Finite Group Databasebeta

← Group #11785619

Character table — Group #11785619

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112222244444444444444444444488888888888888888888888899181818181836363636367272727272727272
order122448823346688812121212242424242424242466666612121212121224242424242424242424242422244882488844448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ51111111-111-1111-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-11-1-11111-1-1-1-1
χ61111111-111-1111-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-1-1-11111
χ71111111-111-1111-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111ii−i−i−i−iii
χ81111111-111-1111-1-111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111−i−iiiii−i−i
χ911111-1-1111111-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-11-11-11-11-1
χ1011111-1-1111111-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-11-11-11-11
χ1111111-1-1111111-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111i−i−iii−i−ii
χ1211111-1-1111111-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111−iii−i−iii−i
χ1311111-1-1-111-111-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1111-11-1-11-11
χ1411111-1-1-111-111-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-111-11-111-11-1
χ1511111-1-1-111-111-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111111-1-1i−i−ii−iii−i
χ1611111-1-1-111-111-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-111111-1-1−iii−ii−i−ii
χ17222-2-20002202202i−2i-2-2-2-200000000220000-2-2000000002i2i2i2i−2i−2i−2i−2i222-2-2000002i−2i00000000
χ18222-2-20002202202i−2i-2-2-2-200000000220000-2-2000000002i2i2i2i−2i−2i−2i−2i-2-2-22200000−2i2i00000000
χ19222-2-2000220220−2i2i-2-2-2-200000000220000-2-200000000−2i−2i−2i−2i2i2i2i2i222-2-200000−2i2i00000000
χ20222-2-2000220220−2i2i-2-2-2-200000000220000-2-200000000−2i−2i−2i−2i2i2i2i2i-2-2-222000002i−2i00000000
χ2122-22-200222-222000-2-2-2-200000000-2-2222222-2-2-2-200000000000022-2-22002-200000000000
χ2222-22-200222-222000-2-2-2-200000000-2-2222222-2-2-2-2000000000000-2-222-200-2200000000000
χ2322-22-200-222222000-2-2-2-200000000-2-2-2-2-2-222222200000000000022-2-2200-2200000000000
χ2422-22-200-222222000-2-2-2-200000000-2-2-2-2-2-2222222000000000000-2-222-2002-200000000000
χ2522-2-2222022022-200222222222222-2-20000-2-20000-2-2-2-20000000022-22-22200-20000000000
χ2622-2-2222022022-200222222222222-2-20000-2-20000-2-2-2-200000000-2-22-22-2-20020000000000
χ2722-2-22-2-20220222002222-2-2-2-2-2-2-2-2-2-20000-2-2000022220000000022-22-2-2-20020000000000
χ2822-2-22-2-20220222002222-2-2-2-2-2-2-2-2-2-20000-2-20000222200000000-2-22-222200-20000000000
χ29444444441-241-244411-2-21111-2-2-2-21-211-2-21-211-2-211-2-211-2-211-2-200000000000000000000
χ3044444444-214-21444-2-211-2-2-2-21111-21-2-211-21-2-211-2-211-2-211-2-21100000000000000000000
χ314444444-41-2-41-24-4-411-2-21111-2-2-2-21-2-1-1221-2-1-12211-2-2-1-122-1-12200000000000000000000
χ324444444-4-21-4-214-4-4-2-211-2-2-2-21111-2122-1-1-2122-1-1-2-21122-1-122-1-100000000000000000000
χ3344444-4-441-241-2-4-4-411-2-2-1-1-1-122221-211-2-21-211-2-2-1-122-1-122-1-12200000000000000000000
χ3444444-4-44-214-21-4-4-4-2-2112222-1-1-1-1-21-2-211-21-2-21122-1-122-1-122-1-100000000000000000000
χ3544444-4-4-41-2-41-2-44411-2-2-1-1-1-122221-2-1-1221-2-1-122-1-12211-2-211-2-200000000000000000000
χ3644444-4-4-4-21-4-21-444-2-2112222-1-1-1-1-2122-1-1-2122-1-122-1-1-2-211-2-21100000000000000000000
χ37444-4-40001-201-204i−4i-1-1223i3i−3i−3i00001-23-300-123-3003i−3i00ii−2i−2i−i−i2i2i00000000000000000000
χ38444-4-40001-201-204i−4i-1-122−3i−3i3i3i00001-2-3300-12-3300−3i3i00ii−2i−2i−i−i2i2i00000000000000000000
