Finite Group Databasebeta

← Group #13018999

Character table — Group #13018999

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222244444444444444455558888888888888881010101016161616161616162020202020202020202020404040404040404040404040408080
order12224444444588881010102020202044444882020202040404040404040404444202020204040404022288888888488888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-1111111111111111-1-1-1-111111111-1-1-1-1-1-1-1ii−i−i-1-1-1iii−i−i−iii−i−ii−i
χ411111111111111111111111-1-1-1-1111111111111111-1-1-1-111111111-1-1-1-1-1-1-1−i−iii-1-1-1−i−i−iiii−i−iii−ii
χ5111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-111111-1-1111111-1-1-1-1-1-1
χ6111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111
χ7111111111111-1-1-1-11111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111ii−i−i-111iii−i−i−i−i−iii−ii
χ8111111111111-1-1-1-11111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111−i−iii-111−i−i−iiiiii−i−ii−i
χ911111111-1-111111111111111111-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-111111111-1-1-11-1-11-1-11111-1-1
χ1011111111-1-111111111111111111-1-1-11111111111111111-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111-111-1-1-1-111
χ1111111111-1-11111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i111i−i−i−iiiii−i−i−ii
χ1211111111-1-11111111111111-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iii111−iiii−i−i−i−iiii−i
χ1311111111-1-111-1-1-1-111111111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-11111-1111-1-11-1-1-1-1-1-111
χ1411111111-1-111-1-1-1-111111111111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-111-111-1111111-1-1
χ1511111111-1-111-1-1-1-11111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111111ii−i−i1-1-1i−i−i−iii−i−iiii−i
χ1611111111-1-111-1-1-1-11111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111111−i−iii1-1-1−iiii−i−iii−i−i−ii
χ17222222-2-222-220000222-2-2-2-22222-20022-2-200000000-2-22222-2-20000-22200000000-200000000000000
χ18222222-2-222-220000222-2-2-2-2-2-2-2-2-20022-2-20000000022-2-222-2-200002-2-200000000200000000000000
χ19222222-2-2-2-2-220000222-2-2-2-2222220022-2-200000000-2-222-2-2220000-2-2-200000000200000000000000
χ20222222-2-2-2-2-220000222-2-2-2-2-2-2-2-220022-2-20000000022-2-2-2-222000022200000000-200000000000000
χ212222-2-22200-22000022222222222000-2-2-2-20000000022-2-200000000-20000002222000-200-200000000
χ222222-2-22200-22000022222222222000-2-2-2-20000000022-2-200000000-2000000-2-2-2-2000200200000000
χ232222-2-22200-2200002222222-2-2-2-2000-2-2-2-200000000-2-2220000000020000002i2i−2i−2i000−2i002i00000000
χ242222-2-22200-2200002222222-2-2-2-2000-2-2-2-200000000-2-222000000002000000−2i−2i2i2i0002i00−2i00000000
χ252222-2-2-2-200220000222-2-2-2-22222000-2-22200000000-2-2-2-2000000002000000000000002-202-2000000
χ262222-2-2-2-200220000222-2-2-2-22222000-2-22200000000-2-2-2-200000000200000000000000-220-22000000
χ272222-2-2-2-200220000222-2-2-2-2-2-2-2-2000-2-22200000000222200000000-2000000000000002i−2i0−2i2i000000
χ282222-2-2-2-200220000222-2-2-2-2-2-2-2-2000-2-22200000000222200000000-200000000000000−2i2i02i−2i000000
χ2922-2-22-2002i−2i02i2i2−i2−i2-22-200002i2i−2i−2i02−22-200i2i2i2i2−i2−i2−i2−i2002i−2i2i−2i0022−2−202-222−2−200000i2−i2000000000000
χ3022-2-22-2002i−2i02i2i2−i2−i2-22-20000−2i−2i2i2i02−22-200i2i2i2i2−i2−i2−i2−i200−2i2i2i−2i0022−2−20-22−2−22200000−i2i2000000000000
χ3122-2-22-2002i−2i02−i2−i2i2i2-22-200002i2i−2i−2i0−222-200−i2−i2−i2−i2i2i2i2i2002i−2i2i−2i00−2−22202-2−2−22200000−i2i2000000000000
