Finite Group Databasebeta

← Group #11774631

Character table — Group #11774631

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11111111444444444444444444888888881212121212121212181818181818181824242424242424242424242424242424242424243636363636363636
order12224444233466666612121212121212126666121212122244444444444444668888121212121212242424242424242488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ511111111-111-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ611111111-111-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ711111111-111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ811111111-111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111i−ii−i11-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111−ii−ii11-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1i−ii−i-1-11111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-1111-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1−ii−ii-1-11111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-111i−i−ii-1-111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-111−iii−i-1-111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1-1-1i−i−ii11-1-111ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1-1-1−iii−i11-1-111−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222222222222222222200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ1822222222-222-222222222222222-2-2-2-2-2-2-2-200000000-2-22222-2-20000000000000000000000000000
χ192222-2-2-2-2222-2222222-2-2-2-2-2-2-2-22222-2-2-2-200000000-2-2-2-222220000000000000000000000000000
χ202222-2-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-222-2-2220000000000000000000000000000
χ2122-2-222-2-20220-2-22-2-2222-2-222-2-20000000000000000002i−2i2i−2i00000000000000000000002−22−2−i2i2−i2i2
χ2222-2-222-2-20220-2-22-2-2222-2-222-2-20000000000000000002i−2i2i−2i0000000000000000000000−22−22i2−i2i2−i2
χ2322-2-222-2-20220-2-22-2-2222-2-222-2-2000000000000000000−2i2i−2i2i00000000000000000000002−22−2i2−i2i2−i2
χ2422-2-222-2-20220-2-22-2-2222-2-222-2-2000000000000000000−2i2i−2i2i0000000000000000000000−22−22−i2i2−i2i2
χ2522-2-2-2-2220220-2-22-2-22-2-222-2-2220000000000000000002i−2i−2i2i0000000000000000000000−i2i2i2−i2−222−2
χ2622-2-2-2-2220220-2-22-2-22-2-222-2-2220000000000000000002i−2i−2i2i0000000000000000000000i2−i2−i2i22−2−22
χ2722-2-2-2-2220220-2-22-2-22-2-222-2-222000000000000000000−2i2i2i−2i0000000000000000000000−i2i2i2−i22−2−22
χ2822-2-2-2-2220220-2-22-2-22-2-222-2-222000000000000000000−2i2i2i−2i0000000000000000000000i2−i2−i2i2−222−2
χ292-22-22i−2i2i−2i02202-2-22-2-22i−2i2i−2i2i−2i2i−2i0000000000002-22i−2i2-200002i−2i0000002-22i−2i000000000000000000
χ302-22-22i−2i2i−2i02202-2-22-2-22i−2i2i−2i2i−2i2i−2i000000000000-22−2i2i2-200002i−2i000000-22−2i2i000000000000000000
χ312-22-22i−2i2i−2i02202-2-22-2-22i−2i2i−2i2i−2i2i−2i000000002-22i−2i0000-220000−2i2i2-2000000002i−2i0000000000000000
χ322-22-22i−2i2i−2i02202-2-22-2-22i−2i2i−2i2i−2i2i−2i00000000-22−2i2i0000-220000−2i2i-2200000000−2i2i0000000000000000
χ332-22-2−2i2i−2i2i02202-2-22-2-2−2i2i−2i2i−2i2i−2i2i0000000000002-2−2i2i2-20000−2i2i0000002-2−2i2i000000000000000000
χ342-22-2−2i2i−2i2i02202-2-22-2-2−2i2i−2i2i−2i2i−2i2i000000000000-222i−2i2-20000−2i2i000000-222i−2i000000000000000000
χ352-22-2−2i2i−2i2i02202-2-22-2-2−2i2i−2i2i−2i2i−2i2i000000002-2−2i2i0000-2200002i−2i2-200000000−2i2i0000000000000000
χ362-22-2−2i2i−2i2i02202-2-22-2-2−2i2i−2i2i−2i2i−2i2i00000000-222i−2i0000-2200002i−2i-22000000002i−2i0000000000000000
χ374444444441-24111-2-2-2-2-2-2-2111111-2-211-2-20000000000000000002222000000-1-1-1-1-1-1-1-100000000
χ384444444441-24111-2-2-2-2-2-2-2111111-2-211-2-2000000000000000000-2-2-2-20000001111111100000000
χ39444444444-214-2-2-21111111-2-2-2-2-2-211-2-2112222222200000000-1-10000-1-1-1-1-1-10000000000000000
χ40444444444-214-2-2-21111111-2-2-2-2-2-211-2-211-2-2-2-2-2-2-2-2000000001100001111110000000000000000
χ4144444444-41-2-4111-2-2-2-2-2-2-21111-1-122-1-12200000000000000000022-2-2000000-1-1-1-1111100000000
