Finite Group Databasebeta

← Group #11771573

Character table — Group #11771573

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222244444444888888888888889999161616161616161618181818181818181818181818181818181818181818727272727272
order122244888833666666441212121224242424242424244444121212121212121244888816161616161616161616161616161616228888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1ii−i−i
χ411111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1−i−iii
χ5111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1
χ6111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11−i−iii
χ8111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11ii−i−i
χ911-1-11-111-1-111-1-111-1-1i−i-1-1111111-1-1-1-1i−ii−iiiii−i−i−i−ii−iii−i−iζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ61-1ζ6−ζ6ζ2−ζ2
χ1011-1-11-111-1-111-1-111-1-1i−i-1-1111111-1-1-1-1i−ii−iiiii−i−i−i−ii−iii−i−i−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ61-1−ζ6ζ6−ζ2ζ2
χ1111-1-11-111-1-111-1-111-1-1i−i-1-1111111-1-1-1-1−ii−iiiiii−i−i−i−i−ii−i−iiiζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2-11−ζ2ζ2−ζ6ζ6
χ1211-1-11-111-1-111-1-111-1-1i−i-1-1111111-1-1-1-1−ii−iiiiii−i−i−i−i−ii−i−iii−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2-11ζ2−ζ2ζ6−ζ6
χ1311-1-11-111-1-111-1-111-1-1−ii-1-1111111-1-1-1-1i−ii−i−i−i−i−iiiiii−iii−i−iζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ2ζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6-11−ζ6ζ6−ζ2ζ2
χ1411-1-11-111-1-111-1-111-1-1−ii-1-1111111-1-1-1-1i−ii−i−i−i−i−iiiiii−iii−i−i−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ2−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6-11ζ6−ζ6ζ2−ζ2
χ1511-1-11-111-1-111-1-111-1-1−ii-1-1111111-1-1-1-1−ii−ii−i−i−i−iiiii−ii−i−iiiζ6ζ6ζ6ζ6−ζ6−ζ6−ζ6−ζ6ζ2ζ2ζ2ζ2−ζ2−ζ2−ζ2−ζ21-1ζ2−ζ2ζ6−ζ6
χ1611-1-11-111-1-111-1-111-1-1−ii-1-1111111-1-1-1-1−ii−ii−i−i−i−iiiii−ii−i−iii−ζ6−ζ6−ζ6−ζ6ζ6ζ6ζ6ζ6−ζ2−ζ2−ζ2−ζ2ζ2ζ2ζ2ζ21-1−ζ2ζ2−ζ6ζ6
χ17222222-2-2-2-222222222002222-2-2-2-2-2-2-2-222220000000022-2-2-2-20000000000000000000000
χ18222222-2-2-2-222222222002222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000
χ192222-2-200002222222200-2-2-2-200000000222200000000-2-2000022−2−222−2−222−2−222−2−2000000
χ202222-2-200002222222200-2-2-2-200000000222200000000-2-20000−2−222−2−222−2−222−2−222000000
χ212222-2-200002222222200-2-2-2-200000000-2-2-2-200000000220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000
χ222222-2-200002222222200-2-2-2-200000000-2-2-2-200000000220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000
χ2322-2-22-2-2-22222-2-222-2-200-2-222-2-2-2-222222i−2i2i−2i000000002i−2i−2i−2i2i2i0000000000000000000000
χ2422-2-22-2-2-22222-2-222-2-200-2-222-2-2-2-22222−2i2i−2i2i00000000−2i2i2i2i−2i−2i0000000000000000000000
χ2522-2-2-22000022-2-222-2-20022-2-2000000002i−2i2i−2i00000000−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i000000
χ2622-2-2-22000022-2-222-2-20022-2-2000000002i−2i2i−2i00000000−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i000000
χ2722-2-2-22000022-2-222-2-20022-2-200000000−2i2i−2i2i000000002i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i000000
χ2822-2-2-22000022-2-222-2-20022-2-200000000−2i2i−2i2i000000002i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i000000
χ292-22-2002−22−22222-2-2-2-200000022−2−222−2−22i−2i−2i2i0000000000i2−i2i2−i2ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3000000
χ302-22-2002−22−22222-2-2-2-200000022−2−222−2−22i−2i−2i2i0000000000i2−i2i2−i2−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3000000
χ312-22-2002−22−22222-2-2-2-200000022−2−222−2−2−2i2i2i−2i0000000000−i2i2−i2i2ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7000000
χ322-22-2002−22−22222-2-2-2-200000022−2−222−2−2−2i2i2i−2i0000000000−i2i2−i2i2−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7000000
χ332-22-200−22−222222-2-2-2-2000000−2−222−2−2222i−2i−2i2i0000000000−i2i2−i2i2ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3ζ5+ζ7−ζ5−ζ7−ζ+ζ3ζ−ζ3−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7−ζ−ζ3ζ+ζ3ζ5−ζ7−ζ5+ζ7000000
χ342-22-200−22−222222-2-2-2-2000000−2−222−2−2222i−2i−2i2i0000000000−i2i2−i2i2−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3−ζ5−ζ7ζ5+ζ7ζ−ζ3−ζ+ζ3ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7ζ+ζ3−ζ−ζ3−ζ5+ζ7ζ5−ζ7000000
