Finite Group Databasebeta

← Group #13020845

Character table — Group #13020845

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222444444444445555888888888888888810101010101010101616161616161616202020202020202020202020202020202020204040404080808080
order12224444888845881010102020202022228888202020204040404040404040444488884040404040404040444444444888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1iiii−i−i−i−i-1-1iiii−i−i−i−i-1-1-1-1ii−i−i
χ611111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1−i−i−i−iiiii-1-1−i−i−i−iiiii-1-1-1-1−i−iii
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i1111−i−iii
χ811111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii1111ii−i−i
χ911111111-1-1-1-111-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11-11-1
χ1011111111-1-1-1-111-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111111111-1-1-11-11
χ1111111111-1-1-1-111-1-111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-11
χ1211111111-1-1-1-111-1-111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1111-11-1
χ1311111111-1-1-1-111-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1iiii−i−i−i−i11−i−i−i−iiiii-1-111i−i−ii
χ1411111111-1-1-1-111-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1−i−i−i−iiiii11iiii−i−i−i−i-1-111−iii−i
χ1511111111-1-1-1-111-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1iiii−i−i−i−i11−i−i−i−iiiii11-1-1−iii−i
χ1611111111-1-1-1-111-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1−i−i−i−iiiii11iiii−i−i−i−i11-1-1i−i−ii
χ17222222-2-22222-22-2-2222-2-2-2-222220000-2-2222222-2-2-2-22-2-22222200000000-200000000-2-20000000000000000
χ18222222-2-22222-22-2-2222-2-2-2-2-2-2-2-20000-2-2222222-2-2-2-2-222-2-2-2-2-200000000200000000220000000000000000
χ19222222-2-2-2-2-2-2-2222222-2-2-2-222220000-2-222-2-2-2-222222-2-22-2-2-2-200000000-200000000220000000000000000
χ20222222-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000-2-222-2-2-2-22222-222-2222200000000200000000-2-20000000000000000
χ212222-2-2220000-2200222222222220000-2-2-2-200000000-222-2000000000000-222-2-222-2-2000000000000000000
χ222222-2-2220000-2200222222222220000-2-2-2-200000000-222-2000000000000-2-2-222-2-222000000000000000000
χ232222-2-2220000-22002222222-2-2-2-20000-2-2-2-2000000002-2-2200000000000022i2i−2i−2i−2i−2i2i2i000000000000000000
χ242222-2-2220000-22002222222-2-2-2-20000-2-2-2-2000000002-2-220000000000002−2i−2i2i2i2i2i−2i−2i000000000000000000
χ252222-2-2-2-200002200222-2-2-2-22222000022-2-200000000-2-2-2-2000000000000200000000002i2i−2i−2i2i2i−2i−2i00000000
χ262222-2-2-2-200002200222-2-2-2-22222000022-2-200000000-2-2-2-200000000000020000000000−2i−2i2i2i−2i−2i2i2i00000000
χ272222-2-2-2-200002200222-2-2-2-2-2-2-2-2000022-2-2000000002222000000000000-2000000000022-2-2-2-22200000000
χ282222-2-2-2-200002200222-2-2-2-2-2-2-2-2000022-2-2000000002222000000000000-20000000000-2-22222-2-200000000
χ2922-2-2002-2i2i2−i2−i202i2−i22-2-222-2-22-22-200000000i2i2−i2−i2i2i2−i2−i202-20i2i2−i2−i2000000000002i−2i002i−2ii2−i22−22−22−22−200000000
χ3022-2-2002-2i2i2−i2−i202i2−i22-2-222-2-22-22-200000000i2i2−i2−i2i2i2−i2−i202-20i2i2−i2−i200000000000−2i2i00−2i2ii2−i2−22−22−22−2200000000
χ3122-2-2002-2i2i2−i2−i202i2−i22-2-222-2-2-22-2200000000i2i2−i2−i2i2i2−i2−i20-220−i2−i2i2i2000000000002-200-22−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ3222-2-2002-2i2i2−i2−i202i2−i22-2-222-2-2-22-2200000000i2i2−i2−i2i2i2−i2−i20-220−i2−i2i2i200000000000-22002-2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ3322-2-2002-2−i2−i2i2i202−i2i22-2-222-2-22-22-200000000−i2−i2i2i2−i2−i2i2i202-20−i2−i2i2i2000000000002i−2i002i−2i−i2i2−22−22−22−2200000000
