Finite Group Databasebeta

← Group #11771038

Character table — Group #11771038

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222224444444444444444888888881818181824242424242424242424242424242424242424242424242436363636363636363636
order1222224444336666661212121212121212666612121212444488888888242424242424242424242424242424242288888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ5111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-11111-1-1-1-1
χ6111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-1-1-11111
χ7111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1-1-11111
χ8111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-1-1-1
χ91111-1-111-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1i−ii−i11-1-111-1-1ii−i−iii−i−i1-1ii−i−iii−i−i
χ101111-1-111-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1−ii−ii11-1-111-1-1−i−iii−i−iii1-1−i−iii−i−iii
χ111111-1-111-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1-11-11i−ii−i-1-111-1-111ii−i−iii−i−i1-1−i−iii−i−iii
χ121111-1-111-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1-11-11−ii−ii-1-111-1-111−i−iii−i−iii1-1ii−i−iii−i−i
χ131111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1i−i−ii1-1-11ii−i−i−i−iii11-1-1-1-111-11−i−iiiii−i−i
χ141111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1i−i−ii-111-1ii−i−i−i−iii-1-11111-1-1-11ii−i−i−i−iii
χ151111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1−iii−i1-1-11−i−iiiii−i−i11-1-1-1-111-11ii−i−i−i−iii
χ161111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1−iii−i-111-1−i−iiiii−i−i-1-11111-1-1-11−i−iiiii−i−i
χ172222222222222222222222222222222222-2-2-2-2000000000000000000000000-2-200000000
χ18222222-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000002200000000
χ192222-2-222-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-222000000000000000000000000-2200000000
χ202222-2-2-2-22222222222-2-2-2-22222-2-2-2-2-2-222-2-2220000000000000000000000002-200000000
χ2122-2-22-22i−2i2i−2i2222-2-2-2-22i2i−2i−2i2i2i−2i−2i22-2-22i−2i2i−2i0000000000000000000000000000002−22−2−i2i2−i2i2
χ2222-2-22-22i−2i2i−2i2222-2-2-2-22i2i−2i−2i2i2i−2i−2i22-2-22i−2i2i−2i000000000000000000000000000000−22−22i2−i2i2−i2
χ2322-2-22-2−2i2i−2i2i2222-2-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i−2i2i0000000000000000000000000000002−22−2i2−i2i2−i2
χ2422-2-22-2−2i2i−2i2i2222-2-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-2−2i2i−2i2i000000000000000000000000000000−22−22−i2i2−i2i2
χ2522-2-2-222i−2i−2i2i2222-2-2-2-22i2i−2i−2i−2i−2i2i2i-2-2222i−2i−2i2i000000000000000000000000000000−i2i2i2−i2−222−2
χ2622-2-2-222i−2i−2i2i2222-2-2-2-22i2i−2i−2i−2i−2i2i2i-2-2222i−2i−2i2i000000000000000000000000000000i2−i2−i2i22−2−22
χ2722-2-2-22−2i2i2i−2i2222-2-2-2-2−2i−2i2i2i2i2i−2i−2i-2-222−2i2i2i−2i000000000000000000000000000000−i2i2i2−i22−2−22
χ2822-2-2-22−2i2i2i−2i2222-2-2-2-2−2i−2i2i2i2i2i−2i−2i-2-222−2i2i2i−2i000000000000000000000000000000i2−i2−i2i2−222−2
χ2944444444441-21-21-21-21111-2-2-2-21-21-2-2-211000022220000-1-1-1-1-1-1-1-1000000000000000000
χ3044444444441-21-21-21-21111-2-2-2-21-21-2-2-2110000-2-2-2-2000011111111000000000000000000
χ314444444444-21-21-21-21-2-2-2-21111-21-2111-2-200000000222200000000-1-1-1-1-1-1-1-10000000000
χ324444444444-21-21-21-21-2-2-2-21111-21-2111-2-200000000-2-2-2-200000000111111110000000000
χ33444444-4-4-4-41-21-21-21-2-1-1-1-122221-21-222-1-100002i2i−2i−2i0000−i−i−i−iiiii000000000000000000
χ34444444-4-4-4-41-21-21-21-2-1-1-1-122221-21-222-1-10000−2i−2i2i2i0000iiii−i−i−i−i000000000000000000
χ35444444-4-4-4-4-21-21-21-212222-1-1-1-1-21-21-1-122000000002i2i−2i−2i00000000−i−i−i−iiiii0000000000
χ36444444-4-4-4-4-21-21-21-212222-1-1-1-1-21-21-1-12200000000−2i−2i2i2i00000000iiii−i−i−i−i0000000000
χ374444-4-444-4-41-21-21-21-211112222-12-12-2-2-1-100002-22-20000-1-111-1-111000000000000000000
