Finite Group Databasebeta

← Group #13019262

Character table — Group #13019262

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222444444455558888888101010101616161616161616161620202020202020202020202020202032324040404040404040404040404080
order12224444224510101044444882020202022444101020202040404040444888888888888202024444888888882
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-1-1-11
χ311111111111111111111-1-111111111-111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1
χ411111111111111111111-1-111111111-111111-1-1-1-1111-1-1-1-111111111-1-111111-1-1-1-1-1-1-1-1-1
χ5111111111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1ii−i−iiiii−i−i−i−i11-1ii−i−i-1-1i−iii−i−i-1
χ6111111111111111-1-1-1-11111111-1-1-1-11111111111-1-1-1−i−iii−i−i−i−iiiii11-1−i−iii-1-1−ii−i−iii-1
χ7111111111111111-1-1-1-11-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1ii−i−i−i−i−i−iiiii-1-1-1−i−iii11i−iii−i−i1
χ8111111111111111-1-1-1-11-1-11111-1-1-1-1-111111-1-1-1-1-1-1-1−i−iiiiiii−i−i−i−i-1-1-1ii−i−i11−ii−i−iii1
χ911111111-1-1111111111-11111111111-1-1-11-1-11111-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-1-1
χ1011111111-1-1111111111-11111111111-1-1-11-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1
χ1111111111-1-1111111111-1-1-1111111111-1-11-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-11111-1-111-1-1-1-11
χ1211111111-1-1111111111-1-1-1111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-111111
χ1311111111-1-111111-1-1-1-1-1111111-1-1-1-1-1-1-11-1-1111111-1ii−i−iiiii−i−i−i−i-1-11−i−iii-1-1i−i−i−iii1
χ1411111111-1-111111-1-1-1-1-1111111-1-1-1-1-1-1-11-1-1111111-1−i−iii−i−i−i−iiiii-1-11ii−i−i-1-1−iiii−i−i1
χ1511111111-1-111111-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-111-1ii−i−i−i−i−i−iiiii111ii−i−i11i−i−i−iii-1
χ1611111111-1-111111-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-111-1−i−iiiiiii−i−i−i−i111−i−iii11−iiii−i−i-1
χ17222222-2-200-222222222000-222-222-2-2000-200000000-2222200000000000000000-2-200000
χ18222222-2-200-222222222000-222-222-2-2000-200000000-2-2-2-2-2000000000000000002200000
χ19222222-2-200-22222-2-2-2-2000-222-2-2-222000-20000000022i2i−2i−2i00000000000000000−2i2i00000
χ20222222-2-200-22222-2-2-2-2000-222-2-2-222000-2000000002−2i−2i2i2i000000000000000002i−2i00000
χ212222-2-22222-222222222-2002-2-22-2-222022-2-2-2000022-200000000000000-20000000000000
χ222222-2-22222-22222-2-2-2-2-2002-2-2222-2-2022-2-2-20000-2-220000000000000020000000000000
χ232222-2-222-2-2-2222222222002-2-22-2-2220-2-2-2220000-2-2-20000000000000020000000000000
χ242222-2-222-2-2-22222-2-2-2-22002-2-2222-2-20-2-2-222000022200000000000000-20000000000000
χ252222-2-2-2-200222222222000-2-2-2-2-2-2-2-20002000000002000000000000000000000002-22-20
χ262222-2-2-2-200222222222000-2-2-2-2-2-2-2-2000200000000200000000000000000000000-22-220
χ272222-2-2-2-20022222-2-2-2-2000-2-2-2-22222000200000000-2000000000000000000000002i−2i−2i2i0
χ282222-2-2-2-20022222-2-2-2-2000-2-2-2-22222000200000000-200000000000000000000000−2i2i2i−2i0
χ2922-2-200-222-2022-2-22i−2i2i−2i000200-2002i−2i02-200000002i−2i000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0001−i−1+i1+i−1−i000000000
χ3022-2-200-222-2022-2-22i−2i2i−2i000200-2002i−2i02-200000002i−2i00000−1+i−1+i1−i1−i−1−i−1−i1+i1+i000−1+i1−i−1−i1+i000000000
χ3122-2-200-222-2022-2-2−2i2i−2i2i000200-200−2i2i02-20000000−2i2i000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0001+i−1−i1−i−1+i000000000
χ3222-2-200-222-2022-2-2−2i2i−2i2i000200-200−2i2i02-20000000−2i2i00000−1−i−1−i1+i1+i−1+i−1+i1−i1−i000−1−i1+i−1+i1−i000000000
χ3322-2-200-22-22022-2-22i−2i2i−2i000200-2002i−2i0-220000000−2i2i000001−i1−i−1+i−1+i1+i1+i−1−i−1−i000−1+i1−i−1−i1+i000000000
