Finite Group Databasebeta

← Group #11791673

Character table — Group #11791673

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222244444444444448888888888999912121212121212121818181824242424242424242424242436363636363636363648484848
order12224444334666666121212121212121212121212121222228888888844444444242424242424242444444444412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ511111-1-1111-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111-1-1-1-1-11111-1-1-1-111-1-1
χ611111-1-1111-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-111
χ711111-1-1111-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1-1-1-1111111-1-1
χ811111-1-1111-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11111-11111-1-1-1-1-1-111
χ91111-111-111-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1ii−i−iii−i−i11-1-11-11-1ii−i−iii−i−i1ii−i−iii−i−i1-11-1
χ101111-111-111-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1ii−i−iii−i−i11-1-1-11-11ii−i−iii−i−i1−i−iii−i−iii-11-11
χ111111-111-111-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1−i−iii−i−iii11-1-11-11-1−i−iii−i−iii1−i−iii−i−iii1-11-1
χ121111-111-111-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1−i−iii−i−iii11-1-1-11-11−i−iii−i−iii1ii−i−iii−i−i-11-11
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1ii−i−i−i−iii11111-1-11ii−i−i−i−iii-1ii−i−i−i−iii1-1-11
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1ii−i−i−i−iii1111-111-1ii−i−i−i−iii-1−i−iiiii−i−i-111-1
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1−i−iiiii−i−i11111-1-11−i−iiiii−i−i-1−i−iiiii−i−i1-1-11
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1−i−iiiii−i−i1111-111-1−i−iiiii−i−i-1ii−i−i−i−iii-111-1
χ172222222222222222222222222222222-2-2-2-200000000-2-2-2-2000000000000-2000000000000
χ1822222-2-2222-2222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2220000000000002000000000000
χ192222-222-222-2222222-2-2-2-2-2-222-2-222-2-2222200000000-2-222000000000000-2000000000000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-222-2-222222200000000-2-2-2-20000000000002000000000000
χ2122-2-2200-222022-2-2-2-222-2-22-2000000002-22-2000000002-200000000000000000002-22-20000
χ2222-2-2200-222022-2-2-2-222-2-22-2000000002-22-2000000002-20000000000000000000-22-220000
χ2322-2-2200-222022-2-2-2-222-2-22-200000000-22-2200000000-220000000000000002-22-200000000
χ2422-2-2200-222022-2-2-2-222-2-22-200000000-22-2200000000-22000000000000000-22-2200000000
χ2522-2-2-200222022-2-2-2-2-2-222-22000000002-22-200000000-220000000000000002i−2i−2i2i00000000
χ2622-2-2-200222022-2-2-2-2-2-222-22000000002-22-200000000-22000000000000000−2i2i2i−2i00000000
χ2722-2-2-200222022-2-2-2-2-2-222-2200000000-22-22000000002-200000000000000000002i−2i−2i2i0000
χ2822-2-2-200222022-2-2-2-2-2-222-2200000000-22-22000000002-20000000000000000000−2i2i2i−2i0000
χ292-22-202i−2i0220-2-22-22-20000002i−2i002i−2i002-2-22i2−i2i2−i22−22−2002i−2i0000i2−i2i2−i22−22−20000000000000
χ302-22-202i−2i0220-2-22-22-20000002i−2i002i−2i002-2-22−i2i2−i2i2−22−22002i−2i0000−i2i2−i2i2−22−220000000000000
χ312-22-202i−2i0220-2-22-22-20000002i−2i002i−2i00-222-22−2−22−i2i2i2−i200−2i2i00002−2−22−i2i2i2−i20000000000000
χ322-22-202i−2i0220-2-22-22-20000002i−2i002i−2i00-222-2−222−2i2−i2−i2i200−2i2i0000−222−2i2−i2−i2i20000000000000
χ332-22-20−2i2i0220-2-22-22-2000000−2i2i00−2i2i002-2-22i2−i2i2−i2−22−2200−2i2i0000i2−i2i2−i2−22−220000000000000
χ342-22-20−2i2i0220-2-22-22-2000000−2i2i00−2i2i002-2-22−i2i2−i2i22−22−200−2i2i0000−i2i2−i2i22−22−20000000000000
χ352-22-20−2i2i0220-2-22-22-2000000−2i2i00−2i2i00-222-22−2−22i2−i2−i2i2002i−2i00002−2−22i2−i2−i2i20000000000000
χ362-22-20−2i2i0220-2-22-22-2000000−2i2i00−2i2i00-222-2−222−2−i2i2i2−i2002i−2i0000−222−2−i2i2i2−i20000000000000
