Finite Group Databasebeta

← Group #11775916

Character table — Group #11775916

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222224444444444444444888888881818181824242424242424242424242424242424242424242424242436363636363636363636
order12224444443366666612121212121212121212121212121212224444448888121212121212121224242424242424244488888888
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
χ5111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-1iiii−i−i−i−i
χ6111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-1−i−i−i−iiiii
χ7111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-1−i−i−i−iiiii
χ8111111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-1iiii−i−i−i−i
χ91111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1i−ii−i11-1-111-1-1ii−i−iii−i−i11ii−i−iii−i−i
χ101111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1−ii−ii11-1-111-1-1−i−iii−i−iii11−i−iii−i−iii
χ111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-11i−ii−i-1-111-1-111ii−i−iii−i−i11−i−iii−i−iii
χ121111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11-11−ii−ii-1-111-1-111−i−iii−i−iii11ii−i−iii−i−i
χ131111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1-111-1-1111-1-1-1-11111-1-1-1-1111-111-1-1-1-111
χ141111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-1111-1-11-111-111-1-1-1-111-1-11111-1-11-1-1-11111-1-1
χ151111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-111-111-11-1-11-1-11111-1-111-1-1-1-1111-1-1-11111-1-1
χ161111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-111-1-111-111-1-111-1-1-11111-1-1-1-11111-1-11-111-1-1-1-111
χ172222222222222222222222222222222222-2-2-2-2000000000000000000000000-2-200000000
χ18222222-2-2-2-2222222222222-2-2-2-222-2-2-2-2-2-2-2-222000000000000000000000000-2200000000
χ192222-2-222-2-222222222-2-2-2-2-2-2-2-2-2-22222-2-22222000000000000000000000000-2-200000000
χ202222-2-2-2-22222222222-2-2-2-22222-2-2-2-2-2-22222-2-2000000000000000000000000-2200000000
χ212-22-22i−2i2-22i−2i222-2-2-22-22i2i−2i−2i2i−2i2i−2i2i−2i2-22-22i−2i0000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ222-22-22i−2i2-22i−2i222-2-2-22-22i2i−2i−2i2i−2i2i−2i2i−2i2-22-22i−2i000000000000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ232-22-22i−2i-22−2i2i222-2-2-22-22i2i−2i−2i−2i2i−2i2i2i−2i-22-22−2i2i0000000000000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i
χ242-22-22i−2i-22−2i2i222-2-2-22-22i2i−2i−2i−2i2i−2i2i2i−2i-22-22−2i2i000000000000000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i
χ252-22-2−2i2i2-2−2i2i222-2-2-22-2−2i−2i2i2i−2i2i−2i2i−2i2i2-22-2−2i2i0000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ262-22-2−2i2i2-2−2i2i222-2-2-22-2−2i−2i2i2i−2i2i−2i2i−2i2i2-22-2−2i2i000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ272-22-2−2i2i-222i−2i222-2-2-22-2−2i−2i2i2i2i−2i2i−2i−2i2i-22-222i−2i0000000000000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i
χ282-22-2−2i2i-222i−2i222-2-2-22-2−2i−2i2i2i2i−2i2i−2i−2i2i-22-222i−2i000000000000000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i
χ2944444444441-2111-2-2-2-2-2-2-211111111-2-2-2-200000000222200000000-1-1-1-1-1-1-1-10000000000
χ3044444444441-2111-2-2-2-2-2-2-211111111-2-2-2-200000000-2-2-2-200000000111111110000000000
χ314444444444-21-2-2-21111111-2-2-2-2-2-2-2-21111000022220000-1-1-1-1-1-1-1-1000000000000000000
χ324444444444-21-2-2-21111111-2-2-2-2-2-2-2-211110000-2-2-2-2000011111111000000000000000000
χ33444444-4-4-4-41-2111-2-2-2-2-2-2-2-1-1-1-111-1-12222000000002i2i−2i−2i00000000−i−i−i−iiiii0000000000
χ34444444-4-4-4-41-2111-2-2-2-2-2-2-2-1-1-1-111-1-1222200000000−2i−2i2i2i00000000iiii−i−i−i−i0000000000
χ35444444-4-4-4-4-21-2-2-211111112222-2-222-1-1-1-1000022-2-20000-1-1-1-11111000000000000000000
χ36444444-4-4-4-4-21-2-2-211111112222-2-222-1-1-1-10000-2-22200001111-1-1-1-1000000000000000000
