Finite Group Databasebeta

← Group #13013932

Character table — Group #13013932

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122224444444444444888888888888888810101010101010101010161616161616161620202040404040404040404040404080808080
order1222444445888810101020202020888820202020404040404040404022444488884040404040404040488888816161616161616168888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ41111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ5111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1
χ6111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−iii
χ8111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiiiii−i−i
χ91111-111-1-1111-1-1111-1-1-1-1ii−i−i-1-1111111-1-1-1-1111-1-11-1-1-1-1iiii−i−i−i−i-111ii−i−iii−i−iii−i−i1-11-1
χ101111-111-1-1111-1-1111-1-1-1-1ii−i−i-1-1111111-1-1-1-1111-1-11-1-1-1-1iiii−i−i−i−i-111ii−i−i−i−iii−i−iii-11-11
χ111111-111-1-1111-1-1111-1-1-1-1ii−i−i-1-1111111-1-1-1-1-1-1-111-11111iiii−i−i−i−i1-1-1−i−iii11-1-1-1-111−iii−i
χ121111-111-1-1111-1-1111-1-1-1-1ii−i−i-1-1111111-1-1-1-1-1-1-111-11111iiii−i−i−i−i1-1-1−i−iii-1-11111-1-1i−i−ii
χ131111-111-1-1111-1-1111-1-1-1-1−i−iii-1-1111111-1-1-1-1111-1-11-1-1-1-1−i−i−i−iiiii-111−i−iiiii−i−iii−i−i-11-11
χ141111-111-1-1111-1-1111-1-1-1-1−i−iii-1-1111111-1-1-1-1111-1-11-1-1-1-1−i−i−i−iiiii-111−i−iii−i−iii−i−iii1-11-1
χ151111-111-1-1111-1-1111-1-1-1-1−i−iii-1-1111111-1-1-1-1-1-1-111-11111−i−i−i−iiiii1-1-1ii−i−i11-1-1-1-111i−i−ii
χ161111-111-1-1111-1-1111-1-1-1-1−i−iii-1-1111111-1-1-1-1-1-1-111-11111−i−i−i−iiiii1-1-1ii−i−i-1-11111-1-1−iii−i
χ172222222222-2-2-2-2222222200002222-2-2-2-2-2-2-2-2222222-2-2-2-2000000002-2-20000000000000000
χ182222222222-2-2-2-2222222200002222-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2220000000000000000
χ1922222-2-22-22000022222220000-2-2-2-20000000022-222-2000000000000-2000000i2−i2i2−i2i2−i2i2−i20000
χ2022222-2-22-22000022222220000-2-2-2-20000000022-222-2000000000000-2000000−i2i2−i2i2−i2i2−i2i20000
χ2122222-2-22-22000022222220000-2-2-2-200000000-2-22-2-2200000000000020000002−22−2−22−220000
χ2222222-2-22-22000022222220000-2-2-2-200000000-2-22-2-220000000000002000000−22−222−22−20000
χ232222-222-2-22-2-222222-2-2-2-20000-2-222-2-2-2-22222222-2-22222200000000-2-2-20000000000000000
χ242222-222-2-22-2-222222-2-2-2-20000-2-222-2-2-2-22222-2-2-222-2-2-2-2-2000000002220000000000000000
χ252222-2-2-2-2220000222-2-2-2-2000022-2-20000000022-2-2-2-200000000000020000002−2−222−2−220000
χ262222-2-2-2-2220000222-2-2-2-2000022-2-20000000022-2-2-2-20000000000002000000−222−2−222−20000
χ272222-2-2-2-2220000222-2-2-2-2000022-2-200000000-2-22222000000000000-2000000i2−i2−i2i2−i2i2i2−i20000
χ282222-2-2-2-2220000222-2-2-2-2000022-2-200000000-2-22222000000000000-2000000−i2i2i2−i2i2−i2−i2i20000
χ2922-2-202-2002002-22-2-20000i2−i2i2−i2002-2000022-2-22-2200-2-2-222i2i2−i2−i2i2i2−i2−i2000i2−i2i2−i2000000000000
χ3022-2-202-2002002-22-2-20000i2−i2i2−i2002-2000022-2-2-22-200222-2-2i2i2−i2−i2i2i2−i2−i2000−i2i2−i2i2000000000000
χ3122-2-202-2002002-22-2-20000−i2i2−i2i2002-2000022-2-22-2200-2-2-222−i2−i2i2i2−i2−i2i2i2000−i2i2−i2i2000000000000
χ3222-2-202-2002002-22-2-20000−i2i2−i2i2002-2000022-2-2-22-200222-2-2−i2−i2i2i2−i2−i2i2i2000i2−i2i2−i2000000000000
χ3322-2-202-200200-222-2-200002−2−22002-20000-2-2222-2200-222-2-222−2−2−2−2220002−2−22000000000000
χ3422-2-202-200200-222-2-200002−2−22002-20000-2-222-22-2002-2-22222−2−2−2−222000−222−2000000000000
χ3522-2-202-200200-222-2-20000−222−2002-20000-2-2222-2200-222-2-2−2−22222−2−2000−222−2000000000000
χ3622-2-202-200200-222-2-20000−222−2002-20000-2-222-22-2002-2-222−2−22222−2−20002−2−22000000000000
χ37444444444-14444-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-10000000000-1-1-1-1-1-1-1-10000000000000000000
χ38444444444-14444-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-10000000000111111110000000000000000000
χ39444444444-1-4-4-4-4-1-1-1-1-1-1-10000-1-1-1-11111111100000000005−55−55−55−50000000000000000000
χ40444444444-1-4-4-4-4-1-1-1-1-1-1-10000-1-1-1-1111111110000000000−55−55−55−550000000000000000000