χ3422-2-2002-2−i2−i2i2i202−i2i22-2-222-2-22-22-200000000−i2−i2i2i2−i2−i2i2i202-20−i2−i2i2i200000000000−2i2i00−2i2i−i2i22−22−22−22−200000000
χ3522-2-2002-2−i2−i2i2i202−i2i22-2-222-2-2-22-2200000000−i2−i2i2i2−i2−i2i2i20-220i2i2−i2−i2000000000002-200-22i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ3622-2-2002-2−i2−i2i2i202−i2i22-2-222-2-2-22-2200000000−i2−i2i2i2−i2−i2i2i20-220i2i2−i2−i200000000000-22002-2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ3722-2-200-22i2i2−i2−i202−i2i22-2-2-2-2222-22-200000000i2i2−i2−i2−i2−i2i2i20-220i2i2−i2−i20000000002-2002-200−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ3822-2-200-22i2i2−i2−i202−i2i22-2-2-2-2222-22-200000000i2i2−i2−i2−i2−i2i2i20-220i2i2−i2−i2000000000-2200-2200−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ3922-2-200-22i2i2−i2−i202−i2i22-2-2-2-222-22-2200000000i2i2−i2−i2−i2−i2i2i202-20−i2−i2i2i20000000002i−2i00−2i2i00i2−i2−222−22−2−2200000000
χ4022-2-200-22i2i2−i2−i202−i2i22-2-2-2-222-22-2200000000i2i2−i2−i2−i2−i2i2i202-20−i2−i2i2i2000000000−2i2i002i−2i00i2−i22−2−22−222−200000000
χ4122-2-200-22−i2−i2i2i202i2−i22-2-2-2-2222-22-200000000−i2−i2i2i2i2i2−i2−i20-220−i2−i2i2i20000000002-2002-200i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ4222-2-200-22−i2−i2i2i202i2−i22-2-2-2-2222-22-200000000−i2−i2i2i2i2i2−i2−i20-220−i2−i2i2i2000000000-2200-2200i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ4322-2-200-22−i2−i2i2i202i2−i22-2-2-2-222-22-2200000000−i2−i2i2i2i2i2−i2−i202-20i2i2−i2−i20000000002i−2i00−2i2i00−i2i22−2−22−222−200000000
χ4422-2-200-22−i2−i2i2i202i2−i22-2-2-2-222-22-2200000000−i2−i2i2i2i2i2−i2−i202-20i2i2−i2−i2000000000−2i2i002i−2i00−i2i2−222−22−2−2200000000
χ452-22-22-2002-22-20200-22-2000022-2-2i2−i2i2−i2002-22-22-20000-20022-22-2i2i2−i2−i2i2i2−i2−i20000000000000000000i2−i2i2−i20000
χ462-22-22-2002-22-20200-22-2000022-2-2−i2i2−i2i2002-22-22-20000-20022-22-2−i2−i2i2i2−i2−i2i2i20000000000000000000−i2i2−i2i20000
χ472-22-22-2002-22-20200-22-20000-2-222i2−i2i2−i2002-22-22-20000200-2-22-22i2i2−i2−i2i2i2−i2−i20000000000000000000−i2i2−i2i20000
χ482-22-22-2002-22-20200-22-20000-2-222−i2i2−i2i2002-22-22-20000200-2-22-22−i2−i2i2i2−i2−i2i2i20000000000000000000i2−i2i2−i20000
χ492-22-22-200-22-220200-22-2000022-2-2i2−i2−i2i2002-2-22-220000-2002-22-22i2i2−i2−i2−i2−i2i2i20000000000000000000i2−i2−i2i20000
χ502-22-22-200-22-220200-22-2000022-2-2−i2i2i2−i2002-2-22-220000-2002-22-22−i2−i2i2i2i2i2−i2−i20000000000000000000−i2i2i2−i20000
χ512-22-22-200-22-220200-22-20000-2-222i2−i2−i2i2002-2-22-220000200-22-22-2i2i2−i2−i2−i2−i2i2i20000000000000000000−i2i2i2−i20000
χ522-22-22-200-22-220200-22-20000-2-222−i2i2i2−i2002-2-22-220000200-22-22-2−i2−i2i2i2i2i2−i2−i20000000000000000000i2−i2−i2i20000
χ534444444444444-144-1-1-1-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1000000000000000000000000000
χ544444444444444-144-1-1-1-1-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-10000000011111111000000000000000000000000000
χ5544444444-4-4-4-44-1-4-4-1-1-1-1-1-1-1000044-4-4-1-1-1-11111111100000000-1-1-1-11111000000000000000000000000000
χ5644444444-4-4-4-44-1-4-4-1-1-1-1-1-1-10000-4-444-1-1-1-111111111000000001111-1-1-1-1000000000000000000000000000
χ57444444-4-44444-4-1-4-4-1-1-111110000000011-1-1-1-1-1-1111100000000i5−i5i5−i5i5−i5i5−i5000000000000000000000000000
χ58444444-4-44444-4-1-4-4-1-1-111110000000011-1-1-1-1-1-1111100000000−i5i5−i5i5−i5i5−i5i5000000000000000000000000000
χ59444444-4-4-4-4-4-4-4-144-1-1-111110000000011-1-11111-1-1-1-100000000i5−i5i5−i5−i5i5−i5i5000000000000000000000000000
χ60444444-4-4-4-4-4-4-4-144-1-1-111110000000011-1-11111-1-1-1-100000000−i5i5−i5i5i5−i5i5−i5000000000000000000000000000
