Finite Group Databasebeta

← Group #11777651

Character table — Group #11777651

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11111111222244444444444444444444444488881212121212121212121212121212121212121212121212121818181824242424242424242424242436363636363636363636
order12224444888833666666121212121212121224242424242424242424242422446666888812121212242424242424242444442466881212242424248888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ511111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ611111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-11111
χ711111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111
χ811111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11-1-11-111i−i-1-1ii−i−ii−i11-1-1ii−i−i
χ101111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i11-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11-1-1-11-1-1−ii11−i−iiii−i-1-111−i−iii
χ111111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii11-1-11-111i−i-1-1ii−i−ii−i-1-111−i−iii
χ121111-1-1-1-1ii−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii11-1-1-11-1-1−ii11−i−iiii−i11-1-1ii−i−i
χ131111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11-1-11-111−ii-1-1−i−iii−ii11-1-1−i−iii
χ141111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii11-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11-1-1-11-1-1i−i11ii−i−i−ii-1-111ii−i−i
χ151111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i11-1-11-111−ii-1-1−i−iii−ii-1-111ii−i−i
χ161111-1-1-1-1−i−iii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i11-1-1-11-1-1i−i11ii−i−i−ii11-1-1−i−iii
χ172222222222222222222222222222222222222222000000000000000000000000-2-2-2-2000000000000-2-200000000
χ1822222222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000-2-2-2-20000000000002200000000
χ192222-2-2-2-22i2i−2i−2i22222222-2-2-2-2-2-2-2-22i2i2i2i−2i−2i−2i−2i2i2i−2i−2i000000000000000000000000-2-222000000000000−2i2i00000000
χ202222-2-2-2-2−2i−2i2i2i22222222-2-2-2-2-2-2-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i000000000000000000000000-2-2220000000000002i−2i00000000
χ2122-2-22i−2i2i−2i00002222-2-2-2-22i−2i2i−2i2i−2i2i−2i000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132-22i−2i0000000000000000000000
χ2222-2-22i−2i2i−2i00002222-2-2-2-22i−2i2i−2i2i−2i2i−2i00000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ132-22i−2i0000000000000000000000
χ2322-2-22i−2i2i−2i00002222-2-2-2-22i−2i2i−2i2i−2i2i−2i0000000000002-22i−2i22-2-200002i2i−2i−2i00000000-22−2i2i0000000000000000000000
χ2422-2-22i−2i2i−2i00002222-2-2-2-22i−2i2i−2i2i−2i2i−2i000000000000-22−2i2i-2-2220000−2i−2i2i2i00000000-22−2i2i0000000000000000000000
χ2522-2-2−2i2i−2i2i00002222-2-2-2-2−2i2i−2i2i−2i2i−2i2i00000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ232-2−2i2i0000000000000000000000
χ2622-2-2−2i2i−2i2i00002222-2-2-2-2−2i2i−2i2i−2i2i−2i2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232-2−2i2i0000000000000000000000
χ2722-2-2−2i2i−2i2i00002222-2-2-2-2−2i2i−2i2i−2i2i−2i2i0000000000002-2−2i2i22-2-20000−2i−2i2i2i00000000-222i−2i0000000000000000000000
χ2822-2-2−2i2i−2i2i00002222-2-2-2-2−2i2i−2i2i−2i2i−2i2i000000000000-222i−2i-2-22200002i2i−2i−2i00000000-222i−2i0000000000000000000000
χ292-22-22i−2i−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1322-2-222-2-2−2i2i2i−2i−2i2i2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000000000000000002−2−i2i21+i−1−i1−i−1+i
χ302-22-22i−2i−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1322-2-222-2-2−2i2i2i−2i−2i2i2i−2i2ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000000000000000000000−22i2−i2−1−i1+i−1+i1−i
χ312-22-22i−2i−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1322-2-222-2-2−2i2i2i−2i−2i2i2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000000000000000002−2−i2i2−1−i1+i−1+i1−i
χ322-22-22i−2i−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1322-2-222-2-2−2i2i2i−2i−2i2i2i−2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000000000000000000000−22i2−i21+i−1−i1−i−1+i
χ332-22-2−2i2i2i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2322-2-222-2-22i−2i−2i2i2i−2i−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000000000000000002−2i2−i21−i−1+i1+i−1−i
