Finite Group Databasebeta

← Group #11773910

Character table — Group #11773910

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444444444488888888121212121212121218181818181824242424242424242424242424242424242424243672727272
order122244443346666661212121212121212121212121212121222444444224444668888121212121212242424242424242448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111-1-111-1111111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111ii−i−i11-1-1-1-1iiii−i−i−i−i-1ii−i−i
χ6111111-1-111-1111111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111−i−iii11-1-1-1-1−i−i−i−iiiii-1−i−iii
χ7111111-1-111-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i-1-11111iiii−i−i−i−i-1−i−iii
χ8111111-1-111-1111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iii-1-11111−i−i−i−iiiii-1ii−i−i
χ91111-1-11111-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-111111-11-1-1-111-1-111-1-111-1-1-11-11-1
χ101111-1-11111-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-11111-11-11-1-111-1-1-1-111-1-111-1-11-11
χ111111-1-11111-111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-111-1-11-11-111-1-11111-1-111-1-1-1-11-11
χ121111-1-11111-111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-11-1111-1-111-1-111-1-111-11-11-1
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111i−i−ii-1-1-1-111ii−i−i−i−iii1i−i−ii
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111−iii−i-1-1-1-111−i−iiiii−i−i1−iii−i
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-1-1-1i−i−ii1111-1-1ii−i−i−i−iii1−iii−i
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1-1-1-1-1−iii−i1111-1-1−i−iiiii−i−i1i−i−ii
χ1722222222222222222222222222222222200000000-2-2-2-2-2-200000000000000000000-20000
χ18222222-2-222-2222222-2-22222-2-222-2-2-2-2-2-200000000-2-2-2-2220000000000000000000020000
χ192222-2-22222-222222222-2-2-2-222-2-2-2-222-2-200000000-2-222-2-20000000000000000000020000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-222-2-22200000000-2-2222200000000000000000000-20000
χ2122-2-2002i−2i2202-2-22-2-22i−2i00002i−2i00002i−2i00002-2002i−2i2-2002i−2i0000002-2002i−2i0000000000000
χ2222-2-2002i−2i2202-2-22-2-22i−2i00002i−2i00002i−2i0000-2200−2i2i2-2002i−2i000000-2200−2i2i0000000000000
χ2322-2-2002i−2i2202-2-22-2-22i−2i00002i−2i00002i−2i002-2002i−2i00-2200−2i2i2-20000002i−2i000000000000000
χ2422-2-2002i−2i2202-2-22-2-22i−2i00002i−2i00002i−2i00-2200−2i2i00-2200−2i2i-22000000−2i2i000000000000000
χ2522-2-200−2i2i2202-2-22-2-2−2i2i0000−2i2i0000−2i2i00002-200−2i2i2-200−2i2i0000002-200−2i2i0000000000000
χ2622-2-200−2i2i2202-2-22-2-2−2i2i0000−2i2i0000−2i2i0000-22002i−2i2-200−2i2i000000-22002i−2i0000000000000
χ2722-2-200−2i2i2202-2-22-2-2−2i2i0000−2i2i0000−2i2i002-200−2i2i00-22002i−2i2-2000000−2i2i000000000000000
χ2822-2-200−2i2i2202-2-22-2-2−2i2i0000−2i2i0000−2i2i00-22002i−2i00-22002i−2i-220000002i−2i000000000000000
χ29444444441-24111-2-2-211-2-2-2-2111111-2-2-2-200000000000000002222000000-1-1-1-1-1-1-1-100000
χ30444444441-24111-2-2-211-2-2-2-2111111-2-2-2-20000000000000000-2-2-2-20000001111111100000
χ3144444444-214-2-2-2111-2-21111-2-2-2-2-2-2111122222222000000-1-10000-1-1-1-1-1-10000000000000
χ3244444444-214-2-2-2111-2-21111-2-2-2-2-2-21111-2-2-2-2-2-2-2-20000001100001111110000000000000
χ33444444-4-41-2-4111-2-2-2-1-1-2-2-2-2-1-111-1-1222200000000000000002i2i−2i−2i000000−i−i−i−iiiii00000
χ34444444-4-41-2-4111-2-2-2-1-1-2-2-2-2-1-111-1-122220000000000000000−2i−2i2i2i000000iiii−i−i−i−i00000
χ35444444-4-4-21-4-2-2-211122111122-2-222-1-1-1-12222-2-2-2-2000000-1-10000-1-111110000000000000
χ36444444-4-4-21-4-2-2-211122111122-2-222-1-1-1-1-2-2-2-2222200000011000011-1-1-1-10000000000000
χ374444-4-4441-2-4111-2-2-211222211-1-1-1-1-2-22200000000000000002-22-2000000-1-111-1-11100000
