Finite Group Databasebeta

← Group #11772385

Character table — Group #11772385

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222244444444888888888888889999161616161616161618181818181818181818181818181818181818181818727272727272
order12442488883366121212126688121224242424242424242244242424242424242424888816161616161616161616161616161616888888
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
χ511111111111111111111-1-111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1
χ611111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11−i−iii
χ811111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11ii−i−i
χ911-1-1-1111-1-11111-1-1-1-1-1-1i−i111111-1-1-1-111-1-1iiii−i−i−i−i-11-1-1111111-1-1-1-11111-1-1-1-1i−ii−ii−i
χ1011-1-1-1111-1-11111-1-1-1-1-1-1i−i111111-1-1-1-111-1-1iiii−i−i−i−i-11-1-111-1-1-1-11111-1-1-1-11111i−i−ii−ii
χ1111-1-1-1111-1-11111-1-1-1-1-1-1i−i111111-1-1-1-1-1-111iiii−i−i−i−i1-111-1-1iiii−i−i−i−i−i−i−i−iiiii−ii-111-1
χ1211-1-1-1111-1-11111-1-1-1-1-1-1i−i111111-1-1-1-1-1-111iiii−i−i−i−i1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−ii1-1-11
χ1311-1-1-1111-1-11111-1-1-1-1-1-1−ii111111-1-1-1-111-1-1−i−i−i−iiiii-11-1-1111111-1-1-1-11111-1-1-1-1−ii−ii−ii
χ1411-1-1-1111-1-11111-1-1-1-1-1-1−ii111111-1-1-1-111-1-1−i−i−i−iiiii-11-1-111-1-1-1-11111-1-1-1-11111−iii−ii−i
χ1511-1-1-1111-1-11111-1-1-1-1-1-1−ii111111-1-1-1-1-1-111−i−i−i−iiiii1-111-1-1iiii−i−i−i−i−i−i−i−iiiiii−i1-1-11
χ1611-1-1-1111-1-11111-1-1-1-1-1-1−ii111111-1-1-1-1-1-111−i−i−i−iiiii1-111-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i-111-1
χ17222222-2-2-2-222222222220022-2-2-2-2-2-2-2-222220000000022-2-2-2-20000000000000000000000
χ18222222-2-2-2-222222222220022-2-2-2-2-2-2-2-2-2-2-2-200000000-2-222220000000000000000000000
χ192222-2-2000022222222-2-200-2-200000000222200000000-2-2000022−2−222−2−222−2−222−2−2000000
χ202222-2-2000022222222-2-200-2-200000000222200000000-2-20000−2−222−2−222−2−222−2−222000000
χ212222-2-2000022222222-2-200-2-200000000-2-2-2-200000000220000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2000000
χ222222-2-2000022222222-2-200-2-200000000-2-2-2-200000000220000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2000000
χ2322-2-22-200002222-2-2-2-22200-2-20000000022-2-2000000002-2000022−2−2−2−22222−2−2−2−222000000
χ2422-2-22-200002222-2-2-2-22200-2-20000000022-2-2000000002-20000−2−22222−2−2−2−22222−2−2000000
χ2522-2-22-200002222-2-2-2-22200-2-200000000-2-22200000000-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000
χ2622-2-22-200002222-2-2-2-22200-2-200000000-2-22200000000-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000
χ2722-2-2-22-2-2222222-2-2-2-2-2-20022-2-2-2-2222222-2-200000000-2222-2-20000000000000000000000
χ2822-2-2-22-2-2222222-2-2-2-2-2-20022-2-2-2-22222-2-222000000002-2-2-2220000000000000000000000
χ292-22i−2i002−2i2−i222-2-22i2i−2i−2i00000022−2−2i2i2−i2−i22-22i−2i0000000000i2−i22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000
χ302-22i−2i002−2i2−i222-2-22i2i−2i−2i00000022−2−2i2i2−i2−i22-22i−2i0000000000i2−i22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000
χ312-22i−2i002−2i2−i222-2-22i2i−2i−2i00000022−2−2i2i2−i2−i2-22−2i2i0000000000−i2i2−22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000
χ322-22i−2i002−2i2−i222-2-22i2i−2i−2i00000022−2−2i2i2−i2−i2-22−2i2i0000000000−i2i2−22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000
χ332-22i−2i00−22−i2i222-2-22i2i−2i−2i000000−2−222−i2−i2i2i22-22i−2i0000000000−i2i2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000
χ342-22i−2i00−22−i2i222-2-22i2i−2i−2i000000−2−222−i2−i2i2i22-22i−2i0000000000−i2i2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000
χ352-22i−2i00−22−i2i222-2-22i2i−2i−2i000000−2−222−i2−i2i2i2-22−2i2i0000000000i2−i22−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000
χ362-22i−2i00−22−i2i222-2-22i2i−2i−2i000000−2−222−i2−i2i2i2-22−2i2i0000000000i2−i22−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000
