Finite Group Databasebeta

← Group #13020847

Character table — Group #13020847

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
χ511111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1ii−i−iii−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−iii−i−iii-1-1−i−i−i−iiiii-1-1-1-1−i−iii
χ711111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−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−iii−i−iii-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
χ1311111111-1-1-1-111-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1ii−i−iii−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−iii−i−iii11iiii−i−i−i−i-1-111−iii−i
χ1511111111-1-1-1-111-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1ii−i−iii−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−iii−i−iii11iiii−i−i−i−i11-1-1i−i−ii
χ1722222-2-220000-2200222222222220000-2-2-2-20000000022-2-2000000000000-22222-2-2-2-2000000000000000000
χ1822222-2-220000-2200222222222220000-2-2-2-20000000022-2-2000000000000-2-2-2-2-22222000000000000000000
χ1922222-2-220000-22002222222-2-2-2-20000-2-2-2-200000000-2-22200000000000022i2i−2i−2i−2i−2i2i2i000000000000000000
χ2022222-2-220000-22002222222-2-2-2-20000-2-2-2-200000000-2-2220000000000002−2i−2i2i2i2i2i−2i−2i000000000000000000
χ212222-222-22222-22-2-2222-2-2-2-222220000-2-2222222-2-2-2-2-2-222222200000000-200000000-2-20000000000000000
χ222222-222-22222-22-2-2222-2-2-2-2-2-2-2-20000-2-2222222-2-2-2-222-2-2-2-2-2-200000000200000000220000000000000000
χ232222-222-2-2-2-2-2-2222222-2-2-2-222220000-2-222-2-2-2-22222-2-222-2-2-2-200000000-200000000220000000000000000
χ242222-222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000-2-222-2-2-2-2222222-2-2222200000000200000000-2-20000000000000000
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
χ2922-2-202-2022-2-202002-2-2000022-2-22−22−2002-222-2-20000002-222-2-222−2−222−2−200000000000000000002−22−20000
χ3022-2-202-2022-2-202002-2-2000022-2-2−22−22002-222-2-20000002-222-2-2−2−222−2−2220000000000000000000−22−220000
χ3122-2-202-2022-2-202002-2-20000-2-2222−22−2002-222-2-2000000-22-2-22222−2−222−2−20000000000000000000−22−220000
χ3222-2-202-2022-2-202002-2-20000-2-222−22−22002-222-2-2000000-22-2-222−2−222−2−22200000000000000000002−22−20000
χ3322-2-202-20-2-22202002-2-2000022-2-22−2−22002-2-2-2220000002-2-2-22222−2−2−2−22200000000000000000002−2−220000
χ3422-2-202-20-2-22202002-2-2000022-2-2−222−2002-2-2-2220000002-2-2-222−2−22222−2−20000000000000000000−222−20000
χ3522-2-202-20-2-22202002-2-20000-2-2222−2−22002-2-2-222000000-2222-2-222−2−2−2−2220000000000000000000−222−20000
χ3622-2-202-20-2-22202002-2-20000-2-222−222−2002-2-2-222000000-2222-2-2−2−22222−2−200000000000000000002−2−220000
χ372-22-2200-22−22−2022−2-22-222-2-22-22-2000000002−22−222−2−22-2002−22−20000000002-22-200002−22−22−22−22−200000000
χ382-22-2200-22−22−2022−2-22-222-2-22-22-2000000002−22−222−2−22-2002−22−2000000000-22-2200002−2−22−22−22−2200000000
χ392-22-2200-22−22−2022−2-22-222-2-2-22-22000000002−22−222−2−2-2200−22−220000000002i−2i−2i2i0000−22i2−i2i2−i2−i2i2−i2i200000000
χ402-22-2200-22−22−2022−2-22-222-2-2-22-22000000002−22−222−2−2-2200−22−22000000000−2i2i2i−2i0000−22−i2i2−i2i2i2−i2i2−i200000000
χ412-22-2200-2−22−2202−22-22-222-2-22-22-200000000−22−22−2−2222-200−22−220000000002-22-20000−22−22−22−22−2200000000
χ422-22-2200-2−22−2202−22-22-222-2-22-22-200000000−22−22−2−2222-200−22−22000000000-22-220000−222−22−22−22−200000000
χ432-22-2200-2−22−2202−22-22-222-2-2-22-2200000000−22−22−2−222-22002−22−20000000002i−2i−2i2i00002−2−i2i2−i2i2i2−i2i2−i200000000
χ442-22-2200-2−22−2202−22-22-222-2-2-22-2200000000−22−22−2−222-22002−22−2000000000−2i2i2i−2i00002−2i2−i2i2−i2−i2i2−i2i200000000
χ452-22-2-20022−22−202−22-22-2-2-2222-22-2000000002−22−2−2−222-22002−22−200000000000002i−2i2i−2i−22i2−i2−i2i2i2−i2−i2i200000000
χ462-22-2-20022−22−202−22-22-2-2-2222-22-2000000002−22−2−2−222-22002−22−20000000000000−2i2i−2i2i−22−i2i2i2−i2−i2i2i2−i200000000
χ472-22-2-20022−22−202−22-22-2-2-222-22-22000000002−22−2−2−2222-200−22−2200000000000002-2-222−22−2−22−222−200000000
χ482-22-2-20022−22−202−22-22-2-2-222-22-22000000002−22−2−2−2222-200−22−220000000000000-222-22−2−222−22−2−2200000000
χ492-22-2-2002−22−22022−2-22-2-2-2222-22-200000000−22−2222−2−2-2200−22−2200000000000002i−2i2i−2i2−2−i2i2i2−i2−i2i2i2−i200000000