χ3222-2-22-2002i−2i02−i2−i2i2i2-22-20000−2i−2i2i2i0−222-200−i2−i2−i2−i2i2i2i2i200−2i2i2i−2i00−2−2220-2222−2−200000i2−i2000000000000
χ3322-2-22-200−2i2i02i2i2−i2−i2-22-200002i2i−2i−2i0−222-200i2i2i2i2−i2−i2−i2−i2002i−2i−2i2i00−2−2220-2222−2−200000−i2i2000000000000
χ3422-2-22-200−2i2i02i2i2−i2−i2-22-20000−2i−2i2i2i0−222-200i2i2i2i2−i2−i2−i2−i200−2i2i−2i2i00−2−22202-2−2−22200000i2−i2000000000000
χ3522-2-22-200−2i2i02−i2−i2i2i2-22-200002i2i−2i−2i02−22-200−i2−i2−i2−i2i2i2i2i2002i−2i−2i2i0022−2−20-22−2−22200000i2−i2000000000000
χ3622-2-22-200−2i2i02−i2−i2i2i2-22-20000−2i−2i2i2i02−22-200−i2−i2−i2−i2i2i2i2i200−2i2i−2i2i0022−2−202-222−2−200000−i2i2000000000000
χ372-2-2200-2200022−22−22-2-222-2-22i−2i2i−2i000000022−2−222−2−22i−2i0000000000000i2−i2i2−i2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000001+i−1−i1−i−1+i00
χ382-2-2200-2200022−22−22-2-222-2-22i−2i2i−2i000000022−2−222−2−22i−2i0000000000000i2−i2i2−i22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000−1−i1+i−1+i1−i00
χ392-2-2200-2200022−22−22-2-222-2-2−2i2i−2i2i000000022−2−222−2−2−2i2i0000000000000−i2i2−i2i2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000−1+i1−i−1−i1+i00
χ402-2-2200-2200022−22−22-2-222-2-2−2i2i−2i2i000000022−2−222−2−2−2i2i0000000000000−i2i2−i2i22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000001−i−1+i1+i−1−i00
χ412-2-2200-220002−22−222-2-222-2-22i−2i2i−2i0000000−2−222−2−2222i−2i0000000000000−i2i2−i2i2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000−1−i1+i−1+i1−i00
χ422-2-2200-220002−22−222-2-222-2-22i−2i2i−2i0000000−2−222−2−2222i−2i0000000000000−i2i2−i2i22ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000001+i−1−i1−i−1+i00
χ432-2-2200-220002−22−222-2-222-2-2−2i2i−2i2i0000000−2−222−2−222−2i2i0000000000000i2−i2i2−i2−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000001−i−1+i1+i−1−i00
χ442-2-2200-220002−22−222-2-222-2-2−2i2i−2i2i0000000−2−222−2−222−2i2i0000000000000i2−i2i2−i22ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000−1+i1−i−1−i1+i00
χ4544444444444-14444-1-1-1-1-1-1-10000444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-100000000000000000000000000
χ4644444444444-1-4-4-4-4-1-1-1-1-1-1-100004-4-4-1-1-1-1111111110000-1-1-1-1111100000000000000000000000000
χ4744444444-4-44-14444-1-1-1-1-1-1-10000-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100001111111100000000000000000000000000
χ4844444444-4-44-1-4-4-4-4-1-1-1-1-1-1-10000-444-1-1-1-11111111100001111-1-1-1-100000000000000000000000000
χ49444444-4-444-4-10000-1-1-111110000-400-1-111i5−i5i5−i5i5−i5i5−i50000-1-111i5−i5i5−i500000000000000000000000000
χ50444444-4-444-4-10000-1-1-111110000-400-1-111−i5i5−i5i5−i5i5−i5i50000-1-111−i5i5−i5i500000000000000000000000000
χ51444444-4-4-4-4-4-10000-1-1-111110000400-1-111i5−i5i5−i5i5−i5i5−i5000011-1-1−i5i5−i5i500000000000000000000000000
χ52444444-4-4-4-4-4-10000-1-1-111110000400-1-111−i5i5−i5i5−i5i5−i5i5000011-1-1i5−i5i5−i500000000000000000000000000
χ5344-4-44-4004i−4i0-12i22i2−2i2−2i21-11i5−i5i5−i50000022−22-11i5−i5ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ390000−ii5−5ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ2900000000000000000000000000
χ5444-4-44-4004i−4i0-12i22i2−2i2−2i21-11−i5i5−i5i50000022−22-11−i5i5ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ290000−ii−55−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ3900000000000000000000000000
χ5544-4-44-4004i−4i0-1−2i2−2i22i22i21-11i5−i5i5−i500000−2222-11i5−i5−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ390000−ii5−5−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ2900000000000000000000000000