χ414444-444-4-4-144-4-4-1-1-111114i4i−4i−4i11-1-1-1-1-1-111110000000000−i−i−i−iiiii0000000000000000000
χ424444-444-4-4-144-4-4-1-1-11111−4i−4i4i4i11-1-1-1-1-1-111110000000000iiii−i−i−i−i0000000000000000000
χ434444-444-4-4-1-4-444-1-1-11111000011-1-11111-1-1-1-10000000000i5−i5i5−i5−i5i5−i5i50000000000000000000
χ444444-444-4-4-1-4-444-1-1-11111000011-1-11111-1-1-1-10000000000−i5i5−i5i5i5−i5i5−i50000000000000000000
χ4544-4-404-400-1004-4-111i5−i5i5−i52i2−2i22i2−2i2i5−i5-11i5i5−i5−i5-1-1110000000000ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ290000000000000000000
χ4644-4-404-400-1004-4-111i5−i5i5−i5−2i22i2−2i22i2i5−i5-11i5i5−i5−i5-1-1110000000000−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ290000000000000000000
χ4744-4-404-400-1004-4-111−i5i5−i5i52i2−2i22i2−2i2−i5i5-11−i5−i5i5i5-1-1110000000000ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ39−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ390000000000000000000
χ4844-4-404-400-1004-4-111−i5i5−i5i5−2i22i2−2i22i2−i5i5-11−i5−i5i5i5-1-1110000000000−ζ13−ζ31−ζ37−ζ39−ζ7−ζ21−ζ23−ζ29ζ13+ζ31+ζ37+ζ39ζ7+ζ21+ζ23+ζ29−ζ7−ζ21−ζ23−ζ29−ζ13−ζ31−ζ37−ζ39ζ7+ζ21+ζ23+ζ29ζ13+ζ31+ζ37+ζ390000000000000000000
χ4944-4-404-400-100-44-111i5−i5i5−i522−22−2222i5−i5-11−i5−i5i5i511-1-10000000000−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ290000000000000000000
χ5044-4-404-400-100-44-111i5−i5i5−i5−222222−22i5−i5-11−i5−i5i5i511-1-10000000000ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ290000000000000000000
χ5144-4-404-400-100-44-111−i5i5−i5i522−22−2222−i5i5-11i5i5−i5−i511-1-10000000000ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ390000000000000000000
χ5244-4-404-400-100-44-111−i5i5−i5i5−222222−22−i5i5-11i5i5−i5−i511-1-10000000000−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ390000000000000000000
χ5344-4-40-4400400004-4-40000000000-44000000004-4-40040000000000000000000000000000000
χ5444-4-40-4400400004-4-40000000000-4400000000-44400-40000000000000000000000000000000
χ554-44-40000042i2−2i200-44-40000000000002i2−2i22i2−2i200000004i−4i022−2222−22000000000000000000000000000
χ564-44-40000042i2−2i200-44-40000000000002i2−2i22i2−2i20000000−4i4i0−2222−2222000000000000000000000000000
χ574-44-4000004−2i22i200-44-4000000000000−2i22i2−2i22i200000004i−4i0−2222−2222000000000000000000000000000
χ584-44-4000004−2i22i200-44-4000000000000−2i22i2−2i22i20000000−4i4i022−2222−22000000000000000000000000000
χ594-4-44400-4040000-4-4444-4-4000000000000000000000022−22−222200000000022−220000000000000000
χ604-4-44400-4040000-4-4444-4-40000000000000000000000−222222−22000000000−22220000000000000000
χ614-4-44-4004040000-4-44-4-444000000000000000000000022−22−2222000000000−22220000000000000000
χ624-4-44-4004040000-4-44-4-4440000000000000000000000−222222−2200000000022−220000000000000000
χ6388888-8-88-8-20000-2-2-2-2-2-2-200002222000000000000000000000000000000000000000000000
χ648888-8-8-8-88-20000-2-2-222220000-2-222000000000000000000000000000000000000000000000
χ6588-8-80-8800-20000-2222i5−2i52i5−2i50000−2i52i52-2000000000000000000000000000000000000000000000
χ6688-8-80-8800-20000-222−2i52i5−2i52i500002i5−2i52-2000000000000000000000000000000000000000000000
χ678-88-800000-24i2−4i2002-222i5−2i5−2i52i500000000−i2i2−i2i210−1010−100000000000000000000000000000000000000
χ688-88-800000-24i2−4i2002-22−2i52i52i5−2i500000000−i2i2−i2i2−1010−10100000000000000000000000000000000000000
χ698-88-800000-2−4i24i2002-222i5−2i5−2i52i500000000i2−i2i2−i2−1010−10100000000000000000000000000000000000000
χ708-88-800000-2−4i24i2002-22−2i52i52i5−2i500000000i2−i2i2−i210−1010−100000000000000000000000000000000000000
χ718-8-88800-80-2000022-2-2-2220000000010−10−101010−10−10100000000000000000000000000000000000000
χ728-8-88800-80-2000022-2-2-22200000000−101010−10−101010−100000000000000000000000000000000000000
χ738-8-88-80080-2000022-222-2-20000000010−10−1010−101010−100000000000000000000000000000000000000
χ748-8-88-80080-2000022-222-2-200000000−101010−1010−10−10100000000000000000000000000000000000000

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