χ3422-2-200-22-22022-2-22i−2i2i−2i000200-2002i−2i0-220000000−2i2i00000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0001−i−1+i1+i−1−i000000000
χ3522-2-200-22-22022-2-2−2i2i−2i2i000200-200−2i2i0-2200000002i−2i000001+i1+i−1−i−1−i1−i1−i−1+i−1+i000−1−i1+i−1+i1−i000000000
χ3622-2-200-22-22022-2-2−2i2i−2i2i000200-200−2i2i0-2200000002i−2i00000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0001+i−1−i1−i−1+i000000000
χ372-2-222-2000002-2-2222-2-202−202-202-20000000022−2−20002i−2i2i−2ii2−i2i2−i2i2−i2i2−i200000002−20000000
χ382-2-222-2000002-2-2222-2-202−202-202-20000000022−2−2000−2i2i−2i2i−i2i2−i2i2−i2i2−i2i200000002−20000000
χ392-2-222-2000002-2-2222-2-20−2202-202-200000000−2−2220002i−2i2i−2i−i2i2−i2i2−i2i2−i2i20000000−220000000
χ402-2-222-2000002-2-2222-2-20−2202-202-200000000−2−222000−2i2i−2i2ii2−i2i2−i2i2−i2i2−i20000000−220000000
χ412-2-222-2000002-2-22-2-22202−202-20-220000000022−2−20002-2-222−22−2−22−220000000−220000000
χ422-2-222-2000002-2-22-2-22202−202-20-220000000022−2−2000-222-2−22−222−22−20000000−220000000
χ432-2-222-2000002-2-22-2-2220−2202-20-2200000000−2−2220002-2-22−22−222−22−200000002−20000000
χ442-2-222-2000002-2-22-2-2220−2202-20-2200000000−2−222000-222-22−22−2−22−2200000002−20000000
χ4544444444444-1-1-1-10000444-1-1-1-100004-1-1-1-1-1-1-1-1-1000000000000000-1-100000000000000
χ4644444444444-1-1-1-100004-4-4-1-1-1-10000-4-1-1-1-1-111110000000000000001100000000000000
χ4744444444-4-44-1-1-1-10000-444-1-1-1-10000-411-111-1-1-1-10000000000000001100000000000000
χ4844444444-4-44-1-1-1-10000-4-4-4-1-1-1-10000411-1111111000000000000000-1-100000000000000
χ494444-4-44444-4-1-1-1-10000-400-111-100000-1-11115−55−50000000000000005−500000000000000
χ504444-4-44444-4-1-1-1-10000-400-111-100000-1-1111−55−55000000000000000−5500000000000000
χ514444-4-444-4-4-4-1-1-1-10000400-111-100000111-1-15−55−5000000000000000−5500000000000000
χ524444-4-444-4-4-4-1-1-1-10000400-111-100000111-1-1−55−550000000000000005−500000000000000
χ5344-4-4004-400044-4-44i−4i4i−4i000-400400−4i4i00000000000000000000000000000000000000000
χ5444-4-4004-400044-4-4−4i4i−4i4i000-4004004i−4i00000000000000000000000000000000000000000
χ554-44-400000004-44-44i−4i−4i4i0000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000000
χ564-44-400000004-44-44i−4i−4i4i00000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000000
χ574-44-400000004-44-4−4i4i4i−4i0000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000000
χ584-44-400000004-44-4−4i4i4i−4i00000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000000
χ594-4-44-44000004-4-4444-4-40000-440-440000000000000000000000000000000000000000000
χ604-4-44-44000004-4-44-4-4440000-4404-40000000000000000000000000000000000000000000
χ61888888-8-800-8-2-2-2-200000002-2-22000000020000000000000000000000000000000000000
χ628888-8-8-8-8008-2-2-2-2000000022220000000-20000000000000000000000000000000000000
χ6388-8-8008-8000-2-2220000000200-2000000002i5−2i500000000000000000000000000000000000
χ6488-8-8008-8000-2-2220000000200-200000000−2i52i500000000000000000000000000000000000
χ6588-8-800-888-80-2-2220000000-200200000-2200000000000000000000000000000000000000
χ6688-8-800-88-880-2-2220000000-2002000002-200000000000000000000000000000000000000
χ678-8-888-800000-222-20000042−420-2200000000000−2−2220000000000000000000000000000000
χ688-8-888-800000-222-200000−42420-220000000000022−2−20000000000000000000000000000000
χ698-8-88-8800000-222-2000000002-20000000000010−10−10100000000000000000000000000000000
χ708-8-88-8800000-222-2000000002-200000000000−101010−100000000000000000000000000000000
χ7116-1616-160000000-44-4400000000000000000000000000000000000000000000000000000000

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