χ372-2−2i2i002−2−i2i222-2-2−2i−2i2i2i00000022−2−2−i2−i2i2i22-2−2i2i0000000000−i2i22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000
χ382-2−2i2i002−2−i2i222-2-2−2i−2i2i2i00000022−2−2−i2−i2i2i22-2−2i2i0000000000−i2i22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000
χ392-2−2i2i002−2−i2i222-2-2−2i−2i2i2i00000022−2−2−i2−i2i2i2-222i−2i0000000000i2−i2−22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000
χ402-2−2i2i002−2−i2i222-2-2−2i−2i2i2i00000022−2−2−i2−i2i2i2-222i−2i0000000000i2−i2−22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000
χ412-2−2i2i00−22i2−i222-2-2−2i−2i2i2i000000−2−222i2i2−i2−i22-2−2i2i0000000000i2−i2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000
χ422-2−2i2i00−22i2−i222-2-2−2i−2i2i2i000000−2−222i2i2−i2−i22-2−2i2i0000000000i2−i2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000
χ432-2−2i2i00−22i2−i222-2-2−2i−2i2i2i000000−2−222i2i2−i2−i2-222i−2i0000000000−i2i22−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000
χ442-2−2i2i00−22i2−i222-2-2−2i−2i2i2i000000−2−222i2i2−i2−i2-222i−2i0000000000−i2i22−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000
χ4544444444441-21-21-21-21-2441-21-21-21-21-2000011-2-211-2-20000000000000000000000000000
χ4644444444441-21-21-21-21-2-4-41-21-21-21-21-20000-1-122-1-1220000000000000000000000000000
χ474444444444-21-21-21-21-2144-21-21-21-21-210000-2-211-2-2110000000000000000000000000000
χ484444444444-21-21-21-21-21-4-4-21-21-21-21-21000022-1-122-1-10000000000000000000000000000
χ49444444-4-4-4-41-21-21-21-21-2001-2-12-12-12-1200003-3003-3000000000000000000000000000000
χ50444444-4-4-4-41-21-21-21-21-2001-2-12-12-12-120000-3300-33000000000000000000000000000000
χ51444444-4-4-4-4-21-21-21-21-2100-212-12-12-12-10000003-3003-30000000000000000000000000000
χ52444444-4-4-4-4-21-21-21-21-2100-212-12-12-12-1000000-3300-330000000000000000000000000000
χ5344-4-4-4444-4-41-21-2-12-12-124i−4i1-21-21-2-12-120000ii−2i−2i−i−i2i2i0000000000000000000000000000
χ5444-4-4-4444-4-41-21-2-12-12-12−4i4i1-21-21-2-12-120000−i−i2i2iii−2i−2i0000000000000000000000000000
χ5544-4-4-4444-4-4-21-212-12-12-14i−4i-21-21-212-12-10000−2i−2iii2i2i−i−i0000000000000000000000000000
χ5644-4-4-4444-4-4-21-212-12-12-1−4i4i-21-21-212-12-100002i2i−i−i−2i−2iii0000000000000000000000000000
χ5744-4-4-44-4-4441-21-2-12-12-12001-2-12-121-21-200003i−3i00−3i3i000000000000000000000000000000
χ5844-4-4-44-4-4441-21-2-12-12-12001-2-12-121-21-20000−3i3i003i−3i000000000000000000000000000000
χ5944-4-4-44-4-444-21-212-12-12-100-212-12-1-21-210000003i−3i00−3i3i0000000000000000000000000000
χ6044-4-4-44-4-444-21-212-12-12-100-212-12-1-21-21000000−3i3i003i−3i0000000000000000000000000000
χ618888-8-800002-42-42-42-4-2400-24000000000000000000000000000000000000000000000000
χ628888-8-80000-42-42-42-424-2004-2000000000000000000000000000000000000000000000000
χ6388-8-88-800002-42-4-24-242-400-24000000000000000000000000000000000000000000000000
χ6488-8-88-80000-42-424-24-2-42004-2000000000000000000000000000000000000000000000000
χ658-88i−8i0042−424i2−4i22-4-242i−4i−2i4i0000002−22−222i2−2i2−i22i20000000000000000000000000000000000000000
χ668-88i−8i0042−424i2−4i2-424-2−4i2i4i−2i000000−22222−2−2i2i22i2−i20000000000000000000000000000000000000000
χ678-88i−8i00−4242−4i24i22-4-242i−4i−2i4i000000−2222−22−i22i2i2−2i20000000000000000000000000000000000000000
χ688-88i−8i00−4242−4i24i2-424-2−4i2i4i−2i00000022−2−2222i2−i2−2i2i20000000000000000000000000000000000000000
χ698-8−8i8i0042−42−4i24i22-4-24−2i4i2i−4i0000002−22−222−i22i2i2−2i20000000000000000000000000000000000000000
χ708-8−8i8i0042−42−4i24i2-424-24i−2i−4i2i000000−22222−22i2−i2−2i2i20000000000000000000000000000000000000000
χ718-8−8i8i00−42424i2−4i22-4-24−2i4i2i−4i000000−2222−22i2−2i2−i22i20000000000000000000000000000000000000000
χ728-8−8i8i00−42424i2−4i2-424-24i−2i−4i2i00000022−2−222−2i2i22i2−i20000000000000000000000000000000000000000

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