Finite Group Databasebeta

← Group #11771632

Character table — Group #11771632

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222224444444444444444888888881818181824242424242424242424242424242424242424242424242436363636363636363636
order1222444444336666661212121212121212121212121212121288884444888812121212121212122424242424242424881616161616161616
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
χ51111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11iiii−i−i−i−i
χ61111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11−i−i−i−iiiii
χ71111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11−i−i−i−iiiii
χ81111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11iiii−i−i−i−i
χ91-11-1i−ii−i1-1111-1-1-11-1iii−i−i−ii−i1-1i−i1-1i−iii−i−i1-1i−iζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ1311-1-1ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-1ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ101-11-1i−ii−i1-1111-1-1-11-1iii−i−i−ii−i1-1i−i1-1i−iii−i−i1-1i−i−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ1311-1-1ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-1−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ111-11-1i−ii−i1-1111-1-1-11-1iii−i−i−ii−i1-1i−i1-1i−iii−i−i-11−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13-1-111−i−iiiζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-1−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ121-11-1i−ii−i1-1111-1-1-11-1iii−i−i−ii−i1-1i−i1-1i−iii−i−i-11−ii−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13-1-111−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-1ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ131-11-1−ii−ii1-1111-1-1-11-1−i−i−iiii−ii1-1−ii1-1−ii−i−iii1-1−ii−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ2311-1-1−i−iii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-1−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ141-11-1−ii−ii1-1111-1-1-11-1−i−i−iiii−ii1-1−ii1-1−ii−i−iii1-1−iiζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ2311-1-1−i−iiiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-1ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ151-11-1−ii−ii1-1111-1-1-11-1−i−i−iiii−ii1-1−ii1-1−ii−i−iii-11i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23-1-111ii−i−i−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-1ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ161-11-1−ii−ii1-1111-1-1-11-1−i−i−iiii−ii1-1−ii1-1−ii−i−iii-11i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23-1-111ii−i−iζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-1−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ172222222222222222222222222222222222-2-2-2-2000000000000000000000000-2-200000000
χ18222222-2-2-2-22222222222-222-2-2-2-2-222-2-2-2-2000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ19222222-2-2-2-22222222222-222-2-2-2-2-222-2-2-2-2000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ202222-2-222-2-222222222-2-22-2-2222-2-2-2-2-2-2220000000000000000000000000000002−22−2−22−22
χ212222-2-222-2-222222222-2-22-2-2222-2-2-2-2-2-222000000000000000000000000000000−22−222−22−2
χ222222-2-2-2-22222222222-2-2-2-2-2-2-2-222-2-222-2-22222000000000000000000000000-2-200000000
χ232-22-22i−2i2i−2i2-2222-2-2-22-22i2i2i−2i−2i−2i2i−2i2-22i−2i2-22i−2i−2i−2i2i2i000000000000000000000000-2200000000
χ242-22-22i−2i−2i2i-22222-2-2-22-22i2i−2i−2i−2i2i−2i2i-222i−2i-22−2i2i0000000000000000000000000000001−i−1+i−1+i1−i−1−i1+i1+i−1−i
χ252-22-22i−2i−2i2i-22222-2-2-22-22i2i−2i−2i−2i2i−2i2i-222i−2i-22−2i2i000000000000000000000000000000−1+i1−i1−i−1+i1+i−1−i−1−i1+i
χ262-22-2−2i2i2i−2i-22222-2-2-22-2−2i−2i2i2i2i−2i2i−2i-22−2i2i-222i−2i0000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i
χ272-22-2−2i2i2i−2i-22222-2-2-22-2−2i−2i2i2i2i−2i2i−2i-22−2i2i-222i−2i000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i
χ282-22-2−2i2i−2i2i2-2222-2-2-22-2−2i−2i−2i2i2i2i−2i2i2-2−2i2i2-2−2i2i2i2i−2i−2i000000000000000000000000-2200000000
χ2944444444441-2111-2-2-2-2-21-2-21111111-2-2-2-200000000222200000000-1-1-1-1-1-1-1-10000000000
χ3044444444441-2111-2-2-2-2-21-2-21111111-2-2-2-200000000-2-2-2-200000000111111110000000000
χ314444444444-21-2-2-211111-211-2-2-2-2-2-2-21111000022220000-1-1-1-1-1-1-1-1000000000000000000
χ324444444444-21-2-2-211111-211-2-2-2-2-2-2-211110000-2-2-2-2000011111111000000000000000000
