Finite Group Databasebeta

← Group #11770926

Character table — Group #11770926

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122224444444444444444488888888121212121212121218181818181824242424242424242424242424242424242424243672727272
order12224444334666666121212121212121212121212121212128888888822444488882424242424242424242424242424242444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1
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
χ511111-1-1111-111111111-1-111-1-111-1-1-1-1-1-1iiii−i−i−i−i-1-111-1-111-1-1iiii−i−i−i−i1111-1-1-1-11ii−i−i
χ611111-1-1111-111111111-1-111-1-111-1-1-1-1-1-1iiii−i−i−i−i-1-111-1-1-1-111iiii−i−i−i−i-1-1-1-111111−i−iii
χ711111-1-1111-111111111-1-111-1-111-1-1-1-1-1-1−i−i−i−iiiii-1-111-1-111-1-1−i−i−i−iiiii1111-1-1-1-11−i−iii
χ811111-1-1111-111111111-1-111-1-111-1-1-1-1-1-1−i−i−i−iiiii-1-111-1-1-1-111−i−i−i−iiiii-1-1-1-111111ii−i−i
χ91111-111-111-1111111-1-111-1-111-1-111-1-1-1-111-1-111-1-1-1-11111i−ii−i11-1-111-1-1ii−i−iii−i−i-1i−ii−i
χ101111-111-111-1111111-1-111-1-111-1-111-1-1-1-111-1-111-1-1-1-11111−ii−ii11-1-111-1-1−i−iii−i−iii-1−ii−ii
χ111111-111-111-1111111-1-111-1-111-1-111-1-1-1-1-1-111-1-111-1-11111i−ii−i-1-111-1-111ii−i−iii−i−i-1−ii−ii
χ121111-111-111-1111111-1-111-1-111-1-111-1-1-1-1-1-111-1-111-1-11111−ii−ii-1-111-1-111−i−iii−i−iii-1i−ii−i
χ131111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii1111-1-1i−i−iiii−i−i−i−iiiii−i−i−i−iii-1-111-1
χ141111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii1111-1-1−iii−iii−i−i−i−iii−i−iiiii−i−i-11-1-11
χ151111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i1111-1-1i−i−ii−i−iiiii−i−iii−i−i−i−iii-11-1-11
χ161111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i1111-1-1−iii−i−i−iiiii−i−i−i−iiiii−i−i-1-111-1
χ1722222222222222222222222222222222200000000-2-2-2-2-2-200000000000000000000-20000
χ1822222-2-2222-222222222-2-222-2-222-2-2-2-2-2-20000000022-2-22200000000000000000000-20000
χ192222-222-222-2222222-2-222-2-222-2-222-2-2-2-20000000022-2-2-2-20000000000000000000020000
χ202222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2222200000000-2-2-2-2220000000000000000000020000
χ2122-2-2200-222022-2-2-2-22200-2-2002-20000002−22−22−22−22-2002-200002−22−22−22−20000000000000
χ2222-2-2200-222022-2-2-2-22200-2-2002-2000000−i2i2−i2i2i2−i2i2−i2-2200-220000−i2i2−i2i2i2−i2i2−i20000000000000
χ2322-2-2200-222022-2-2-2-22200-2-2002-2000000i2−i2i2−i2−i2i2−i2i2-2200-220000i2−i2i2−i2−i2i2−i2i20000000000000
χ2422-2-2200-222022-2-2-2-22200-2-2002-2000000−22−22−22−222-2002-20000−22−22−22−220000000000000
χ2522-2-2-200222022-2-2-2-2-2-2002200-220000002−2−222−2−22-22002-200002−2−222−2−220000000000000
χ2622-2-2-200222022-2-2-2-2-2-2002200-22000000−i2i2i2−i2i2−i2−i2i22-200-220000−i2i2i2−i2i2−i2−i2i20000000000000
χ2722-2-2-200222022-2-2-2-2-2-2002200-22000000i2−i2−i2i2−i2i2i2−i22-200-220000i2−i2−i2i2−i2i2i2−i20000000000000
χ2822-2-2-200222022-2-2-2-2-2-2002200-22000000−222−2−222−2-22002-20000−222−2−222−20000000000000
χ29444444441-241-211-2-211-2-211-2-2-2-21111-2-200000000000000222200000000-1-1-1-1-1-1-1-100000
χ30444444441-241-211-2-211-2-211-2-2-2-21111-2-200000000000000-2-2-2-2000000001111111100000
χ3144444444-214-21-2-211-2-211-2-21111-2-2-2-211222222220000000000-1-1-1-1-1-1-1-10000000000000
χ3244444444-214-21-2-211-2-211-2-21111-2-2-2-211-2-2-2-2-2-2-2-20000000000111111110000000000000
χ3344444-4-441-2-41-211-2-211221122-2-2-1-1-1-1220000000000000022-2-200000000-1-1-1-1111100000
χ3444444-4-441-2-41-211-2-211221122-2-2-1-1-1-12200000000000000-2-222000000001111-1-1-1-100000
χ3544444-4-44-21-4-21-2-211-2-2-1-1-2-2-1-1112222-1-12i2i2i2i−2i−2i−2i−2i0000000000−i−i−i−iiiii0000000000000
χ3644444-4-44-21-4-21-2-211-2-2-1-1-2-2-1-1112222-1-1−2i−2i−2i−2i2i2i2i2i0000000000iiii−i−i−i−i0000000000000
χ374444-444-41-2-41-211-2-2-1-1-2-2-1-1-2-22211-1-122000000000000002i−2i2i−2i00000000−i−iii−i−iii00000
χ384444-444-41-2-41-211-2-2-1-1-2-2-1-1-2-22211-1-12200000000000000−2i2i−2i2i00000000ii−i−iii−i−i00000
