Finite Group Databasebeta

← Group #11777057

Character table — Group #11777057

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111444444444444444444888888881212121212121212181818181818181824242424242424242424242424242424242424243636363636363636
order1222444423346666661212121212121212666612121212888888884444444488882424242424242424242424242424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111-111-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111-111-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111-111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111-111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−i-1-111-1-111i−ii−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ101111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−iii−i−i-1-111-1-111−ii−iiii−i−iii−i−i−i−iii−i−iii-1-111-1-111
χ111111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii-1-111-1-111i−ii−i−i−iii−i−iiiii−i−iii−i−i-1-111-1-111
χ121111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii−i−iii-1-111-1-111−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ131111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii-1-1-1-11111i−i−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111
χ141111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii-1-1-1-11111−iii−iii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1
χ151111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i-1-1-1-11111i−i−ii−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1
χ161111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i-1-1-1-11111−iii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111
χ17222222222222222222222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222-222-222222222222222-2-2-2-2-2-2-2-200000000-2-22222-2-20000000000000000000000000000
χ192222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22222-2-2-2-20000000022-2-222-2-20000000000000000000000000000
χ202222-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-22222000000002222-2-2-2-20000000000000000000000000000
χ2122-2-222-2-20220-2-2-2-2222222-2-2-2-20000000000000000002i−2i2i−2i00000000000000000000002−22−2−i2i2−i2i2
χ2222-2-222-2-20220-2-2-2-2222222-2-2-2-20000000000000000002i−2i2i−2i0000000000000000000000−22−22i2−i2i2−i2
χ2322-2-222-2-20220-2-2-2-2222222-2-2-2-2000000000000000000−2i2i−2i2i00000000000000000000002−22−2i2−i2i2−i2
χ2422-2-222-2-20220-2-2-2-2222222-2-2-2-2000000000000000000−2i2i−2i2i0000000000000000000000−22−22−i2i2−i2i2
χ2522-2-2-2-2220220-2-2-2-222-2-2-2-222220000000000000000002i−2i−2i2i00000000000000000000002−2−22−i2i2i2−i2
χ2622-2-2-2-2220220-2-2-2-222-2-2-2-222220000000000000000002i−2i−2i2i0000000000000000000000−222−2i2−i2−i2i2
χ2722-2-2-2-2220220-2-2-2-222-2-2-2-22222000000000000000000−2i2i2i−2i00000000000000000000002−2−22i2−i2−i2i2
χ2822-2-2-2-2220220-2-2-2-222-2-2-2-22222000000000000000000−2i2i2i−2i0000000000000000000000−222−2−i2i2i2−i2
χ292-22-22i−2i2i−2i022022-2-2-2-22i2i−2i−2i2i2i−2i−2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i00002-2000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000
χ302-22-22i−2i2i−2i022022-2-2-2-22i2i−2i−2i2i2i−2i−2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i00002-200000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000
χ312-22-22i−2i2i−2i022022-2-2-2-22i2i−2i−2i2i2i−2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−2i2i0000-2200002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ322-22-22i−2i2i−2i022022-2-2-2-22i2i−2i−2i2i2i−2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2i2i0000-220000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ332-22-2−2i2i−2i2i022022-2-2-2-2−2i−2i2i2i−2i−2i2i2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i2i00002-200000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000
χ342-22-2−2i2i−2i2i022022-2-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2i2i00002-2000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000
χ352-22-2−2i2i−2i2i022022-2-2-2-2−2i−2i2i2i−2i−2i2i2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300002i−2i0000-220000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ362-22-2−2i2i−2i2i022022-2-2-2-2−2i−2i2i2i−2i−2i2i2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002i−2i0000-2200002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ374444444441-241-21-21-21-21-21-21-211-2-211-2-20000000000000000222200000000-1-1-1-1-1-1-1-100000000
χ384444444441-241-21-21-21-21-21-21-211-2-211-2-20000000000000000-2-2-2-2000000001111111100000000
