Finite Group Databasebeta

← Group #13019259

Character table — Group #13019259

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size11112222444444455558888888101010101616161616161616161620202020202020202020202020202032324040404040404040404040404080
order12224444444510101044444882020202022444202020202040404040444888888888888202044444888888884
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-1-1iii−i−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−i−i−iiii-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−iii11iii−i−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−i−i−iiii1
χ911111111-1-1111111111-11111111111-11-1-1-1-11111-1-11111111111111-1-1-1-1-1-1-1111-1-11-1-1-1
χ1011111111-1-1111111111-11111111111-11-1-1-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-111-1
χ1111111111-1-1111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-11111-1-11-1-11-1-11
χ1211111111-1-1111111111-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-111-1111
χ1311111111-1-111111-1-1-1-1-1111111-1-1-1-1-11-1-1-1-1111111-1ii−i−iiiii−i−i−i−i-1-11−i−iii-1-1i−i−i−iii1
χ1411111111-1-111111-1-1-1-1-1111111-1-1-1-1-11-1-1-1-1111111-1−i−iii−i−i−i−iiiii-1-11ii−i−i-1-1−iiii−i−i1
χ1511111111-1-111111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1ii−i−i−i−i−i−iiiii111ii−i−i11i−i−i−iii-1
χ1611111111-1-111111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1−i−iiiiiii−i−i−i−i111−i−iii11−iiii−i−i-1
χ17222222-2-200-22222222200022-2-222-2-20-20000000000-2222200000000000000000-200-2000
χ18222222-2-200-22222222200022-2-222-2-20-20000000000-2-2-2-2-2000000000000000002002000
χ19222222-2-200-22222-2-2-2-200022-2-2-2-2220-2000000000022i2i−2i−2i00000000000000000−2i002i000
χ20222222-2-200-22222-2-2-2-200022-2-2-2-2220-200000000002−2i−2i2i2i000000000000000002i00−2i000
χ212222-2-22222-222222222-200-2-222-2-2220-2-2-222000022-200000000000000-20000000000000
χ222222-2-22222-22222-2-2-2-2-200-2-22222-2-20-2-2-2220000-2-220000000000000020000000000000
χ232222-2-222-2-2-222222222200-2-222-2-2220-222-2-20000-2-2-20000000000000020000000000000
χ242222-2-222-2-2-22222-2-2-2-2200-2-22222-2-20-222-2-2000022200000000000000-20000000000000
χ252222-2-2-2-200222222222000-2-2-2-2-2-2-2-2020000000000200000000000000000000002-202-20
χ262222-2-2-2-200222222222000-2-2-2-2-2-2-2-202000000000020000000000000000000000-220-220
χ272222-2-2-2-20022222-2-2-2-2000-2-2-2-22222020000000000-200000000000000000000002i−2i0−2i2i0
χ282222-2-2-2-20022222-2-2-2-2000-2-2-2-22222020000000000-20000000000000000000000−2i2i02i−2i0
χ2922-2-22-20000022-2-222-2-202−22-2002-20000000022−2−20002-22-222−2−222−2−200000002−20000000
χ3022-2-22-20000022-2-222-2-202−22-2002-20000000022−2−2000-22-22−2−222−2−22200000002−20000000
χ3122-2-22-20000022-2-222-2-20−222-2002-200000000−2−2220002-22-2−2−222−2−2220000000−220000000
χ3222-2-22-20000022-2-222-2-20−222-2002-200000000−2−222000-22-2222−2−222−2−20000000−220000000
χ3322-2-22-20000022-2-2-2-22202−22-200-220000000022−2−20002i−2i−2i2ii2i2−i2−i2−i2−i2i2i20000000−220000000
χ3422-2-22-20000022-2-2-2-22202−22-200-220000000022−2−2000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i20000000−220000000
χ3522-2-22-20000022-2-2-2-2220−222-200-2200000000−2−2220002i−2i−2i2i−i2−i2i2i2i2i2−i2−i200000002−20000000
χ3622-2-22-20000022-2-2-2-2220−222-200-2200000000−2−222000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i200000002−20000000