χ352-22-200−22−222222-2-2-2-2000000−2−222−2−222−2i2i2i−2i0000000000i2−i2i2−i2ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7ζ+ζ3−ζ−ζ3ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3−ζ5−ζ7ζ5+ζ7−ζ+ζ3ζ−ζ3000000
χ362-22-200−22−222222-2-2-2-2000000−2−222−2−222−2i2i2i−2i0000000000i2−i2i2−i2−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7−ζ−ζ3ζ+ζ3−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3ζ5+ζ7−ζ5−ζ7ζ−ζ3−ζ+ζ3000000
χ372-2-22002−2−2222-2-2-2-22200000022−2−2−2−22222-2-200000000002−2−22ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000
χ382-2-22002−2−2222-2-2-2-22200000022−2−2−2−22222-2-200000000002−2−22−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000
χ392-2-22002−2−2222-2-2-2-22200000022−2−2−2−222-2-2220000000000−222−2ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000
χ402-2-22002−2−2222-2-2-2-22200000022−2−2−2−222-2-2220000000000−222−2−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000
χ412-2-2200−222−222-2-2-2-222000000−2−22222−2−222-2-20000000000−222−2ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000
χ422-2-2200−222−222-2-2-2-222000000−2−22222−2−222-2-20000000000−222−2−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000
χ432-2-2200−222−222-2-2-2-222000000−2−22222−2−2-2-22200000000002−2−22ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000
χ442-2-2200−222−222-2-2-2-222000000−2−22222−2−2-2-22200000000002−2−22−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000
χ4544444444441-21-21-21-2441-21-21-21-21-21-2000011-2-211-2-20000000000000000000000000000
χ4644444444441-21-21-21-2-4-41-21-21-21-21-21-20000-1-122-1-1220000000000000000000000000000
χ474444444444-21-21-21-2144-21-21-21-21-21-210000-2-211-2-2110000000000000000000000000000
χ484444444444-21-21-21-21-4-4-21-21-21-21-21-21000022-1-122-1-10000000000000000000000000000
χ49444444-4-4-4-41-21-21-21-2001-21-2-12-12-12-1200003-3003-3000000000000000000000000000000
χ50444444-4-4-4-41-21-21-21-2001-21-2-12-12-12-120000-3300-33000000000000000000000000000000
χ51444444-4-4-4-4-21-21-21-2100-21-212-12-12-12-10000003-3003-30000000000000000000000000000
χ52444444-4-4-4-4-21-21-21-2100-21-212-12-12-12-1000000-3300-330000000000000000000000000000
χ5344-4-44-444-4-41-2-121-2-124i−4i-121-21-21-2-12-120000ii−2i−2i−i−i2i2i0000000000000000000000000000
χ5444-4-44-444-4-41-2-121-2-12−4i4i-121-21-21-2-12-120000−i−i2i2iii−2i−2i0000000000000000000000000000
χ5544-4-44-444-4-4-212-1-212-14i−4i2-1-21-21-212-12-10000−2i−2iii2i2i−i−i0000000000000000000000000000
χ5644-4-44-444-4-4-212-1-212-1−4i4i2-1-21-21-212-12-100002i2i−i−i−2i−2iii0000000000000000000000000000
χ5744-4-44-4-4-4441-2-121-2-1200-121-2-12-121-21-200003i−3i00−3i3i000000000000000000000000000000
χ5844-4-44-4-4-4441-2-121-2-1200-121-2-12-121-21-20000−3i3i003i−3i000000000000000000000000000000
χ5944-4-44-4-4-444-212-1-212-1002-1-212-12-1-21-210000003i−3i00−3i3i0000000000000000000000000000
χ6044-4-44-4-4-444-212-1-212-1002-1-212-12-1-21-21000000−3i3i003i−3i0000000000000000000000000000
χ618888-8-800002-42-42-42-400-24-24000000000000000000000000000000000000000000000000
χ628888-8-80000-42-42-42-42004-24-2000000000000000000000000000000000000000000000000
χ6388-8-8-8800002-4-242-4-24002-4-24000000000000000000000000000000000000000000000000
χ6488-8-8-880000-424-2-424-200-424-2000000000000000000000000000000000000000000000000
χ658-88-80042−4242−422-42-4-24-240000002−22−2222−22−2220000000000000000000000000000000000000000
χ668-88-80042−4242−42-42-424-24-2000000−22222−2−22222−20000000000000000000000000000000000000000
χ678-88-800−4242−42422-42-4-24-24000000−2222−22−2222−220000000000000000000000000000000000000000
χ688-88-800−4242−4242-42-424-24-200000022−2−22222−2−2220000000000000000000000000000000000000000
χ698-8-880042−42−42422-4-24-242-40000002−22−222−2222−220000000000000000000000000000000000000000
χ708-8-880042−42−4242-424-24-2-42000000−22222−222−2−2220000000000000000000000000000000000000000
χ718-8-8800−424242−422-4-24-242-4000000−2222−222−22−2220000000000000000000000000000000000000000
χ728-8-8800−424242−42-424-24-2-4200000022−2−222−22222−20000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.