χ4244444444-41-2-4111-2-2-2-2-2-2-21111-1-122-1-122000000000000000000-2-2220000001111-1-1-1-100000000
χ4344444444-4-21-4-2-2-21111111-2-2-2-222-1-122-1-12222-2-2-2-200000000-1-100001111-1-10000000000000000
χ4444444444-4-21-4-2-2-21111111-2-2-2-222-1-122-1-1-2-2-2-2222200000000110000-1-1-1-1110000000000000000
χ454444-4-4-4-441-2-4111-2-2-22222-1-1-1-111-2-2-1-1220000000000000000002i−2i2i−2i000000−i−iii−i−iii00000000
χ464444-4-4-4-441-2-4111-2-2-22222-1-1-1-111-2-2-1-122000000000000000000−2i2i−2i2i000000ii−i−iii−i−i00000000
χ474444-4-4-4-44-21-4-2-2-2111-1-1-1-12222-2-21122-1-122-2-222-2-200000000-1-10000-1-111110000000000000000
χ484444-4-4-4-44-21-4-2-2-2111-1-1-1-12222-2-21122-1-1-2-222-2-2220000000011000011-1-1-1-10000000000000000
χ494444-4-4-4-4-41-24111-2-2-22222-1-1-1-1-1-12211-2-20000000000000000002i−2i−2i2i000000−i−iiiii−i−i00000000
χ504444-4-4-4-4-41-24111-2-2-22222-1-1-1-1-1-12211-2-2000000000000000000−2i2i2i−2i000000ii−i−i−i−iii00000000
χ514444-4-4-4-4-4-214-2-2-2111-1-1-1-1222222-1-1-2-21122-2-2-2-22200000000-1-1000011-1-1110000000000000000
χ524444-4-4-4-4-4-214-2-2-2111-1-1-1-1222222-1-1-2-211-2-22222-2-200000000110000-1-111-1-10000000000000000
χ534-44-44i−4i4i−4i0-210-2221-1-1i−ii−i−2i2i−2i2i003-3003i−3i2-22i−2i2-22i−2i00000000-110000-11−ii−ii0000000000000000
χ544-44-44i−4i4i−4i0-210-2221-1-1i−ii−i−2i2i−2i2i003-3003i−3i-22−2i2i-22−2i2i000000001-100001-1i−ii−i0000000000000000
χ554-44-44i−4i4i−4i0-210-2221-1-1i−ii−i−2i2i−2i2i00-3300−3i3i2-22i−2i-22−2i2i00000000-1100001-1i−i−ii0000000000000000
χ564-44-44i−4i4i−4i0-210-2221-1-1i−ii−i−2i2i−2i2i00-3300−3i3i-22−2i2i2-22i−2i000000001-10000-11−iii−i0000000000000000
χ574-44-4−4i4i−4i4i0-210-2221-1-1−ii−ii2i−2i2i−2i003-300−3i3i2-2−2i2i2-2−2i2i00000000-110000-11i−ii−i0000000000000000
χ584-44-4−4i4i−4i4i0-210-2221-1-1−ii−ii2i−2i2i−2i003-300−3i3i-222i−2i-222i−2i000000001-100001-1−ii−ii0000000000000000
χ594-44-4−4i4i−4i4i0-210-2221-1-1−ii−ii2i−2i2i−2i00-33003i−3i2-2−2i2i-222i−2i00000000-1100001-1−iii−i0000000000000000
χ604-44-4−4i4i−4i4i0-210-2221-1-1−ii−ii2i−2i2i−2i00-33003i−3i-222i−2i2-2−2i2i000000001-10000-11i−i−ii0000000000000000
χ614-4-444i−4i−4i4i01-20-11-12-22−2i2i2i−2ii−i−ii3-3003i−3i000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ624-4-444i−4i−4i4i01-20-11-12-22−2i2i2i−2ii−i−ii3-3003i−3i000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ634-4-444i−4i−4i4i01-20-11-12-22−2i2i2i−2ii−i−ii-3300−3i3i000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ644-4-444i−4i−4i4i01-20-11-12-22−2i2i2i−2ii−i−ii-3300−3i3i000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ654-4-444i−4i−4i4i0440-44-4-44-44i−4i−4i4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ664-4-44−4i4i4i−4i01-20-11-12-222i−2i−2i2i−iii−i3-300−3i3i000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ674-4-44−4i4i4i−4i01-20-11-12-222i−2i−2i2i−iii−i3-300−3i3i000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ684-4-44−4i4i4i−4i01-20-11-12-222i−2i−2i2i−iii−i-33003i−3i000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ694-4-44−4i4i4i−4i01-20-11-12-222i−2i−2i2i−iii−i-33003i−3i000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ704-4-44−4i4i4i−4i0440-44-4-44-4−4i4i4i−4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ7188-8-888-8-802-40-2-2244-4-4-44422-2-20000000000000000000000000000000000000000000000000000
χ7288-8-888-8-80-42044-4-2-2222-2-2-4-4440000000000000000000000000000000000000000000000000000
χ7388-8-8-8-88802-40-2-2244-444-4-4-2-2220000000000000000000000000000000000000000000000000000
χ7488-8-8-8-8880-42044-4-2-22-2-22244-4-40000000000000000000000000000000000000000000000000000
χ758-88-88i−8i8i−8i02-402-2-2-444−4i4i−4i4i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ768-88-8−8i8i−8i8i02-402-2-2-4444i−4i4i−4i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ778-8-888i−8i−8i8i0-4204-44-22-22i−2i−2i2i−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ788-8-88−8i8i8i−8i0-4204-44-22-2−2i2i2i−2i4i−4i−4i4i0000000000000000000000000000000000000000000000000000

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