χ5644-4-44-4004i−4i0-1−2i2−2i22i22i21-11−i5i5−i5i500000−2222-11−i5i5−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ290000−ii−55ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ3900000000000000000000000000
χ5744-4-44-400−4i4i0-12i22i2−2i2−2i21-11i5−i5i5−i500000−2222-11i5−i5ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ390000i−i−55−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ2900000000000000000000000000
χ5844-4-44-400−4i4i0-12i22i2−2i2−2i21-11−i5i5−i5i500000−2222-11−i5i5ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ290000i−i5−5ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ3900000000000000000000000000
χ5944-4-44-400−4i4i0-1−2i2−2i22i22i21-11i5−i5i5−i50000022−22-11i5−i5−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ390000i−i−55ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ2900000000000000000000000000
χ6044-4-44-400−4i4i0-1−2i2−2i22i22i21-11−i5i5−i5i50000022−22-11−i5i5−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ290000i−i5−5−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ3900000000000000000000000000
χ6144-4-4-440000040000-44-400004i4i−4i−4i000-44000000000000−4i4i0000000000000000000000000000000000
χ6244-4-4-440000040000-44-40000−4i−4i4i4i000-440000000000004i−4i0000000000000000000000000000000000
χ634-44-4000000042i−2i−2i2i-4-4400004-4-4400000002i2i−2i−2i−2i−2i2i2i000000000000000−2i2i2i−2i0000000000000000000
χ644-44-4000000042i−2i−2i2i-4-440000-444-400000002i2i−2i−2i−2i−2i2i2i0000000000000002i−2i−2i2i0000000000000000000
χ654-44-400000004−2i2i2i−2i-4-4400004-4-440000000−2i−2i2i2i2i2i−2i−2i0000000000000002i−2i−2i2i0000000000000000000
χ664-44-400000004−2i2i2i−2i-4-440000-444-40000000−2i−2i2i2i2i2i−2i−2i000000000000000−2i2i2i−2i0000000000000000000
χ674-4-44004-4000400004-4-4-4-4444i−4i4i−4i000000000000000−4i4i000000000000000000000000000000000000
χ684-4-44004-4000400004-4-4-4-444−4i4i−4i4i0000000000000004i−4i000000000000000000000000000000000000
χ698888-8-88800-8-20000-2-2-2-2-2-2-2000000022220000000000000000000000000000000000000000000000
χ708888-8-8-8-8008-20000-2-2-22222000000022-2-20000000000000000000000000000000000000000000000
χ7188-8-8-8800000-200002-222i5−2i52i5−2i500000002-2−2i52i50000000000000000000000000000000000000000000000
χ7288-8-8-8800000-200002-22−2i52i5−2i52i500000002-22i5−2i50000000000000000000000000000000000000000000000
χ738-88-80000000-24i−4i−4i4i22-22i5−2i5−2i52i500000000000−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ3800000000000000000000000000000000000000
χ748-88-80000000-24i−4i−4i4i22-2−2i52i52i5−2i500000000000ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ3800000000000000000000000000000000000000
χ758-88-80000000-2−4i4i4i−4i22-22i5−2i5−2i52i500000000000ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ3800000000000000000000000000000000000000
χ768-88-80000000-2−4i4i4i−4i22-2−2i52i52i5−2i500000000000−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ3800000000000000000000000000000000000000
χ778-8-88008-8000-20000-22222-2-200000000000i10−i10−i10i10i10−i10−i10i1000000000000000000000000000000000000000
χ788-8-88008-8000-20000-22222-2-200000000000−i10i10i10−i10−i10i10i10−i1000000000000000000000000000000000000000
χ798-8-8800-88000-242−4242−42-222-2-22200000000000−2−222−2−22200000000000000000000000000000000000000
χ808-8-8800-88000-2−4242−4242-222-2-2220000000000022−2−222−2−200000000000000000000000000000000000000

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