χ502-22-2-2002−22−22022−2-22-2-2-2222-22-200000000−22−2222−2−2-2200−22−220000000000000−2i2i−2i2i2−2i2−i2−i2i2i2−i2−i2i200000000
χ512-22-2-2002−22−22022−2-22-2-2-222-22-2200000000−22−2222−2−22-2002−22−200000000000002-2-22−22−222−22−2−2200000000
χ522-22-2-2002−22−22022−2-22-2-2-222-22-2200000000−22−2222−2−22-2002−22−20000000000000-222-2−222−2−22−222−200000000
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
χ574444-444-44444-4-1-4-4-1-1-111110000000011-1-1-1-1-1-1111100000000i5−i5i5−i5i5−i5i5−i5000000000000000000000000000
χ584444-444-44444-4-1-4-4-1-1-111110000000011-1-1-1-1-1-1111100000000−i5i5−i5i5−i5i5−i5i5000000000000000000000000000
χ594444-444-4-4-4-4-4-4-144-1-1-111110000000011-1-11111-1-1-1-100000000i5−i5i5−i5−i5i5−i5i5000000000000000000000000000
χ604444-444-4-4-4-4-4-4-144-1-1-111110000000011-1-11111-1-1-1-100000000−i5i5−i5i5i5−i5i5−i5000000000000000000000000000
χ6144-4-404-4044-4-40-100-111i5−i5i5−i5000022−2222−22i5−i5-11-1-111i5−i5i5−i500000000−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39000000000000000000000000000
χ6244-4-404-4044-4-40-100-111i5−i5i5−i50000−2222−2222i5−i5-11-1-111i5−i5i5−i500000000ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39000000000000000000000000000
χ6344-4-404-4044-4-40-100-111−i5i5−i5i5000022−2222−22−i5i5-11-1-111−i5i5−i5i500000000ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29000000000000000000000000000
χ6444-4-404-4044-4-40-100-111−i5i5−i5i50000−2222−2222−i5i5-11-1-111−i5i5−i5i500000000−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29000000000000000000000000000
χ6544-4-404-40-4-4440-100-111i5−i5i5−i5000022−22−2222i5−i5-1111-1-1−i5i5−i5i500000000−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39000000000000000000000000000
χ6644-4-404-40-4-4440-100-111i5−i5i5−i50000−222222−22i5−i5-1111-1-1−i5i5−i5i500000000ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39000000000000000000000000000
χ6744-4-404-40-4-4440-100-111−i5i5−i5i5000022−22−2222−i5i5-1111-1-1i5−i5i5−i500000000ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29000000000000000000000000000
χ6844-4-404-40-4-4440-100-111−i5i5−i5i50000−222222−22−i5i5-1111-1-1i5−i5i5−i500000000−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29000000000000000000000000000
χ6944-4-40-440000004004-4-4000044-4-4000000-440000000000-44000000000000000000000000000000000000000
χ7044-4-40-440000004004-4-40000-4-444000000-4400000000004-4000000000000000000000000000000000000000
χ714-4-44000022−22−22220400-4-4400004-4-440000000022−22−22220000000022−22−222200000000000000000000000000000000000
χ724-4-44000022−22−22220400-4-440000-444-40000000022−22−222200000000−222222−2200000000000000000000000000000000000
χ734-4-440000−222222−220400-4-4400004-4-4400000000−222222−2200000000−222222−2200000000000000000000000000000000000
χ744-4-440000−222222−220400-4-440000-444-400000000−222222−220000000022−22−222200000000000000000000000000000000000
χ7588888-8-880000-8-200-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000000000000000000
χ768888-8-8-8-800008-200-2-2-2222200000000-2-222000000000000000000000000000000000000000000000000000
χ7788-8-80-88000000-200-2222i5−2i52i5−2i500000000−2i52i52-2000000000000000000000000000000000000000000000000000
χ7888-8-80-88000000-200-222−2i52i5−2i52i5000000002i5−2i52-2000000000000000000000000000000000000000000000000000
χ798-88-8800-842−4242−420-242−422-22-2-222000000000000−22−22−2−2220000000000000000000000000000000000000000000
χ808-88-8800-8−4242−42420-2−42422-22-2-2220000000000002−22−222−2−20000000000000000000000000000000000000000000
χ818-88-8-800842−4242−420-2−42422-2222-2-2000000000000−22−2222−2−20000000000000000000000000000000000000000000
χ828-88-8-8008−4242−42420-242−422-2222-2-20000000000002−22−2−2−2220000000000000000000000000000000000000000000
χ838-8-88000042−42−42420-20022-22i5−2i5−2i52i5000000000000−222−2i10−i10−i10i100000000000000000000000000000000000000000000
χ848-8-88000042−42−42420-20022-2−2i52i52i5−2i5000000000000−222−2−i10i10i10−i100000000000000000000000000000000000000000000
χ858-8-880000−424242−420-20022-22i5−2i5−2i52i50000000000002−2−22−i10i10i10−i100000000000000000000000000000000000000000000
χ868-8-880000−424242−420-20022-2−2i52i52i5−2i50000000000002−2−22i10−i10−i10i100000000000000000000000000000000000000000000

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