Finite Group Databasebeta

← Group #13088702

Character table — Group #13088702

Order 1440.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222224444444444444444555566666688888888888810101010101010101212121212121212121212122020202030303030303030303030303030303030303090909090
order12443366121212123561012121515202030306060606022442466121215151530303060606060606066661212121210102020303030306060606066121224668888121224242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−i−iii−i−i
χ61111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iii-1-1−i−i−i−iiiii−i−iii
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i11iiii−i−i−i−i−i−iii
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii11−i−i−i−iiiiiii−i−i
χ911-1-11111-1-1-1-11111-1-111-1-111-1-1-1-111-1-11-111-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11-111i−ii−i-1-1ii−i−iii−i−ii−ii−i
χ1011-1-11111-1-1-1-11111-1-111-1-111-1-1-1-111-1-11-111-1-1111111-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-11-111−ii−ii-1-1−i−iii−i−iii−ii−ii
χ1111-1-11111-1-1-1-11111-1-111-1-111-1-1-1-111-1-1-11-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-11-1-1i−ii−i11ii−i−iii−i−i−ii−ii
χ1211-1-11111-1-1-1-11111-1-111-1-111-1-1-1-111-1-1-11-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111111-1-1-11-1-1−ii−ii11−i−iii−i−iiii−ii−i
χ1311-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1111-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-11-1-11-1-111111-1-1-1-1111-1-11
χ1411-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1111-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-11-1-1-111-111-1-11111-1-1-111-1
χ1511-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1-1-111-11-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1111-1111-1-11-1-111-1-1-1-111-111-1
χ1611-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1-1-111-11-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1111-111-111-1-1-1-1-11111-1-11-1-11
χ1722222-12-122-1-1-12-12-1-1-1-122-1-1-1-1-1-1222222-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-10000-1-1000000000000
χ1822222-12-122-1-1-12-12-1-1-1-122-1-1-1-1-1-12222-2-211112-1-12-1-122-1-1-1-122-1-1-1-122-2-2-2-211111111-1-1-1-1-2-211000011000000000000
χ1922222-12-122-1-1-12-12-1-1-1-122-1-1-1-1-1-1-2-2-2-222-1-1-1-12-1-12-1-122-1-1-1-1-2-21111-2-22222-1-1-1-1-1-1-1-11111-2-211000011000000000000
χ2022222-12-122-1-1-12-12-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-211112-1-12-1-122-1-1-1-1-2-21111-2-2-2-2-2-211111111111122-1-10000-1-1000000000000
χ212222-12-12-1-122-12-12-1-122222222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1000000000000-1-1-1-10000222200-1-1-1-1-1-1-1-10000
χ222222-12-12-1-122-12-12-1-122222222222222000000-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1000000000000-1-1-1-10000-2-2-2-200111111110000
χ232222-12-12-1-122-12-12-1-12222222222-2-2-2-2000000-1-1-1-1-1-1-1-1-1-1-1-111-2-2-2-211000000000000111100002i2i−2i−2i00−i−i−i−iiiii0000
χ242222-12-12-1-122-12-12-1-12222222222-2-2-2-2000000-1-1-1-1-1-1-1-1-1-1-1-111-2-2-2-21100000000000011110000−2i−2i2i2i00iiii−i−i−i−i0000
χ2522-2-22-12-1-2-211-12-1211-1-1-2-2-1-1111122-2-22-2-1-1112-1-12-1-1-2-2111122-1-111-2-222-2-2-1-1-1-11111-1-1112-2-1-1000011000000000000
χ2622-2-22-12-1-2-211-12-1211-1-1-2-2-1-1111122-2-2-2211-1-12-1-12-1-1-2-2111122-1-111-2-2-2-2221111-1-1-1-1-1-111-22110000-1-1000000000000