χ39444-4-40001-201-20−4i4i-1-1223i3i−3i−3i00001-2-3300-12-33003i−3i00−i−i2i2iii−2i−2i00000000000000000000
χ40444-4-40001-201-20−4i4i-1-122−3i−3i3i3i00001-23-300-123-300−3i3i00−i−i2i2iii−2i−2i00000000000000000000
χ41444-4-4000-210-2104i−4i22-1-100003i3i−3i−3i-21003-32-1003-3003i−3i−2i−2iii2i2i−i−i00000000000000000000
χ42444-4-4000-210-2104i−4i22-1-10000−3i−3i3i3i-2100-332-100-3300−3i3i−2i−2iii2i2i−i−i00000000000000000000
χ43444-4-4000-210-210−4i4i22-1-100003i3i−3i−3i-2100-332-100-33003i−3i2i2i−i−i−2i−2iii00000000000000000000
χ44444-4-4000-210-210−4i4i22-1-10000−3i−3i3i3i-21003-32-1003-300−3i3i2i2i−i−i−2i−2iii00000000000000000000
χ4544-44-40041-2-41-2000-1-1223i3i−3i−3i0000-1211-2-21-2-1-122−3i3i003i−3i003i−3i0000000000000000000000
χ4644-44-40041-2-41-2000-1-122−3i−3i3i3i0000-1211-2-21-2-1-1223i−3i00−3i3i00−3i3i0000000000000000000000
χ4744-44-4004-21-4-2100022-1-100003i3i−3i−3i2-1-2-211-2122-1-100−3i3i003i−3i003i−3i00000000000000000000
χ4844-44-4004-21-4-2100022-1-10000−3i−3i3i3i2-1-2-211-2122-1-1003i−3i00−3i3i00−3i3i00000000000000000000
χ4944-44-400-41-241-2000-1-1223i3i−3i−3i0000-12-1-1221-211-2-2−3i3i00−3i3i00−3i3i0000000000000000000000
χ5044-44-400-41-241-2000-1-122−3i−3i3i3i0000-12-1-1221-211-2-23i−3i003i−3i003i−3i0000000000000000000000
χ5144-44-400-4-214-2100022-1-100003i3i−3i−3i2-122-1-1-21-2-21100−3i3i00−3i3i00−3i3i00000000000000000000
χ5244-44-400-4-214-2100022-1-10000−3i−3i3i3i2-122-1-1-21-2-211003i−3i003i−3i003i−3i00000000000000000000
χ5344-4-444401-201-2-40011-2-21111-2-2-2-2-123-300-12-3300-1-1223-300-330000000000000000000000
χ5444-4-444401-201-2-40011-2-21111-2-2-2-2-12-3300-123-300-1-122-33003-30000000000000000000000
χ5544-4-44440-210-21-400-2-211-2-2-2-211112-1003-32-100-3322-1-1003-300-3300000000000000000000
χ5644-4-44440-210-21-400-2-211-2-2-2-211112-100-332-1003-322-1-100-33003-300000000000000000000
χ5744-4-44-4-401-201-240011-2-2-1-1-1-12222-123-300-12-330011-2-2-33003-30000000000000000000000
χ5844-4-44-4-401-201-240011-2-2-1-1-1-12222-12-3300-123-30011-2-23-300-330000000000000000000000
χ5944-4-44-4-40-210-21400-2-2112222-1-1-1-12-1003-32-100-33-2-21100-33003-300000000000000000000
χ6044-4-44-4-40-210-21400-2-2112222-1-1-1-12-100-332-1003-3-2-211003-300-3300000000000000000000
χ614-400022−220440-4-4000000022−2222−2222−2222−220000000000000000000000004-400022−220000000000000
χ624-400022−220440-4-4000000022−2222−2222−2222−22000000000000000000000000-44000−22220000000000000
χ634-4000−22220440-4-40000000−2222−2222−2222−22220000000000000000000000004-4000−22220000000000000
χ644-4000−22220440-4-40000000−2222−2222−2222−2222000000000000000000000000-4400022−220000000000000
χ658-800042−4202-40-240006i−6i004ζ+2ζ3−4ζ−2ζ3−2ζ−4ζ32ζ+4ζ3−2222−222200000000000000000000000000000000000000000000
χ668-800042−4202-40-24000−6i6i00−2ζ−4ζ32ζ+4ζ34ζ+2ζ3−4ζ−2ζ3−2222−222200000000000000000000000000000000000000000000
χ678-800042−420-4204-2000006i−6i−2222−22224ζ+2ζ3−4ζ−2ζ3−2ζ−4ζ32ζ+4ζ300000000000000000000000000000000000000000000
χ688-800042−420-4204-200000−6i6i−2222−2222−2ζ−4ζ32ζ+4ζ34ζ+2ζ3−4ζ−2ζ300000000000000000000000000000000000000000000
χ698-8000−424202-40-240006i−6i00−4ζ−2ζ34ζ+2ζ32ζ+4ζ3−2ζ−4ζ322−2222−2200000000000000000000000000000000000000000000
χ708-8000−424202-40-24000−6i6i002ζ+4ζ3−2ζ−4ζ3−4ζ−2ζ34ζ+2ζ322−2222−2200000000000000000000000000000000000000000000
χ718-8000−42420-4204-2000006i−6i22−2222−22−4ζ−2ζ34ζ+2ζ32ζ+4ζ3−2ζ−4ζ300000000000000000000000000000000000000000000
χ728-8000−42420-4204-200000−6i6i22−2222−222ζ+4ζ3−2ζ−4ζ3−4ζ−2ζ34ζ+2ζ300000000000000000000000000000000000000000000

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