Finite Group Databasebeta

← Group #11775162

Character table — Group #11775162

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222224444444444444444888888881818181824242424242424242424242424242424242424242424242436363636363636363636
order1222444444336666661212121212121212121212121212121222442244666688881212121224242424242424244444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1
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
χ5111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11iiii−i−i−i−i
χ6111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11−i−i−i−iiiii
χ7111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i11−i−i−i−iiiii
χ8111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii11iiii−i−i−i−i
χ91111-1-111-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-1111-11-111-1-1i−ii−i11-1-1ii−i−iii−i−i1-1ii−i−iii−i−i
χ101111-1-111-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-1111-11-111-1-1−ii−ii11-1-1−i−iii−i−iii1-1−i−iii−i−iii
χ111111-1-111-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-111-11-11-1-111i−ii−i-1-111ii−i−iii−i−i1-1−i−iii−i−iii
χ121111-1-111-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-111-11-11-1-111−ii−ii-1-111−i−iii−i−iii1-1ii−i−iii−i−i
χ131111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-11-1-1111-1-11-1-11-1-11111-1-1-1-1111-111-1-1-1-111
χ141111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-11-1-1111-1-1-111-1-1-111-1-11111-1-11-1-1-11111-1-1
χ151111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-111-1-1-1111-1-1111-1-111-1-1-1-1111-1-1-11111-1-1
χ161111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-111-1-1-111-111-111-1-1-1-11111-1-11-111-1-1-1-111
χ172222222222222222222222222222222222-2-2-2-2000000000000000000000000-2-200000000
χ18222222-2-2-2-222222222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000-2-200000000
χ192222-2-222-2-222222222-2-22222-2-2-2-2-2-222-2-222-2-2000000000000000000000000-2200000000
χ202222-2-2-2-2222222222222-2-2-2-222-2-2-2-2-2-222-2-222000000000000000000000000-2200000000
χ2122-2-22-22i−2i2i−2i222-2-22-2-22i−2i2i2i−2i−2i2i−2i22-2-22i−2i2i−2i0000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i
χ2222-2-22-22i−2i2i−2i222-2-22-2-22i−2i2i2i−2i−2i2i−2i22-2-22i−2i2i−2i000000000000000000000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i
χ2322-2-22-2−2i2i−2i2i222-2-22-2-2−2i2i−2i−2i2i2i−2i2i22-2-2−2i2i−2i2i0000000000000000000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i
χ2422-2-22-2−2i2i−2i2i222-2-22-2-2−2i2i−2i−2i2i2i−2i2i22-2-2−2i2i−2i2i000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i
χ2522-2-2-222i−2i−2i2i222-2-22-2-2−2i2i2i2i−2i−2i−2i2i-2-2222i−2i−2i2i0000000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i
χ2622-2-2-222i−2i−2i2i222-2-22-2-2−2i2i2i2i−2i−2i−2i2i-2-2222i−2i−2i2i000000000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i
χ2722-2-2-22−2i2i2i−2i222-2-22-2-22i−2i−2i−2i2i2i2i−2i-2-222−2i2i2i−2i0000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i
χ2822-2-2-22−2i2i2i−2i222-2-22-2-22i−2i−2i−2i2i2i2i−2i-2-222−2i2i2i−2i000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i
χ2944444444441-2111-2-2-211-2-2-2-2111-21-211-2-200000000000022220000-1-1-1-1-1-1-1-10000000000
χ3044444444441-2111-2-2-211-2-2-2-2111-21-211-2-2000000000000-2-2-2-20000111111110000000000
χ314444444444-21-2-2-2111-2-21111-2-2-21-21-2-21100002222-1-1-1-10000-1-1-1-1000000000000000000
χ324444444444-21-2-2-2111-2-21111-2-2-21-21-2-2110000-2-2-2-2111100001111000000000000000000
χ33444444-4-4-4-41-2111-2-2-2-1-12222-1-11-21-2-1-1220000000000002i2i−2i−2i0000−i−i−i−iiiii0000000000
χ34444444-4-4-4-41-2111-2-2-2-1-12222-1-11-21-2-1-122000000000000−2i−2i2i2i0000iiii−i−i−i−i0000000000
χ35444444-4-4-4-4-21-2-2-211122-1-1-1-122-21-2122-1-1000022-2-2-1-1-1-100001111000000000000000000
χ36444444-4-4-4-4-21-2-2-211122-1-1-1-122-21-2122-1-10000-2-22211110000-1-1-1-1000000000000000000