χ2722-2-22-12-1-2-211-12-1211-1-1-2-2-1-11111-2-2222-2-1-1112-1-12-1-1-2-21111-2-211-1-12222-2-2-1-1-1-1111111-1-1-22110000-1-1000000000000
χ2822-2-22-12-1-2-211-12-1211-1-1-2-2-1-11111-2-222-2211-1-12-1-12-1-1-2-21111-2-211-1-122-2-2221111-1-1-1-111-1-12-2-1-1000011000000000000
χ2922-2-2-12-1211-2-2-12-121122-2-222-2-2-2-222-2-2000000-1-1-1-1-1-1111111-1-122-2-211000000000000-1-11100002i−2i2i−2i00−i−iii−i−iii0000
χ3022-2-2-12-1211-2-2-12-121122-2-222-2-2-2-222-2-2000000-1-1-1-1-1-1111111-1-122-2-211000000000000-1-1110000−2i2i−2i2i00ii−i−iii−i−i0000
χ3122-2-2-12-1211-2-2-12-121122-2-222-2-2-2-2-2-222000000-1-1-1-1-1-111111111-2-222-1-100000000000011-1-100002-2-2200-1-11111-1-10000
χ3222-2-2-12-1211-2-2-12-121122-2-222-2-2-2-2-2-222000000-1-1-1-1-1-111111111-2-222-1-100000000000011-1-10000-222-20011-1-1-1-1110000
χ332-22i−2i22-2-22i−2i2i−2i22-2-22i−2i222i−2i-2-22i2i−2i−2i2-22i−2i000000222-2-2-22i−2i2i2i−2i−2i2-22-22i−2i2i−2i0000000000002-22i−2i0000000000000000000000
χ342-22i−2i22-2-22i−2i2i−2i22-2-22i−2i222i−2i-2-22i2i−2i−2i-22−2i2i000000222-2-2-22i−2i2i2i−2i−2i-22-22−2i2i−2i2i000000000000-22−2i2i0000000000000000000000
χ352-22i−2i2-1-212i−2i−ii-121-2−ii-1-12i−2i11−i−iii2-22i−2i00−i3i33−32-1-1-2112i−2i−i−iii2-2-11−ii2i−2i0000−i3−i3i3i333−3−3-11−ii00−i3i300003−3000000000000
χ362-22i−2i2-1-212i−2i−ii-121-2−ii-1-12i−2i11−i−iii2-22i−2i00i3−i3−332-1-1-2112i−2i−i−iii2-2-11−ii2i−2i0000i3i3−i3−i3−3−333-11−ii00i3−i30000−33000000000000
χ372-22i−2i2-1-212i−2i−ii-121-2−ii-1-12i−2i11−i−iii-22−2i2i00−i3i33−32-1-1-2112i−2i−i−iii-221-1i−i−2i2i0000−i3−i3i3i333−3−31-1i−i00i3−i30000−33000000000000
χ382-22i−2i2-1-212i−2i−ii-121-2−ii-1-12i−2i11−i−iii-22−2i2i00i3−i3−332-1-1-2112i−2i−i−iii-221-1i−i−2i2i0000i3i3−i3−i3−3−3331-1i−i00−i3i300003−3000000000000
χ392-22i−2i-121-2−ii2i−2i-121-2−ii222i−2i-2-22i2i−2i−2i2-22i−2i000000-1-1-1111−ii−i−iii-112-22i−2i−ii000000000000-11−ii0000000000ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ1090000
χ402-22i−2i-121-2−ii2i−2i-121-2−ii222i−2i-2-22i2i−2i−2i2-22i−2i000000-1-1-1111−ii−i−iii-112-22i−2i−ii000000000000-11−ii0000000000−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ1090000
χ412-22i−2i-121-2−ii2i−2i-121-2−ii222i−2i-2-22i2i−2i−2i-22−2i2i000000-1-1-1111−ii−i−iii1-1-22−2i2ii−i0000000000001-1i−i0000000000ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ1190000
χ422-22i−2i-121-2−ii2i−2i-121-2−ii222i−2i-2-22i2i−2i−2i-22−2i2i000000-1-1-1111−ii−i−iii1-1-22−2i2ii−i0000000000001-1i−i0000000000−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ1190000
χ432-2−2i2i22-2-2−2i2i−2i2i22-2-2−2i2i22−2i2i-2-2−2i−2i2i2i2-2−2i2i000000222-2-2-2−2i2i−2i−2i2i2i2-22-2−2i2i−2i2i0000000000002-2−2i2i0000000000000000000000
χ442-2−2i2i22-2-2−2i2i−2i2i22-2-2−2i2i22−2i2i-2-2−2i−2i2i2i-222i−2i000000222-2-2-2−2i2i−2i−2i2i2i-22-222i−2i2i−2i000000000000-222i−2i0000000000000000000000
χ452-2−2i2i2-1-21−2i2ii−i-121-2i−i-1-1−2i2i11ii−i−i2-2−2i2i00−i3i3−332-1-1-211−2i2iii−i−i2-2-11i−i−2i2i0000−i3−i3i3i3−3−333-11i−i00−i3i30000−33000000000000
χ462-2−2i2i2-1-21−2i2ii−i-121-2i−i-1-1−2i2i11ii−i−i2-2−2i2i00i3−i33−32-1-1-211−2i2iii−i−i2-2-11i−i−2i2i0000i3i3−i3−i333−3−3-11i−i00i3−i300003−3000000000000
χ472-2−2i2i2-1-21−2i2ii−i-121-2i−i-1-1−2i2i11ii−i−i-222i−2i00−i3i3−332-1-1-211−2i2iii−i−i-221-1−ii2i−2i0000−i3−i3i3i3−3−3331-1−ii00i3−i300003−3000000000000
χ482-2−2i2i2-1-21−2i2ii−i-121-2i−i-1-1−2i2i11ii−i−i-222i−2i00i3−i33−32-1-1-211−2i2iii−i−i-221-1−ii2i−2i0000i3i3−i3−i333−3−31-1−ii00−i3i30000−33000000000000