χ39444444444-214-21-21-21-21-21-21-21-2-211-2-21122222222000000000000-1-1-1-1-1-1-1-10000000000000000
χ40444444444-214-21-21-21-21-21-21-21-2-211-2-211-2-2-2-2-2-2-2-2000000000000111111110000000000000000
χ4144444444-41-2-41-21-21-21-21-21-21-2-1-122-1-122000000000000000022-2-200000000-1-1-1-1111100000000
χ4244444444-41-2-41-21-21-21-21-21-21-2-1-122-1-1220000000000000000-2-222000000001111-1-1-1-100000000
χ4344444444-4-21-4-21-21-21-21-21-21-2122-1-122-1-12222-2-2-2-2000000000000-1-1-1-111110000000000000000
χ4444444444-4-21-4-21-21-21-21-21-21-2122-1-122-1-1-2-2-2-222220000000000001111-1-1-1-10000000000000000
χ454444-4-4-4-441-2-41-21-21-2-12-12-12-1211-2-2-1-12200000000000000002i−2i2i−2i00000000−i−iii−i−iii00000000
χ464444-4-4-4-441-2-41-21-21-2-12-12-12-1211-2-2-1-1220000000000000000−2i2i−2i2i00000000ii−i−iii−i−i00000000
χ474444-4-4-4-44-21-4-21-21-212-12-12-12-1-2-21122-1-12i2i−2i−2i2i2i−2i−2i000000000000−i−iii−i−iii0000000000000000
χ484444-4-4-4-44-21-4-21-21-212-12-12-12-1-2-21122-1-1−2i−2i2i2i−2i−2i2i2i000000000000ii−i−iii−i−i0000000000000000
χ494444-4-4-4-4-41-241-21-21-2-12-12-12-12-1-12211-2-200000000000000002i−2i−2i2i00000000−i−iiiii−i−i00000000
χ504444-4-4-4-4-41-241-21-21-2-12-12-12-12-1-12211-2-20000000000000000−2i2i2i−2i00000000ii−i−i−i−iii00000000
χ514444-4-4-4-4-4-214-21-21-212-12-12-12-122-1-1-2-2112i2i−2i−2i−2i−2i2i2i000000000000−i−iiiii−i−i0000000000000000
χ524444-4-4-4-4-4-214-21-21-212-12-12-12-122-1-1-2-211−2i−2i2i2i2i2i−2i−2i000000000000ii−i−i−i−iii0000000000000000
χ534-44-44i−4i4i−4i0-210-212-12-1−2ii2i−i−2ii2i−i003-3003i−3i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000000000000000
χ544-44-44i−4i4i−4i0-210-212-12-1−2ii2i−i−2ii2i−i003-3003i−3i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000000000000000
χ554-44-44i−4i4i−4i0-210-212-12-1−2ii2i−i−2ii2i−i00-3300−3i3i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ130000000000000000
χ564-44-44i−4i4i−4i0-210-212-12-1−2ii2i−i−2ii2i−i00-3300−3i3i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ130000000000000000
χ574-44-4−4i4i−4i4i0-210-212-12-12i−i−2ii2i−i−2ii003-300−3i3i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000000000000000
χ584-44-4−4i4i−4i4i0-210-212-12-12i−i−2ii2i−i−2ii003-300−3i3i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000000000000000
χ594-44-4−4i4i−4i4i0-210-212-12-12i−i−2ii2i−i−2ii00-33003i−3i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ230000000000000000
χ604-44-4−4i4i−4i4i0-210-212-12-12i−i−2ii2i−i−2ii00-33003i−3i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ230000000000000000
χ614-4-444i−4i−4i4i01-20-121-2-12i−2i−i2i−i2ii−2i3-3003i−3i000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ624-4-444i−4i−4i4i01-20-121-2-12i−2i−i2i−i2ii−2i3-3003i−3i000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ634-4-444i−4i−4i4i01-20-121-2-12i−2i−i2i−i2ii−2i-3300−3i3i000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ644-4-444i−4i−4i4i01-20-121-2-12i−2i−i2i−i2ii−2i-3300−3i3i000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ654-4-444i−4i−4i4i0440-4-444-4-44i4i−4i−4i−4i−4i4i4i0000000000000000000000000000000000000000000000000000
χ664-4-44−4i4i4i−4i01-20-121-2-12−i2ii−2ii−2i−i2i3-300−3i3i000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ674-4-44−4i4i4i−4i01-20-121-2-12−i2ii−2ii−2i−i2i3-300−3i3i000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ684-4-44−4i4i4i−4i01-20-121-2-12−i2ii−2ii−2i−i2i-33003i−3i000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ694-4-44−4i4i4i−4i01-20-121-2-12−i2ii−2ii−2i−i2i-33003i−3i000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ704-4-44−4i4i4i−4i0440-4-444-4-4−4i−4i4i4i4i4i−4i−4i0000000000000000000000000000000000000000000000000000
χ7188-8-888-8-802-40-24-242-42-42-4-24-240000000000000000000000000000000000000000000000000000
χ7288-8-888-8-80-4204-24-2-42-42-424-24-20000000000000000000000000000000000000000000000000000
χ7388-8-8-8-88802-40-24-242-4-24-242-42-40000000000000000000000000000000000000000000000000000
χ7488-8-8-8-8880-4204-24-2-424-24-2-42-420000000000000000000000000000000000000000000000000000
χ758-88-88i−8i8i−8i02-402-4-24-242i−4i−2i4i2i−4i−2i4i0000000000000000000000000000000000000000000000000000
χ768-88-8−8i8i−8i8i02-402-4-24-24−2i4i2i−4i−2i4i2i−4i0000000000000000000000000000000000000000000000000000
χ778-8-888i−8i−8i8i0-4204-2-424-2−4i2i4i−2i4i−2i−4i2i0000000000000000000000000000000000000000000000000000
χ788-8-88−8i8i8i−8i0-4204-2-424-24i−2i−4i2i−4i2i4i−2i0000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.