χ384444-4-444-4-41-21-21-21-211112222-12-12-2-2-1-10000-22-22000011-1-111-1-1000000000000000000
χ394444-4-444-4-4-21-21-21-21-2-2-2-2-1-1-1-12-12-11122000000002i−2i2i−2i00000000−i−iii−i−iii0000000000
χ404444-4-444-4-4-21-21-21-21-2-2-2-2-1-1-1-12-12-1112200000000−2i2i−2i2i00000000ii−i−iii−i−i0000000000
χ414444-4-4-4-4441-21-21-21-2-1-1-1-1-2-2-2-2-12-12221100002i−2i−2i2i0000−i−iiiii−i−i000000000000000000
χ424444-4-4-4-4441-21-21-21-2-1-1-1-1-2-2-2-2-12-1222110000−2i2i2i−2i0000ii−i−i−i−iii000000000000000000
χ434444-4-4-4-444-21-21-21-21222211112-12-1-1-1-2-2000000002-2-2200000000-1-11111-1-10000000000
χ444444-4-4-4-444-21-21-21-21222211112-12-1-1-1-2-200000000-222-20000000011-1-1-1-1110000000000
χ4544-4-44-44i−4i4i−4i1-21-2-12-12ii−i−i−2i−2i2i2i1-2-12−2i2ii−i000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ4644-4-44-44i−4i4i−4i1-21-2-12-12ii−i−i−2i−2i2i2i1-2-12−2i2ii−i000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ4744-4-44-44i−4i4i−4i-21-212-12-1−2i−2i2i2iii−i−i-212-1i−i−2i2i00000000000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000
χ4844-4-44-44i−4i4i−4i-21-212-12-1−2i−2i2i2iii−i−i-212-1i−i−2i2i00000000000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000
χ4944-4-44-4−4i4i−4i4i1-21-2-12-12−i−iii2i2i−2i−2i1-2-122i−2i−ii000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ5044-4-44-4−4i4i−4i4i1-21-2-12-12−i−iii2i2i−2i−2i1-2-122i−2i−ii000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ5144-4-44-4−4i4i−4i4i-21-212-12-12i2i−2i−2i−i−iii-212-1−ii2i−2i00000000000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000
χ5244-4-44-4−4i4i−4i4i-21-212-12-12i2i−2i−2i−i−iii-212-1−ii2i−2i00000000000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000
χ5344-4-4-444i−4i−4i4i1-21-2-12-12ii−i−i2i2i−2i−2i-121-2−2i2i−ii000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13000000000000000000
χ5444-4-4-444i−4i−4i4i1-21-2-12-12ii−i−i2i2i−2i−2i-121-2−2i2i−ii000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13000000000000000000
χ5544-4-4-444i−4i−4i4i-21-212-12-1−2i−2i2i2i−i−iii2-1-21i−i2i−2i00000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000
χ5644-4-4-444i−4i−4i4i-21-212-12-1−2i−2i2i2i−i−iii2-1-21i−i2i−2i00000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000
χ5744-4-4-44−4i4i4i−4i1-21-2-12-12−i−iii−2i−2i2i2i-121-22i−2ii−i000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23000000000000000000
χ5844-4-4-44−4i4i4i−4i1-21-2-12-12−i−iii−2i−2i2i2i-121-22i−2ii−i000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23000000000000000000
χ5944-4-4-44−4i4i4i−4i-21-212-12-12i2i−2i−2iii−i−i2-1-21−ii−2i2i00000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000
χ6044-4-4-44−4i4i4i−4i-21-212-12-12i2i−2i−2iii−i−i2-1-21−ii−2i2i00000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000
χ614-44-400000044-4-444-4-400000000000000004i−4i000000000000000000000000000000000000
χ624-44-400000044-4-444-4-40000000000000000−4i4i000000000000000000000000000000000000
χ634-4-4400000044-4-4-4-4440000000000000000004-40000000000000000000000000000000000
χ644-4-4400000044-4-4-4-444000000000000000000-440000000000000000000000000000000000
χ658-88-80000002-4-242-4-246i−6i6i−6i00000000000000000000000000000000000000000000000000
χ668-88-80000002-4-242-4-24−6i6i−6i6i00000000000000000000000000000000000000000000000000
χ678-88-8000000-424-2-424-200006i−6i6i−6i0000000000000000000000000000000000000000000000
χ688-88-8000000-424-2-424-20000−6i6i−6i6i0000000000000000000000000000000000000000000000
χ698-8-880000002-4-24-242-46-6-6600000000000000000000000000000000000000000000000000
χ708-8-880000002-4-24-242-4-666-600000000000000000000000000000000000000000000000000
χ718-8-88000000-424-24-2-4200006-6-660000000000000000000000000000000000000000000000
χ728-8-88000000-424-24-2-420000-666-60000000000000000000000000000000000000000000000

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