Finite Group Databasebeta

← Group #11777804

Character table — Group #11777804

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222244444444888888888888889999161616161616161618181818181818181818181818181818181818181818727272727272
order12224488883366666644121212122424242424242424444412121212121212124488888888888888888888248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1ii−i−i
χ411111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-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
χ7111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−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−iiiii−i−i−i−iiiii11ii−i−i
χ9111111-1-1-1-1111111111-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-11-1
χ10111111-1-1-1-1111111111-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11-11
χ11111111-1-1-1-1111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111iiii−i−i−i−i−i−i−i−iiiii1-1i−i−ii
χ12111111-1-1-1-1111111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111−i−i−i−iiiiiiiii−i−i−i−i1-1−iii−i
χ13111111-1-1-1-111111111-111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-11-11
χ14111111-1-1-1-111111111-111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-11-1
χ15111111-1-1-1-111111111-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11−iii−i
χ16111111-1-1-1-111111111-111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11i−i−ii
χ172222-2-200002222222200-2-2-2-200000000222200000000-2-2000022-2-222-2-200000000000000
χ182222-2-200002222222200-2-2-2-200000000222200000000-2-20000-2-222-2-22200000000000000
χ192222-2-200002222222200-2-2-2-200000000-2-2-2-2000000002200002i2i−2i−2i−2i−2i2i2i00000000000000
χ202222-2-200002222222200-2-2-2-200000000-2-2-2-200000000220000−2i−2i2i2i2i2i−2i−2i00000000000000
χ2122-2-22-2000022-2-2-2-22200-2-222000000002i2i−2i−2i000000002i−2i0000000000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000
χ2222-2-22-2000022-2-2-2-22200-2-222000000002i2i−2i−2i000000002i−2i000000000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000
χ2322-2-22-2000022-2-2-2-22200-2-22200000000−2i−2i2i2i00000000−2i2i0000000000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000
χ2422-2-22-2000022-2-2-2-22200-2-22200000000−2i−2i2i2i00000000−2i2i000000000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000
χ2522-2-2-222i2i−2i−2i22-2-2-2-2220022-2-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i00000000−2i2i22-2-20000000000000000000000
χ2622-2-2-222i2i−2i−2i22-2-2-2-2220022-2-22i2i2i2i−2i−2i−2i−2i−2i−2i2i2i000000002i−2i-2-2220000000000000000000000
χ2722-2-2-22−2i−2i2i2i22-2-2-2-2220022-2-2−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i00000000−2i2i-2-2220000000000000000000000
χ2822-2-2-22−2i−2i2i2i22-2-2-2-2220022-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i000000002i−2i22-2-20000000000000000000000
χ292-22-200i2−i2i2−i222-2-222-2-2000000i2i2−i2−i2i2i2−i2−i22-22-20000000000i2−i2i2−i2002i−2i002i−2i2−22−22−22−2000000
χ302-22-200i2−i2i2−i222-2-222-2-2000000i2i2−i2−i2i2i2−i2−i22-22-20000000000i2−i2i2−i200−2i2i00−2i2i−22−22−22−22000000
χ312-22-200i2−i2i2−i222-2-222-2-2000000i2i2−i2−i2i2i2−i2−i2-22-220000000000−i2i2−i2i2002-200-22−i2i2−i2i2i2−i2i2−i2000000
χ322-22-200i2−i2i2−i222-2-222-2-2000000i2i2−i2−i2i2i2−i2−i2-22-220000000000−i2i2−i2i200-22002-2i2−i2i2−i2−i2i2−i2i2000000
χ332-22-200−i2i2−i2i222-2-222-2-2000000−i2−i2i2i2−i2−i2i2i22-22-20000000000−i2i2−i2i2002i−2i002i−2i−22−22−22−22000000
χ342-22-200−i2i2−i2i222-2-222-2-2000000−i2−i2i2i2−i2−i2i2i22-22-20000000000−i2i2−i2i200−2i2i00−2i2i2−22−22−22−2000000
χ352-22-200−i2i2−i2i222-2-222-2-2000000−i2−i2i2i2−i2−i2i2i2-22-220000000000i2−i2i2−i2002-200-22i2−i2i2−i2−i2i2−i2i2000000