χ33444444-4-4-4-41-2111-2-2-2-2-2-1-2-2-1-1-1-1-1112222000000000000000000003−33−33−33−30000000000
χ34444444-4-4-4-41-2111-2-2-2-2-2-1-2-2-1-1-1-1-111222200000000000000000000−33−33−33−330000000000
χ35444444-4-4-4-4-21-2-2-21111121122222-2-2-1-1-1-1000000000000−i3i3−i3i3−i3i3−i3i3000000000000000000
χ36444444-4-4-4-4-21-2-2-21111121122222-2-2-1-1-1-1000000000000i3−i3i3−i3i3−i3i3−i3000000000000000000
χ374444-4-444-4-41-2111-2-2-222122111-1-1-1-122-2-200000000000000000000−i3i3−i3i3i3−i3i3−i30000000000
χ384444-4-444-4-41-2111-2-2-222122111-1-1-1-122-2-200000000000000000000i3−i3i3−i3−i3i3−i3i30000000000
χ394444-4-444-4-4-21-2-2-2111-1-1-2-1-1-2-2-22222-1-111000000000000−i3i3−i3i3i3−i3i3−i3000000000000000000
χ404444-4-444-4-4-21-2-2-2111-1-1-2-1-1-2-2-22222-1-111000000000000i3−i3i3−i3−i3i3−i3i3000000000000000000
χ414444-4-4-4-4441-2111-2-2-222-122-1-1-111-1-1-2-222000000002i2i−2i−2i00000000−i−i−i−iiiii0000000000
χ424444-4-4-4-4441-2111-2-2-222-122-1-1-111-1-1-2-22200000000−2i−2i2i2i00000000iiii−i−i−i−i0000000000
χ434444-4-4-4-444-21-2-2-2111-1-12-1-1222-2-22211-1-1000022-2-20000-1-1-1-11111000000000000000000
χ444444-4-4-4-444-21-2-2-2111-1-12-1-1222-2-22211-1-10000-2-22200001111-1-1-1-1000000000000000000
χ4544-4-400000044-44-44-4-4000000000000000022−2222−220000000000000000000000000000000000
χ4644-4-400000044-44-44-4-40000000000000000−2222−22220000000000000000000000000000000000
χ474-44-44i−4i4i−4i4-41-21-1-12-22−2i−2ii2i2i−ii−i1-1i−i-22−2i2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ130000000000
χ484-44-44i−4i4i−4i4-41-21-1-12-22−2i−2ii2i2i−ii−i1-1i−i-22−2i2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ130000000000
χ494-44-44i−4i4i−4i4-4-21-222-11-1ii−2i−i−i2i−2i2i-22−2i2i1-1i−i00002-22i−2i0000-1-111−i−iii000000000000000000
χ504-44-44i−4i4i−4i4-4-21-222-11-1ii−2i−i−i2i−2i2i-22−2i2i1-1i−i0000-22−2i2i000011-1-1ii−i−i000000000000000000
χ514-44-44i−4i−4i4i-441-21-1-12-22−2i−2i−i2i2ii−ii-11i−i2-22i−2i00000000000000000000ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ230000000000
χ524-44-44i−4i−4i4i-441-21-1-12-22−2i−2i−i2i2ii−ii-11i−i2-22i−2i00000000000000000000−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ230000000000
χ534-44-44i−4i−4i4i-44-21-222-11-1ii2i−i−i−2i2i−2i2-2−2i2i-11−ii000000000000−i3i3i3−i33−3−33000000000000000000
χ544-44-44i−4i−4i4i-44-21-222-11-1ii2i−i−i−2i2i−2i2-2−2i2i-11−ii000000000000i3−i3−i3i3−333−3000000000000000000
χ554-44-4−4i4i4i−4i-441-21-1-12-222i2ii−2i−2i−ii−i-11−ii2-2−2i2i00000000000000000000−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ130000000000
χ564-44-4−4i4i4i−4i-441-21-1-12-222i2ii−2i−2i−ii−i-11−ii2-2−2i2i00000000000000000000ζ7−ζ23−ζ7+ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ130000000000
χ574-44-4−4i4i4i−4i-44-21-222-11-1−i−i−2iii2i−2i2i2-22i−2i-11i−i000000000000−i3i3i3−i3−333−3000000000000000000
χ584-44-4−4i4i4i−4i-44-21-222-11-1−i−i−2iii2i−2i2i2-22i−2i-11i−i000000000000i3−i3−i3i33−3−33000000000000000000
χ594-44-4−4i4i−4i4i4-41-21-1-12-222i2i−i−2i−2ii−ii1-1−ii-222i−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ230000000000
χ604-44-4−4i4i−4i4i4-41-21-1-12-222i2i−i−2i−2ii−ii1-1−ii-222i−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ230000000000
χ614-44-4−4i4i−4i4i4-4-21-222-11-1−i−i2iii−2i2i−2i-222i−2i1-1−ii00002-2−2i2i0000-1-111ii−i−i000000000000000000
χ624-44-4−4i4i−4i4i4-4-21-222-11-1−i−i2iii−2i2i−2i-222i−2i1-1−ii0000-222i−2i000011-1-1−i−iii000000000000000000
χ634-4-4400000044-4-44-4-440000000000000000−2i22i22i2−2i20000000000000000000000000000000000
χ644-4-4400000044-4-44-4-4400000000000000002i2−2i2−2i22i20000000000000000000000000000000000
χ6588-8-80000002-4-22-2-444006i00−6i−6i6i0000000000000000000000000000000000000000000000
χ6688-8-80000002-4-22-2-44400−6i006i6i−6i0000000000000000000000000000000000000000000000
χ6788-8-8000000-424-442-2-26-606-60000000000000000000000000000000000000000000000000
χ6888-8-8000000-424-442-2-2-660-660000000000000000000000000000000000000000000000000
χ698-8-880000002-4-2-2244-4006006-6-60000000000000000000000000000000000000000000000
χ708-8-880000002-4-2-2244-400-600-6660000000000000000000000000000000000000000000000
χ718-8-88000000-4244-4-2-226i−6i0−6i6i0000000000000000000000000000000000000000000000000
χ728-8-88000000-4244-4-2-22−6i6i06i−6i0000000000000000000000000000000000000000000000000

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