χ372-22-2002-22-202-2-222i−2i2i−2i00000-22002i−2i00002-200002i−2i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0001+i−1−i1−i−1+i000000000
χ382-22-2002-22-202-2-222i−2i2i−2i00000-22002i−2i00002-200002i−2i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000−1−i1+i−1+i1−i000000000
χ392-22-2002-22-202-2-22−2i2i−2i2i00000-2200−2i2i00002-20000−2i2i000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0001−i−1+i1+i−1−i000000000
χ402-22-2002-22-202-2-22−2i2i−2i2i00000-2200−2i2i00002-20000−2i2i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000−1+i1−i−1−i1+i000000000
χ412-22-2002-2-2202-2-222i−2i2i−2i00000-22002i−2i0000-220000−2i2i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000−1−i1+i−1+i1−i000000000
χ422-22-2002-2-2202-2-222i−2i2i−2i00000-22002i−2i0000-220000−2i2i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0001+i−1−i1−i−1+i000000000
χ432-22-2002-2-2202-2-22−2i2i−2i2i00000-2200−2i2i0000-2200002i−2i000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000−1+i1−i−1−i1+i000000000
χ442-22-2002-2-2202-2-22−2i2i−2i2i00000-2200−2i2i0000-2200002i−2i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0001−i−1+i1+i−1−i000000000
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
χ4744444444-4-44-1-1-1-10000-444-1-1-1-10000-4-11111-1-1-1-10000000000000001100000000000000
χ4844444444-4-44-1-1-1-10000-4-4-4-1-1-1-100004-111111111000000000000000-1-100000000000000
χ494444-4-44444-4-1-1-1-10000-40011-1-100000111-1-15−55−50000000000000005−500000000000000
χ504444-4-44444-4-1-1-1-10000-40011-1-100000111-1-1−55−55000000000000000−5500000000000000
χ514444-4-444-4-4-4-1-1-1-1000040011-1-1000001-1-1115−55−5000000000000000−5500000000000000
χ524444-4-444-4-4-4-1-1-1-1000040011-1-1000001-1-111−55−550000000000000005−500000000000000
χ5344-4-4-440000044-4-444-4-4000-4400-440000000000000000000000000000000000000000000
χ5444-4-4-440000044-4-4-4-444000-44004-40000000000000000000000000000000000000000000
χ554-44-400-440004-4-444i−4i4i−4i000004-400−4i4i00000000000000000000000000000000000000000
χ564-44-400-440004-4-44−4i4i−4i4i000004-4004i−4i00000000000000000000000000000000000000000
χ574-4-4400000004-44-44i−4i−4i4i0000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000000
χ584-4-4400000004-44-44i−4i−4i4i00000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000000
χ594-4-4400000004-44-4−4i4i4i−4i0000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000000
χ604-4-4400000004-44-4−4i4i4i−4i00000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000000
χ61888888-8-800-8-2-2-2-20000000-2-222000002000000000000000000000000000000000000000
χ628888-8-8-8-8008-2-2-2-20000000222200000-2000000000000000000000000000000000000000
χ6388-8-88-800000-2-2220000042−42-22000000000000−2−2220000000000000000000000000000000
χ6488-8-88-800000-2-22200000−4242-2200000000000022−2−20000000000000000000000000000000
χ6588-8-8-8800000-2-22200000002-200000000000010−10−10100000000000000000000000000000000
χ6688-8-8-8800000-2-22200000002-2000000000000−101010−100000000000000000000000000000000
χ678-88-8008-88-80-222-20000000002-200000000-2200000000000000000000000000000000000
χ688-88-8008-8-880-222-20000000002-2000000002-200000000000000000000000000000000000
χ698-88-800-88000-222-2000000000-220000002i5−2i50000000000000000000000000000000000000
χ708-88-800-88000-222-2000000000-22000000−2i52i50000000000000000000000000000000000000
χ7116-16-16160000000-44-4400000000000000000000000000000000000000000000000000000000

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