χ374444-4-444-4-41-2111-2-2-22222-1-1-1-1-1-111-2-222000000002i−2i2i−2i00000000−i−iii−i−iii0000000000
χ384444-4-444-4-41-2111-2-2-22222-1-1-1-1-1-111-2-22200000000−2i2i−2i2i00000000ii−i−iii−i−i0000000000
χ394444-4-444-4-4-21-2-2-2111-1-1-1-1222222-2-211-1-100002-22-20000-1-111-1-111000000000000000000
χ404444-4-444-4-4-21-2-2-2111-1-1-1-1222222-2-211-1-10000-22-22000011-1-111-1-1000000000000000000
χ414444-4-4-4-4441-2111-2-2-222221111-1-1-1-122-2-2000000002-2-2200000000-1-11111-1-10000000000
χ424444-4-4-4-4441-2111-2-2-222221111-1-1-1-122-2-200000000-222-20000000011-1-1-1-1110000000000
χ434444-4-4-4-444-21-2-2-2111-1-1-1-1-2-2-2-22222-1-11100002-2-220000-1-11111-1-1000000000000000000
χ444444-4-4-4-444-21-2-2-2111-1-1-1-1-2-2-2-22222-1-1110000-222-2000011-1-1-1-111000000000000000000
χ4544-4-400000044-44-44-4-400000000000000004-4000000000000000000000000000000000000
χ4644-4-400000044-44-44-4-40000000000000000-44000000000000000000000000000000000000
χ474-44-44i−4i4-44i−4i1-21-1-12-22−2i−2i2i2ii−ii−ii−i1-1-22−2i2i00000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
χ484-44-44i−4i4-44i−4i1-21-1-12-22−2i−2i2i2ii−ii−ii−i1-1-22−2i2i00000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000
χ494-44-44i−4i4-44i−4i-21-222-11-1ii−i−i−2i2i−2i2i−2i2i-221-1i−i000000000000−i3i33−3−i3i33−3000000000000000000
χ504-44-44i−4i4-44i−4i-21-222-11-1ii−i−i−2i2i−2i2i−2i2i-221-1i−i000000000000i3−i3−33i3−i3−33000000000000000000
χ514-44-44i−4i-44−4i4i1-21-1-12-22−2i−2i2i2i−ii−iii−i-112-22i−2i00000000000000000000ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000
χ524-44-44i−4i-44−4i4i1-21-1-12-22−2i−2i2i2i−ii−iii−i-112-22i−2i00000000000000000000−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000
χ534-44-44i−4i-44−4i4i-21-222-11-1ii−i−i2i−2i2i−2i−2i2i2-2-11−ii000000000000−i3i33−3i3−i3−33000000000000000000
χ544-44-44i−4i-44−4i4i-21-222-11-1ii−i−i2i−2i2i−2i−2i2i2-2-11−ii000000000000i3−i3−33−i3i33−3000000000000000000
χ554-44-4−4i4i4-4−4i4i1-21-1-12-222i2i−2i−2i−ii−ii−ii1-1-222i−2i00000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000
χ564-44-4−4i4i4-4−4i4i1-21-1-12-222i2i−2i−2i−ii−ii−ii1-1-222i−2i00000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000
χ574-44-4−4i4i4-4−4i4i-21-222-11-1−i−iii2i−2i2i−2i2i−2i-221-1−ii000000000000−i3i3−33−i3i3−33000000000000000000
χ584-44-4−4i4i4-4−4i4i-21-222-11-1−i−iii2i−2i2i−2i2i−2i-221-1−ii000000000000i3−i33−3i3−i33−3000000000000000000
χ594-44-4−4i4i-444i−4i1-21-1-12-222i2i−2i−2ii−ii−i−ii-112-2−2i2i00000000000000000000−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000
χ604-44-4−4i4i-444i−4i1-21-1-12-222i2i−2i−2ii−ii−i−ii-112-2−2i2i00000000000000000000ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000
χ614-44-4−4i4i-444i−4i-21-222-11-1−i−iii−2i2i−2i2i2i−2i2-2-11i−i000000000000−i3i3−33i3−i33−3000000000000000000
χ624-44-4−4i4i-444i−4i-21-222-11-1−i−iii−2i2i−2i2i2i−2i2-2-11i−i000000000000i3−i33−3−i3i3−33000000000000000000
χ634-4-4400000044-4-44-4-440000000000000000004i−4i0000000000000000000000000000000000
χ644-4-4400000044-4-44-4-44000000000000000000−4i4i0000000000000000000000000000000000
χ6588-8-80000002-4-22-2-44400006i−6i−6i6i0000000000000000000000000000000000000000000000
χ6688-8-80000002-4-22-2-4440000−6i6i6i−6i0000000000000000000000000000000000000000000000
χ6788-8-8000000-424-442-2-26-66-600000000000000000000000000000000000000000000000000
χ6888-8-8000000-424-442-2-2-66-6600000000000000000000000000000000000000000000000000
χ698-8-880000002-4-2-2244-4000066-6-60000000000000000000000000000000000000000000000
χ708-8-880000002-4-2-2244-40000-6-6660000000000000000000000000000000000000000000000
χ718-8-88000000-4244-4-2-226i−6i−6i6i00000000000000000000000000000000000000000000000000
χ728-8-88000000-4244-4-2-22−6i6i6i−6i00000000000000000000000000000000000000000000000000

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