χ37444444441-241-211-2-21111-2-21111-2-2-2-200002222222200000000-1-1-1-1-1-1-1-10000000000000
χ38444444441-241-211-2-21111-2-21111-2-2-2-20000-2-2-2-2-2-2-2-200000000111111110000000000000
χ3944444444-214-21-2-211-2-2-2-211-2-2-2-211110000000000000000222200000000000000000-1-1-1-1
χ4044444444-214-21-2-211-2-2-2-211-2-2-2-211110000000000000000-2-2-2-2000000000000000001111
χ4144444-4-441-2-41-211-2-21111-2-2-1-1-1-1222200002222-2-2-2-200000000-1-1-1-111110000000000000
χ4244444-4-441-2-41-211-2-21111-2-2-1-1-1-122220000-2-2-2-22222000000001111-1-1-1-10000000000000
χ4344444-4-44-21-4-21-2-211-2-2-2-2112222-1-1-1-1000000000000000022-2-200000000000000000-1-111
χ4444444-4-44-21-4-21-2-211-2-2-2-2112222-1-1-1-10000000000000000-2-2220000000000000000011-1-1
χ454444-444-41-2-41-211-2-2-1-1-1-12211-1-1-2-22200002i2i−2i−2i2i2i−2i−2i00000000−i−iii−i−iii0000000000000
χ464444-444-41-2-41-211-2-2-1-1-1-12211-1-1-2-2220000−2i−2i2i2i−2i−2i2i2i00000000ii−i−iii−i−i0000000000000
χ474444-444-4-21-4-21-2-2112222-1-1-2-22211-1-100000000000000002-22-200000000000000000-11-11
χ484444-444-4-21-4-21-2-2112222-1-1-2-22211-1-10000000000000000-22-22000000000000000001-11-1
χ494444-4-4-4-41-241-211-2-2-1-1-1-122-1-11122-2-200002i2i−2i−2i−2i−2i2i2i00000000−i−iiiii−i−i0000000000000
χ504444-4-4-4-41-241-211-2-2-1-1-1-122-1-11122-2-20000−2i−2i2i2i2i2i−2i−2i00000000ii−i−i−i−iii0000000000000
χ514444-4-4-4-4-214-21-2-2112222-1-122-2-2-1-11100000000000000002-2-2200000000000000000-111-1
χ524444-4-4-4-4-214-21-2-2112222-1-122-2-2-1-1110000000000000000-222-2000000000000000001-1-11
χ534-44-404i−4i01-20-121-1-223i−3i3i−3i00i−i3-3−2i2i0000002ζ−2ζ2ζ3−2ζ3−2ζ32ζ32ζ−2ζ00000000−ζζ−ζ3ζ3ζ3−ζ3−ζζ0000000000000
χ544-44-404i−4i01-20-121-1-223i−3i3i−3i00i−i3-3−2i2i000000−2ζ2ζ−2ζ32ζ32ζ3−2ζ3−2ζ2ζ00000000ζ−ζζ3−ζ3−ζ3ζ3ζ−ζ0000000000000
χ554-44-404i−4i01-20-121-1-22−3i3i−3i3i00i−i-33−2i2i0000002ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ32ζ300000000−ζ3ζ3−ζζ−ζζζ3−ζ30000000000000
χ564-44-404i−4i01-20-121-1-22−3i3i−3i3i00i−i-33−2i2i000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ3−2ζ300000000ζ3−ζ3ζ−ζζ−ζ−ζ3ζ30000000000000
χ574-44-40−4i4i01-20-121-1-223i−3i3i−3i00−ii-332i−2i0000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ2ζ00000000−ζζ−ζ3ζ3−ζ3ζ3ζ−ζ0000000000000
χ584-44-40−4i4i01-20-121-1-223i−3i3i−3i00−ii-332i−2i000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ−2ζ00000000ζ−ζζ3−ζ3ζ3−ζ3−ζζ0000000000000
χ594-44-40−4i4i01-20-121-1-22−3i3i−3i3i00−ii3-32i−2i0000002ζ3−2ζ32ζ−2ζ−2ζ2ζ2ζ3−2ζ300000000−ζ3ζ3−ζζζ−ζ−ζ3ζ30000000000000
χ604-44-40−4i4i01-20-121-1-22−3i3i−3i3i00−ii3-32i−2i000000−2ζ32ζ3−2ζ2ζ2ζ−2ζ−2ζ32ζ300000000ζ3−ζ3ζ−ζ−ζζζ3−ζ30000000000000
χ614-4-440000440-4-4-44-440000000000000044-4-40000000000000000000000000000000000000
χ624-4-440000440-4-4-44-4400000000000000-4-4440000000000000000000000000000000000000
χ6388-8-8800-82-402-4-2-24422-2-2-440000000000000000000000000000000000000000000000000
χ6488-8-8800-8-420-4244-2-2-4-4442-20000000000000000000000000000000000000000000000000
χ6588-8-8-80082-402-4-2-244-2-2224-40000000000000000000000000000000000000000000000000
χ6688-8-8-8008-420-4244-2-244-4-4-220000000000000000000000000000000000000000000000000
χ678-88-808i−8i0-4204-2-442-2000000−4i4i002i−2i0000000000000000000000000000000000000000000
χ688-88-80−8i8i0-4204-2-442-20000004i−4i00−2i2i0000000000000000000000000000000000000000000
χ698-8-8800002-40-24-224-46i−6i−6i6i000000000000000000000000000000000000000000000000000
χ708-8-8800002-40-24-224-4−6i6i6i−6i000000000000000000000000000000000000000000000000000
χ718-8-880000-4204-24-4-220000000000006i−6i00000000000000000000000000000000000000000
χ728-8-880000-4204-24-4-22000000000000−6i6i00000000000000000000000000000000000000000

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