-2-22-22002-2002-22-2-22-222-22-2-22-22000022-2-20000002-2000000000000000000
χ342-22-2-22-22002-2002-22-2-22-22-22-222-22-2000022-2-2000000-220000000000000000002-22-2-22-22002-2002-22-2-22-22-22-222-22-2000022-2-2000000-22000000000000000000
χ352-22-2-22-2200-22002-22-2-22-222-22-2-22-220000-2-222000000-220000000000000000002-22-2-22-2200-22002-22-2-22-222-22-2-22-220000-2-222000000-22000000000000000000
χ362-22-2-22-2200-22002-22-2-22-22-22-222-22-20000-2-2220000002-20000000000000000002-22-2-22-2200-22002-22-2-22-22-22-222-22-20000-2-2220000002-2000000000000000000
χ372-2-222-2-2200002-22-2-222-2-222-2-222-2-220000000022-2-200002-200000000000000002-2-222-2-2200002-22-2-222-2-222-2-222-2-220000000022-2-200002-20000000000000000
χ382-2-222-2-2200002-22-2-222-2-22-222-2-222-20000000022-2-20000-2200000000000000002-2-222-2-2200002-22-2-222-2-22-222-2-222-20000000022-2-20000-220000000000000000
χ392-2-222-2-220000-222-2-222-2-222-2-222-2-2200000000-2-2220000-2200000000000000002-2-222-2-220000-222-2-222-2-222-2-222-2-2200000000-2-2220000-220000000000000000
χ402-2-222-2-220000-222-2-222-2-22-222-2-222-200000000-2-22200002-200000000000000002-2-222-2-220000-222-2-222-2-22-222-2-222-200000000-2-22200002-20000000000000000
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χ422-2-22-222-20000002-2-22-222-22i−2i−2i2i−2i2i2i−2i0000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000002-2-22-222-20000002-2-22-222-22i−2i−2i2i−2i2i2i−2i0000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.