χ614-44-44-4004-44-40-1001-11i5−i5i5−i500002i2−2i22i2−2i2i5−i5-11-11-11i5−i5i5−i500000000ζ7+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−ζ39000000000000000000000000000
χ624-44-44-4004-44-40-1001-11i5−i5i5−i50000−2i22i2−2i22i2i5−i5-11-11-11i5−i5i5−i500000000−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+ζ39000000000000000000000000000
χ634-44-44-4004-44-40-1001-11−i5i5−i5i500002i2−2i22i2−2i2−i5i5-11-11-11−i5i5−i5i500000000ζ13+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−ζ29000000000000000000000000000
χ644-44-44-4004-44-40-1001-11−i5i5−i5i50000−2i22i2−2i22i2−i5i5-11-11-11−i5i5−i5i500000000−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+ζ29000000000000000000000000000
χ654-44-44-400-44-440-1001-11i5−i5i5−i500002i2−2i2−2i22i2i5−i5-111-11-1−i5i5−i5i500000000ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39000000000000000000000000000
χ664-44-44-400-44-440-1001-11i5−i5i5−i50000−2i22i22i2−2i2i5−i5-111-11-1−i5i5−i5i500000000−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39000000000000000000000000000
χ674-44-44-400-44-440-1001-11−i5i5−i5i500002i2−2i2−2i22i2−i5i5-111-11-1i5−i5i5−i500000000ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29000000000000000000000000000
χ684-44-44-400-44-440-1001-11−i5i5−i5i50000−2i22i22i2−2i2−i5i5-111-11-1i5−i5i5−i500000000−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29000000000000000000000000000
χ694-44-4-440000000400-44-4000044-4-4000000-4400000000400-4000000000000000000000000000000000000000
χ704-44-4-440000000400-44-40000-4-444000000-4400000000-4004000000000000000000000000000000000000000
χ714-4-4400002i2−2i2−2i22i20400-4-4400004-4-44000000002i2−2i2−2i22i2000000002i2−2i2−2i22i200000000000000000000000000000000000
χ724-4-4400002i2−2i2−2i22i20400-4-440000-444-4000000002i2−2i2−2i22i200000000−2i22i22i2−2i200000000000000000000000000000000000
χ734-4-440000−2i22i22i2−2i20400-4-4400004-4-4400000000−2i22i22i2−2i200000000−2i22i22i2−2i200000000000000000000000000000000000
χ744-4-440000−2i22i22i2−2i20400-4-440000-444-400000000−2i22i22i2−2i2000000002i2−2i2−2i22i200000000000000000000000000000000000
χ758888-8-8880000-8-200-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000000000000000000
χ768888-8-8-8-800008-200-2-2-2222200000000-2-222000000000000000000000000000000000000000000000000000
χ7788-8-8008-84i24i2−4i2−4i20-24i2−4i2-222-2-222000000000000−i2−i2i2i2−i2−i2i2i20000000000000000000000000000000000000000000
χ7888-8-8008-8−4i2−4i24i24i20-2−4i24i2-222-2-222000000000000i2i2−i2−i2i2i2−i2−i20000000000000000000000000000000000000000000
χ7988-8-800-884i24i2−4i2−4i20-2−4i24i2-22222-2-2000000000000−i2−i2i2i2i2i2−i2−i20000000000000000000000000000000000000000000
χ8088-8-800-88−4i2−4i24i24i20-24i2−4i2-22222-2-2000000000000i2i2−i2−i2−i2−i2i2i20000000000000000000000000000000000000000000
χ818-88-8-880000000-2002-222i5−2i52i5−2i500000000−2i52i52-2000000000000000000000000000000000000000000000000000
χ828-88-8-880000000-2002-22−2i52i5−2i52i5000000002i5−2i52-2000000000000000000000000000000000000000000000000000
χ838-8-8800004i2−4i2−4i24i20-20022-22i5−2i5−2i52i5000000000000−i2i2i2−i2−101010−100000000000000000000000000000000000000000000
χ848-8-8800004i2−4i2−4i24i20-20022-2−2i52i52i5−2i5000000000000−i2i2i2−i210−10−10100000000000000000000000000000000000000000000
χ858-8-880000−4i24i24i2−4i20-20022-22i5−2i5−2i52i5000000000000i2−i2−i2i210−10−10100000000000000000000000000000000000000000000
χ868-8-880000−4i24i24i2−4i20-20022-2−2i52i52i5−2i5000000000000i2−i2−i2i2−101010−100000000000000000000000000000000000000000000

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