χ342-22-2−2i2i2i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2322-2-222-2-22i−2i−2i2i2i−2i−2i2i−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000000000000000000−22−i2i2−1+i1−i−1−i1+i
χ352-22-2−2i2i2i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2322-2-222-2-22i−2i−2i2i2i−2i−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000000000000000002−2i2−i2−1+i1−i−1−i1+i
χ362-22-2−2i2i2i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2322-2-222-2-22i−2i−2i2i2i−2i−2i2i2ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000000000000000000000−22−i2i21−i−1+i1+i−1−i
χ374444444444441-21-21-21-211-2-2-2-21111111111-2-2-2-22222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ384444444444441-21-21-21-211-2-2-2-21111111111-2-2-2-2-2-2-2-21111-2-2-2-211111111111100000000000000000000000000
χ39444444444444-21-21-21-21-2-21111-2-2-2-2-2-2-2-2-2-21111000000000000000000000000000022-1-122-1-1-1-1-1-10000000000
χ40444444444444-21-21-21-21-2-21111-2-2-2-2-2-2-2-2-2-211110000000000000000000000000000-2-211-2-21111110000000000
χ4144444444-4-4-4-41-21-21-21-211-2-2-2-211-1-1-1-1-1-1-1-122222222-1-1-1-1-2-2-2-2-1-1-1-11111111100000000000000000000000000
χ4244444444-4-4-4-41-21-21-21-211-2-2-2-211-1-1-1-1-1-1-1-12222-2-2-2-2111122221111-1-1-1-1-1-1-1-100000000000000000000000000
χ4344444444-4-4-4-4-21-21-21-21-2-21111-2-222222222-1-1-1-1000000000000000000000000000022-1-1-2-2-1-111110000000000
χ4444444444-4-4-4-4-21-21-21-21-2-21111-2-222222222-1-1-1-10000000000000000000000000000-2-2112211-1-1-1-10000000000
χ454444-4-4-4-44i4i−4i−4i1-21-21-21-2-1-12222-1-1iiii−i−i−i−i−2i−2i2i2i22-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii00000000000000000000000000
χ464444-4-4-4-44i4i−4i−4i1-21-21-21-2-1-12222-1-1iiii−i−i−i−i−2i−2i2i2i-2-2221111−2i−2i2i2i-1-1-1-1iiii−i−i−i−i00000000000000000000000000
χ474444-4-4-4-44i4i−4i−4i-21-21-21-2122-1-1-1-122−2i−2i−2i−2i2i2i2i2iii−i−i00000000000000000000000000002-2-1-12i−2i11−i−iii0000000000
χ484444-4-4-4-44i4i−4i−4i-21-21-21-2122-1-1-1-122−2i−2i−2i−2i2i2i2i2iii−i−i0000000000000000000000000000-2211−2i2i-1-1ii−i−i0000000000
χ494444-4-4-4-4−4i−4i4i4i1-21-21-21-2-1-12222-1-1−i−i−i−iiiii2i2i−2i−2i22-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i00000000000000000000000000
χ504444-4-4-4-4−4i−4i4i4i1-21-21-21-2-1-12222-1-1−i−i−i−iiiii2i2i−2i−2i-2-22211112i2i−2i−2i-1-1-1-1−i−i−i−iiiii00000000000000000000000000
χ514444-4-4-4-4−4i−4i4i4i-21-21-21-2122-1-1-1-1222i2i2i2i−2i−2i−2i−2i−i−iii00000000000000000000000000002-2-1-1−2i2i11ii−i−i0000000000
χ524444-4-4-4-4−4i−4i4i4i-21-21-21-2122-1-1-1-1222i2i2i2i−2i−2i−2i−2i−i−iii0000000000000000000000000000-22112i−2i-1-1−i−iii0000000000
χ5344-4-44i−4i4i−4i00001-21-2-12-12i−i−2i2i−2i2ii−i3ζ7+3ζ23−3ζ7−3ζ233ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ13−3ζ5−3ζ133ζ5+3ζ1300002-22i−2i-1-1112ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−i−iii−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000000000000000000000
χ5444-4-44i−4i4i−4i00001-21-2-12-12i−i−2i2i−2i2ii−i3ζ7+3ζ23−3ζ7−3ζ233ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ13−3ζ5−3ζ133ζ5+3ζ130000-22−2i2i11-1-1−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ii−i−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000000000000000000000
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χ5644-4-44i−4i4i−4i00001-21-2-12-12i−i−2i2i−2i2ii−i−3ζ7−3ζ233ζ7+3ζ23−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ133ζ5+3ζ13−3ζ5−3ζ130000-22−2i2i11-1-12ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13ii−i−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000000000000000000000
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χ624-44-44i−4i−4i4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ131-2-121-2-12−ii−2i2i2i−2ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000i3−i3i3−i30000−33−33ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ1300000000000000000000000000
χ634-44-44i−4i−4i4i4ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13-212-1-212-12i−2ii−i−ii−2i2i−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13000000000000000000000000000000−i3i3003−3−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.