χ384444-4-4441-2-4111-2-2-211222211-1-1-1-1-2-2220000000000000000-22-2200000011-1-111-1-100000
χ394444-4-444-21-4-2-2-2111-2-2-1-1-1-1-2-2222211-1-122-2-222-2-2000000-1-1000011-1-1110000000000000
χ404444-4-444-21-4-2-2-2111-2-2-1-1-1-1-2-2222211-1-1-2-222-2-222000000110000-1-111-1-10000000000000
χ414444-4-4-4-41-24111-2-2-2-1-12222-1-1-1-11122-2-200000000000000002i−2i−2i2i000000−i−iiiii−i−i00000
χ424444-4-4-4-41-24111-2-2-2-1-12222-1-1-1-11122-2-20000000000000000−2i2i2i−2i000000ii−i−i−i−iii00000
χ434444-4-4-4-4-214-2-2-211122-1-1-1-12222-2-2-1-11122-2-2-2-222000000-1-100001111-1-10000000000000
χ444444-4-4-4-4-214-2-2-211122-1-1-1-12222-2-2-1-111-2-22222-2-2000000110000-1-1-1-1110000000000000
χ4544-4-4004i−4i-210-2221-1-1−2i2i33-3-3−2i2i0000i−i3i−3i2-22-22i−2i2i−2i000000-110000-11−ii−ii0000000000000
χ4644-4-4004i−4i-210-2221-1-1−2i2i33-3-3−2i2i0000i−i3i−3i-22-22−2i2i−2i2i0000001-100001-1i−ii−i0000000000000
χ4744-4-4004i−4i-210-2221-1-1−2i2i-3-333−2i2i0000i−i−3i3i2-2-222i−2i−2i2i000000-1100001-1−iii−i0000000000000
χ4844-4-4004i−4i-210-2221-1-1−2i2i-3-333−2i2i0000i−i−3i3i-222-2−2i2i2i−2i0000001-10000-11i−i−ii0000000000000
χ4944-4-400−4i4i-210-2221-1-12i−2i33-3-32i−2i0000−ii−3i3i2-22-2−2i2i−2i2i000000-110000-11i−ii−i0000000000000
χ5044-4-400−4i4i-210-2221-1-12i−2i33-3-32i−2i0000−ii−3i3i-22-222i−2i2i−2i0000001-100001-1−ii−ii0000000000000
χ5144-4-400−4i4i-210-2221-1-12i−2i-3-3332i−2i0000−ii3i−3i2-2-22−2i2i2i−2i000000-1100001-1i−i−ii0000000000000
χ5244-4-400−4i4i-210-2221-1-12i−2i-3-3332i−2i0000−ii3i−3i-222-22i−2i−2i2i0000001-10000-11−iii−i0000000000000
χ534-44-40000440-44-4-44-4000000000000000000000000004i−4i000000000000000000000000000
χ544-44-40000440-44-4-44-400000000000000000000000000−4i4i000000000000000000000000000
χ554-4-444i−4i001-20-1-1122-23i−3i2i−2i2i−2i−3i3ii−i3-3000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000
χ564-4-444i−4i001-20-1-1122-23i−3i2i−2i2i−2i−3i3ii−i3-3000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000
χ574-4-444i−4i001-20-1-1122-2−3i3i2i−2i2i−2i3i−3ii−i-33000000000000000000000000000000ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300000
χ584-4-444i−4i001-20-1-1122-2−3i3i2i−2i2i−2i3i−3ii−i-33000000000000000000000000000000−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300000
χ594-4-444i−4i00440-4-44-4-4400−4i4i−4i4i004i−4i000000000000000000000000000000000000000000000
χ604-4-44−4i4i001-20-1-1122-23i−3i−2i2i−2i2i−3i3i−ii-33000000000000000000000000000000−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300000
χ614-4-44−4i4i001-20-1-1122-23i−3i−2i2i−2i2i−3i3i−ii-33000000000000000000000000000000ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300000
χ624-4-44−4i4i001-20-1-1122-2−3i3i−2i2i−2i2i3i−3i−ii3-3000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000
χ634-4-44−4i4i001-20-1-1122-2−3i3i−2i2i−2i2i3i−3i−ii3-3000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000
χ644-4-44−4i4i00440-4-44-4-44004i−4i4i−4i00−4i4i000000000000000000000000000000000000000000000
χ6588-8-8008i−8i2-402-2-2-4442i−2i00002i−2i0000−4i4i00000000000000000000000000000000000000000
χ6688-8-800−8i8i2-402-2-2-444−2i2i0000−2i2i00004i−4i00000000000000000000000000000000000000000
χ678-88-800002-40-22-24-44660000-6-600000000000000000000000000000000000000000000000
χ688-88-800002-40-22-24-44-6-600006600000000000000000000000000000000000000000000000
χ698-88-80000-4204-44-22-2006i−6i−6i6i0000000000000000000000000000000000000000000000000
χ708-88-80000-4204-44-22-200−6i6i6i−6i0000000000000000000000000000000000000000000000000
χ718-8-888i−8i00-42044-4-2-2200−2i2i−2i2i00−4i4i000000000000000000000000000000000000000000000
χ728-8-88−8i8i00-42044-4-2-22002i−2i2i−2i004i−4i000000000000000000000000000000000000000000000

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