χ492-2−2i2i-121-2i−i−2i2i-121-2i−i22−2i2i-2-2−2i−2i2i2i2-2−2i2i000000-1-1-1111i−iii−i−i-112-2−2i2ii−i000000000000-11i−i0000000000ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ1190000
χ502-2−2i2i-121-2i−i−2i2i-121-2i−i22−2i2i-2-2−2i−2i2i2i2-2−2i2i000000-1-1-1111i−iii−i−i-112-2−2i2ii−i000000000000-11i−i0000000000−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ1190000
χ512-2−2i2i-121-2i−i−2i2i-121-2i−i22−2i2i-2-2−2i−2i2i2i-222i−2i000000-1-1-1111i−iii−i−i1-1-222i−2i−ii0000000000001-1−ii0000000000ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ1090000
χ522-2−2i2i-121-2i−i−2i2i-121-2i−i22−2i2i-2-2−2i−2i2i2i-222i−2i000000-1-1-1111i−iii−i−i1-1-222i−2i−ii0000000000001-1−ii0000000000−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ1090000
χ534444444444444-14-144-1-1-1-1-1-1-1-1-1-10000444444-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ544444444444444-14-144-1-1-1-1-1-1-1-1-1-10000-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-10000000011111111111100000000000000000000000000
χ5544444-24-244-2-2-2-1-2-1-2-21−i1521+i152-1-11−i1521+i1521−i1521+i1521−i1521+i152000044-2-2-2-2-11−i1521+i152-11−i1521+i152-1-11−i1521+i1521−i1521+i15200000000-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i15200000000000000000000000000
χ5644444-24-244-2-2-2-1-2-1-2-21−i1521+i152-1-11−i1521+i1521−i1521+i1521−i1521+i1520000-4-42222-11−i1521+i152-11−i1521+i152-1-11−i1521+i1521−i1521+i152000000001111−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i15200000000000000000000000000
χ5744444-24-244-2-2-2-1-2-1-2-21+i1521−i152-1-11+i1521−i1521+i1521−i1521+i1521−i152000044-2-2-2-2-11+i1521−i152-11+i1521−i152-1-11+i1521−i1521+i1521−i15200000000-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i15200000000000000000000000000
χ5844444-24-244-2-2-2-1-2-1-2-21+i1521−i152-1-11+i1521−i1521+i1521−i1521+i1521−i1520000-4-42222-11+i1521−i152-11+i1521−i152-1-11+i1521−i1521+i1521−i152000000001111−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i15200000000000000000000000000
χ594444-2-2-2-2-2-2-2-2141411-2-244-2-2-2-2-2-24444000000-211-211-2-21111-2-2-2-2-2-2-2-200000000000011110000000000000000000000
χ604444-2-2-2-2-2-2-2-2141411-2-244-2-2-2-2-2-2-4-4-4-4000000-211-211-2-2111122222222000000000000-1-1-1-10000000000000000000000
χ6144-4-44444-4-4-4-44-14-1-4-4-1-111-1-1111100004-444-4-4-1-1-1-1-1-111111100000000-1-111-1-1-1-1111100000000000000000000000000
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χ928-88i−8i-4-444−4i4i−4i4i2-2-222i−2i1−i151+i15−2i2i−1+i15−1−i152ζ14+2ζ22+2ζ86+2ζ1182ζ38+2ζ46+2ζ62+2ζ94−2ζ14−2ζ22−2ζ86−2ζ118−2ζ38−2ζ46−2ζ62−2ζ9400000000001−1+i152−1−i152-11−i1521+i152i−i−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ94ζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ940000000000000000000000000000000000000000000000
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χ958-8−8i8i-4-4444i−4i4i−4i2-2-22−2i2i1−i151+i152i−2i−1+i15−1−i15−2ζ14−2ζ22−2ζ86−2ζ118−2ζ38−2ζ46−2ζ62−2ζ942ζ14+2ζ22+2ζ86+2ζ1182ζ38+2ζ46+2ζ62+2ζ9400000000001−1+i152−1−i152-11−i1521+i152−iiζ14+ζ22+ζ86+ζ118ζ38+ζ46+ζ62+ζ94−ζ14−ζ22−ζ86−ζ118−ζ38−ζ46−ζ62−ζ940000000000000000000000000000000000000000000000
χ968-8−8i8i-4-4444i−4i4i−4i2-2-22−2i2i1+i151−i152i−2i−1−i15−1+i15−2ζ38−2ζ46−2ζ62−2ζ94−2ζ14−2ζ22−2ζ86−2ζ1182ζ38+2ζ46+2ζ62+2ζ942ζ14+2ζ22+2ζ86+2ζ11800000000001−1−i152−1+i152-11+i1521−i152−iiζ38+ζ46+ζ62+ζ94ζ14+ζ22+ζ86+ζ118−ζ38−ζ46−ζ62−ζ94−ζ14−ζ22−ζ86−ζ1180000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.