χ394444-444-4-21-4-21-2-21122112211-1-1-2-222-1-122-2-222-2-20000000000-1-111-1-1110000000000000
χ404444-444-4-21-4-21-2-21122112211-1-1-2-222-1-1-2-222-2-222000000000011-1-111-1-10000000000000
χ414444-4-4-4-41-241-211-2-2-1-122-1-12222-1-111-2-2000000000000002i−2i−2i2i00000000−i−iiiii−i−i00000
χ424444-4-4-4-41-241-211-2-2-1-122-1-12222-1-111-2-200000000000000−2i2i2i−2i00000000ii−i−i−i−iii00000
χ434444-4-4-4-4-214-21-2-21122-1-122-1-1-1-122-2-2112i2i−2i−2i−2i−2i2i2i0000000000−i−iiiii−i−i0000000000000
χ444444-4-4-4-4-214-21-2-21122-1-122-1-1-1-122-2-211−2i−2i2i2i2i2i−2i−2i0000000000ii−i−i−i−iii0000000000000
χ4544-4-4400-4-210-2122-1-1-2-23i−3i223i−3i1-100003i−3i2ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ130000000000000
χ4644-4-4400-4-210-2122-1-1-2-23i−3i223i−3i1-100003i−3i−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ130000000000000
χ4744-4-4400-4-210-2122-1-1-2-2−3i3i22−3i3i1-10000−3i3i−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ230000000000000
χ4844-4-4400-4-210-2122-1-1-2-2−3i3i22−3i3i1-10000−3i3i2ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ230000000000000
χ4944-4-4-4004-210-2122-1-1223i−3i-2-23i−3i-110000−3i3i2ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ130000000000−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ130000000000000
χ5044-4-4-4004-210-2122-1-1223i−3i-2-23i−3i-110000−3i3i−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ130000000000ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ130000000000000
χ5144-4-4-4004-210-2122-1-122−3i3i-2-2−3i3i-1100003i−3i−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ230000000000ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ230000000000000
χ5244-4-4-4004-210-2122-1-122−3i3i-2-2−3i3i-1100003i−3i2ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ230000000000−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ230000000000000
χ534-44-40000440-4-44-44-4000000000000000000000000004i−4i000000000000000000000000000
χ544-44-40000440-4-44-44-400000000000000000000000000−4i4i000000000000000000000000000
χ554-4-4404i−4i01-20-12-112-23i−3i2i−2i3i−3i−2i2i00i−i3-30000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000
χ564-4-4404i−4i01-20-12-112-23i−3i2i−2i3i−3i−2i2i00i−i3-30000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000
χ574-4-4404i−4i01-20-12-112-2−3i3i2i−2i−3i3i−2i2i00i−i-330000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000
χ584-4-4404i−4i01-20-12-112-2−3i3i2i−2i−3i3i−2i2i00i−i-330000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000
χ594-4-4404i−4i0440-4-4-44-4400−4i4i004i−4i004i−4i0000000000000000000000000000000000000000000
χ604-4-440−4i4i01-20-12-112-23i−3i−2i2i3i−3i2i−2i00−ii-330000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000
χ614-4-440−4i4i01-20-12-112-23i−3i−2i2i3i−3i2i−2i00−ii-330000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000
χ624-4-440−4i4i01-20-12-112-2−3i3i−2i2i−3i3i2i−2i00−ii3-30000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000
χ634-4-440−4i4i01-20-12-112-2−3i3i−2i2i−3i3i2i−2i00−ii3-30000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000
χ644-4-440−4i4i0440-4-4-44-44004i−4i00−4i4i00−4i4i0000000000000000000000000000000000000000000
χ6588-8-8800-82-402-4-2-2442200-2-200-44000000000000000000000000000000000000000000000
χ6688-8-8-80082-402-4-2-244-2-20022004-4000000000000000000000000000000000000000000000
χ678-88-800002-40-242-2-446i−6i00−6i6i0000000000000000000000000000000000000000000000000
χ688-88-800002-40-242-2-44−6i6i006i−6i0000000000000000000000000000000000000000000000000
χ698-88-80000-4204-2-442-2006600-6-600000000000000000000000000000000000000000000000
χ708-88-80000-4204-2-442-200-6-6006600000000000000000000000000000000000000000000000
χ718-8-8808i−8i0-4204-24-4-2200−2i2i002i−2i00−4i4i0000000000000000000000000000000000000000000
χ728-8-880−8i8i0-4204-24-4-22002i−2i00−2i2i004i−4i0000000000000000000000000000000000000000000

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