χ374444-4-444-4-41-2111-2-2-2-1-1-2-2-2-2-1-1-12-1211220000000000002i−2i2i−2i0000−i−iii−i−iii0000000000
χ384444-4-444-4-41-2111-2-2-2-1-1-2-2-2-2-1-1-12-121122000000000000−2i2i−2i2i0000ii−i−iii−i−i0000000000
χ394444-4-444-4-4-21-2-2-2111221111222-12-1-2-2-1-100002-22-2-1-1110000-1-111000000000000000000
χ404444-4-444-4-4-21-2-2-2111221111222-12-1-2-2-1-10000-22-2211-1-1000011-1-1000000000000000000
χ414444-4-4-4-4441-2111-2-2-211222211-12-12-1-1-2-20000000000002-2-220000-1-11111-1-10000000000
χ424444-4-4-4-4441-2111-2-2-211222211-12-12-1-1-2-2000000000000-222-2000011-1-1-1-1110000000000
χ434444-4-4-4-444-21-2-2-2111-2-2-1-1-1-1-2-22-12-1221100002-2-22-1-111000011-1-1000000000000000000
χ444444-4-4-4-444-21-2-2-2111-2-2-1-1-1-1-2-22-12-122110000-222-211-1-10000-1-111000000000000000000
χ4544-4-44-44i−4i4i−4i1-21-1-1-222i−i−2i−2i2i2ii−i1-2-12i−i−2i2i00000000000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ130000000000
χ4644-4-44-44i−4i4i−4i1-21-1-1-222i−i−2i−2i2i2ii−i1-2-12i−i−2i2i00000000000000000000ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ130000000000
χ4744-4-44-44i−4i4i−4i-21-2221-1-1−2i2iii−i−i−2i2i-212-1−2i2ii−i00000000−i3i3−i3i300003−33−3000000000000000000
χ4844-4-44-44i−4i4i−4i-21-2221-1-1−2i2iii−i−i−2i2i-212-1−2i2ii−i00000000i3−i3i3−i30000−33−33000000000000000000
χ4944-4-44-4−4i4i−4i4i1-21-1-1-222−ii2i2i−2i−2i−ii1-2-12−ii2i−2i00000000000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ230000000000
χ5044-4-44-4−4i4i−4i4i1-21-1-1-222−ii2i2i−2i−2i−ii1-2-12−ii2i−2i00000000000000000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ230000000000
χ5144-4-44-4−4i4i−4i4i-21-2221-1-12i−2i−i−iii2i−2i-212-12i−2i−ii00000000−i3i3−i3i30000−33−33000000000000000000
χ5244-4-44-4−4i4i−4i4i-21-2221-1-12i−2i−i−iii2i−2i-212-12i−2i−ii00000000i3−i3i3−i300003−33−3000000000000000000
χ5344-4-4-444i−4i−4i4i1-21-1-1-222−ii−2i−2i2i2i−ii-121-2i−i2i−2i00000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000
χ5444-4-4-444i−4i−4i4i1-21-1-1-222−ii−2i−2i2i2i−ii-121-2i−i2i−2i00000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000
χ5544-4-4-444i−4i−4i4i-21-2221-1-12i−2iii−i−i2i−2i2-1-21−2i2i−ii00000000−i3i3i3−i300003−3−33000000000000000000
χ5644-4-4-444i−4i−4i4i-21-2221-1-12i−2iii−i−i2i−2i2-1-21−2i2i−ii00000000i3−i3−i3i30000−333−3000000000000000000
χ5744-4-4-44−4i4i4i−4i1-21-1-1-222i−i2i2i−2i−2ii−i-121-2−ii−2i2i00000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000
χ5844-4-4-44−4i4i4i−4i1-21-1-1-222i−i2i2i−2i−2ii−i-121-2−ii−2i2i00000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000
χ5944-4-4-44−4i4i4i−4i-21-2221-1-1−2i2i−i−iii−2i2i2-1-212i−2ii−i00000000−i3i3i3−i30000−333−3000000000000000000
χ6044-4-4-44−4i4i4i−4i-21-2221-1-1−2i2i−i−iii−2i2i2-1-212i−2ii−i00000000i3−i3−i3i300003−3−33000000000000000000
χ614-44-400000044-44-4-44-40000000000000000004i−4i0000000000000000000000000000000000
χ624-44-400000044-44-4-44-4000000000000000000−4i4i0000000000000000000000000000000000
χ634-4-4400000044-4-44-4-4400000000000000004-4000000000000000000000000000000000000
χ644-4-4400000044-4-44-4-440000000000000000-44000000000000000000000000000000000000
χ658-88-80000002-4-22-24-44660000-6-60000000000000000000000000000000000000000000000
χ668-88-80000002-4-22-24-44-6-60000660000000000000000000000000000000000000000000000
χ678-88-8000000-424-44-22-2006i−6i6i−6i000000000000000000000000000000000000000000000000
χ688-88-8000000-424-44-22-200−6i6i−6i6i000000000000000000000000000000000000000000000000
χ698-8-880000002-4-2-2244-46i−6i0000−6i6i0000000000000000000000000000000000000000000000
χ708-8-880000002-4-2-2244-4−6i6i00006i−6i0000000000000000000000000000000000000000000000
χ718-8-88000000-4244-4-2-22006-6-66000000000000000000000000000000000000000000000000
χ728-8-88000000-4244-4-2-2200-666-6000000000000000000000000000000000000000000000000

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