χ362-22-200−i2i2−i2i222-2-222-2-2000000−i2−i2i2i2−i2−i2i2i2-22-220000000000i2−i2i2−i200-22002-2−i2i2−i2i2i2−i2i2−i2000000
χ372-2-22002−2−222222-2-2-2-200000022−2−2−2−2222i−2i−2i2i0000000000−i2i2i2−i22ζ−2ζ002ζ3−2ζ3001+i−1−i−1−i1+i−1+i1−i1−i−1+i000000
χ382-2-22002−2−222222-2-2-2-200000022−2−2−2−2222i−2i−2i2i0000000000−i2i2i2−i2−2ζ2ζ00−2ζ32ζ300−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000
χ392-2-22002−2−222222-2-2-2-200000022−2−2−2−222−2i2i2i−2i0000000000i2−i2−i2i22ζ3−2ζ3002ζ−2ζ00−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000
χ402-2-22002−2−222222-2-2-2-200000022−2−2−2−222−2i2i2i−2i0000000000i2−i2−i2i2−2ζ32ζ300−2ζ2ζ001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000
χ412-2-2200−222−22222-2-2-2-2000000−2−22222−2−22i−2i−2i2i0000000000i2−i2−i2i22ζ−2ζ002ζ3−2ζ300−1−i1+i1+i−1−i1−i−1+i−1+i1−i000000
χ422-2-2200−222−22222-2-2-2-2000000−2−22222−2−22i−2i−2i2i0000000000i2−i2−i2i2−2ζ2ζ00−2ζ32ζ3001+i−1−i−1−i1+i−1+i1−i1−i−1+i000000
χ432-2-2200−222−22222-2-2-2-2000000−2−22222−2−2−2i2i2i−2i0000000000−i2i2i2−i22ζ3−2ζ3002ζ−2ζ001−i−1+i−1+i1−i−1−i1+i1+i−1−i000000
χ442-2-2200−222−22222-2-2-2-2000000−2−22222−2−2−2i2i2i−2i0000000000−i2i2i2−i2−2ζ32ζ300−2ζ2ζ00−1+i1−i1−i−1+i1+i−1−i−1−i1+i000000
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
χ49444444-4-4-4-41-21-21-21-24-41-21-2-12-12-12-120000-1-12211-2-20000000000000000000000000000
χ50444444-4-4-4-41-21-21-21-2-441-21-2-12-12-12-12000011-2-2-1-1220000000000000000000000000000
χ51444444-4-4-4-4-21-21-21-214-4-21-212-12-12-12-1000022-1-1-2-2110000000000000000000000000000
χ52444444-4-4-4-4-21-21-21-21-44-21-212-12-12-12-10000-2-21122-1-10000000000000000000000000000
χ5344-4-4-444i4i−4i−4i1-2-12-121-2001-2-12i−2ii−2i−i2i−i2i00003i−3i003-3000000000000000000000000000000
χ5444-4-4-444i4i−4i−4i1-2-12-121-2001-2-12i−2ii−2i−i2i−i2i0000−3i3i00-33000000000000000000000000000000
χ5544-4-4-444i4i−4i−4i-212-12-1-2100-212-1−2ii−2ii2i−i2i−i0000003i−3i003-30000000000000000000000000000
χ5644-4-4-444i4i−4i−4i-212-12-1-2100-212-1−2ii−2ii2i−i2i−i000000−3i3i00-330000000000000000000000000000
χ5744-4-4-44−4i−4i4i4i1-2-12-121-2001-2-12−i2i−i2ii−2ii−2i00003i−3i00-33000000000000000000000000000000
χ5844-4-4-44−4i−4i4i4i1-2-12-121-2001-2-12−i2i−i2ii−2ii−2i0000−3i3i003-3000000000000000000000000000000
χ5944-4-4-44−4i−4i4i4i-212-12-1-2100-212-12i−i2i−i−2ii−2ii0000003i−3i00-330000000000000000000000000000
χ6044-4-4-44−4i−4i4i4i-212-12-1-2100-212-12i−i2i−i−2ii−2ii000000−3i3i003-30000000000000000000000000000
χ618888-8-800002-42-42-42-400-24-24000000000000000000000000000000000000000000000000
χ628888-8-80000-42-42-42-42004-24-2000000000000000000000000000000000000000000000000
χ6388-8-88-800002-4-24-242-400-242-4000000000000000000000000000000000000000000000000
χ6488-8-88-80000-424-24-2-42004-2-42000000000000000000000000000000000000000000000000
χ658-88-8004i2−4i24i2−4i22-4-242-4-24000000i2−2i2−i22i2i2−2i2−i22i20000000000000000000000000000000000000000
χ668-88-8004i2−4i24i2−4i2-424-2-424-2000000−2i2i22i2−i2−2i2i22i2−i20000000000000000000000000000000000000000
χ678-88-800−4i24i2−4i24i22-4-242-4-24000000−i22i2i2−2i2−i22i2i2−2i20000000000000000000000000000000000000000
χ688-88-800−4i24i2−4i24i2-424-2-424-20000002i2−i2−2i2i22i2−i2−2i2i20000000000000000000000000000000000000000
χ698-8-880042−42−42422-42-4-24-240000002−22−222−2222−220000000000000000000000000000000000000000
χ708-8-880042−42−4242-42-424-24-2000000−22222−222−2−2220000000000000000000000000000000000000000
χ718-8-8800−424242−422-42-4-24-24000000−2222−222−22−2220000000000000000000000000000000000000000
χ728-8-8800−424242−42-42-424-24-200000022−2−222−22222−20000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.