Finite Group Databasebeta

← Group #11713113

Character table — Group #11713113

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size11111111222233333333444466668888888812121212121212121212121212121212121212121616161616161616161616162424242424242424
order12224444888822224444448888883666121212122244444444888888888812121212242424242424242424448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-111111111111111-1-1111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ511111111-1-1-1-11111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111-1-1-1-11111111111-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111-1-1-1-111111111-1-111-1-1-1-11111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ811111111-1-1-1-111111111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1ii−i−i1111-1-1-1-11-1i−iii−i−i1111-1-1-1-1111-1-1-111-1-1i−iii−i−iii−i−i11-1-1ii−i−iii−i−i1-11-1i−ii−i
χ101111-1-1-1-1ii−i−i1111-1-1-1-11-1i−iii−i−i1111-1-1-1-1-1-11-111-1-111i−i−i−iii−i−iii11-1-1ii−i−iii−i−i-11-11−ii−ii
χ111111-1-1-1-1ii−i−i1111-1-1-1-1-11−iiii−i−i1111-1-1-1-111-11-1-111-1-1−iiii−i−iii−i−i-1-111ii−i−i−i−iii-11-11−ii−ii
χ121111-1-1-1-1ii−i−i1111-1-1-1-1-11−iiii−i−i1111-1-1-1-1-1-1-1111-1-111−ii−i−iii−i−iii-1-111ii−i−i−i−iii1-11-1i−ii−i
χ131111-1-1-1-1−i−iii1111-1-1-1-11-1−ii−i−iii1111-1-1-1-1111-1-1-111-1-1−ii−i−iii−i−iii11-1-1−i−iii−i−iii1-11-1−ii−ii
χ141111-1-1-1-1−i−iii1111-1-1-1-11-1−ii−i−iii1111-1-1-1-1-1-11-111-1-111−iiii−i−iii−i−i11-1-1−i−iii−i−iii-11-11i−ii−i
χ151111-1-1-1-1−i−iii1111-1-1-1-1-11i−i−i−iii1111-1-1-1-111-11-1-111-1-1i−i−i−iii−i−iii-1-111−i−iiiii−i−i-11-11i−ii−i
χ161111-1-1-1-1−i−iii1111-1-1-1-1-11i−i−i−iii1111-1-1-1-1-1-1-1111-1-111i−iii−i−iii−i−i-1-111−i−iiiii−i−i1-11-1−ii−ii
χ172222222222222222222222222222-1-1-1-1-1-1-1-100220000002200000000-1-1-1-1-1-1-1-1-1-1-1-100000000
χ1822222222222222222222-2-2-2-22222-1-1-1-1-1-1-1-100-2-2000000-2-2000000001111-1-1-1-1111100000000
χ1922222222-2-2-2-22222222222-2-2-2-2-2-2-1-1-1-1-1-1-1-10022000000-2-200000000-1-1-1-11111111100000000
χ2022222222-2-2-2-222222222-2-222-2-2-2-2-1-1-1-1-1-1-1-100-2-2000000220000000011111111-1-1-1-100000000
χ212222-2-2-2-22i2i−2i−2i2222-2-2-2-22-22i−2i2i2i−2i−2i-1-1-1-11111002-20000002i−2i00000000-1-111−i−iii−i−iii00000000
χ222222-2-2-2-22i2i−2i−2i2222-2-2-2-2-22−2i2i2i2i−2i−2i-1-1-1-1111100-22000000−2i2i0000000011-1-1−i−iiiii−i−i00000000
χ232222-2-2-2-2−2i−2i2i2i2222-2-2-2-22-2−2i2i−2i−2i2i2i-1-1-1-11111002-2000000−2i2i00000000-1-111ii−i−iii−i−i00000000
χ242222-2-2-2-2−2i−2i2i2i2222-2-2-2-2-222i−2i−2i−2i2i2i-1-1-1-1111100-220000002i−2i0000000011-1-1ii−i−i−i−iii00000000
χ2522-2-22i−2i2i−2i00002-22-22i2i−2i−2i0000000022-2-22i−2i2i−2i2-2002i−2i2-22i−2i000000000000000000000000000000
χ2622-2-22i−2i2i−2i00002-22-22i2i−2i−2i0000000022-2-22i−2i2i−2i-2200−2i2i-22−2i2i000000000000000000000000000000
χ2722-2-2−2i2i−2i2i00002-22-2−2i−2i2i2i0000000022-2-2−2i2i−2i2i2-200−2i2i2-2−2i2i000000000000000000000000000000
χ2822-2-2−2i2i−2i2i00002-22-2−2i−2i2i2i0000000022-2-2−2i2i−2i2i-22002i−2i-222i−2i000000000000000000000000000000
χ292-22-22i−2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-222-22i−2i2i−2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-22-22i−2i−2i2i000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ302-22-22i−2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-222-22i−2i2i−2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-11-11−iii−i000000000000000000003−3−i3i3ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ312-22-22i−2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-222-22i−2i2i−2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23-11-11−iii−i00000000000000000000−33i3−i3ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ322-22-22i−2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-222-22i−2i2i−2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232-22-22i−2i−2i2i0000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
χ332-22-22i−2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-222-22i−2i2i−2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-11-11−iii−i000000000000000000003−3−i3i3−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ342-22-22i−2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-222-22i−2i2i−2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23-11-11−iii−i00000000000000000000−33i3−i3−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ352-22-2−2i2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-222-2−2i2i−2i2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22-2−2i2i2i−2i0000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ362-22-2−2i2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-222-2−2i2i−2i2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-11-11i−i−ii000000000000000000003−3i3−i3−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ372-22-2−2i2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-222-2−2i2i−2i2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-11-11i−i−ii00000000000000000000−33−i3i3−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ382-22-2−2i2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-222-2−2i2i−2i2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22-2−2i2i2i−2i000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ392-22-2−2i2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-222-2−2i2i−2i2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-11-11i−i−ii000000000000000000003−3i3−i3ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ402-22-2−2i2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-222-2−2i2i−2i2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-11-11i−i−ii00000000000000000000−33−i3i3ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ412-2-2222-2-20000-2-2222-2-22000000002-2-2222-2-20000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ422-2-2222-2-20000-2-2222-2-22000000002-2-2222-2-2000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ432-2-22-2-2220000-2-222-222-2000000002-2-22-2-2220000000000002-2-222-2-2200000000000000000000
χ442-2-22-2-2220000-2-222-222-2000000002-2-22-2-222000000000000-222-2-222-200000000000000000000
χ45333333333333-1-1-1-1-1-1-1-13333-1-1-1-10000000011-1-111-1-1-1-1-1-11111-1-1-1-100000000000011-1-111-1-1
χ46333333333333-1-1-1-1-1-1-1-13333-1-1-1-100000000-1-1-1-1-1-11111-1-1-1-1-1-11111000000000000-1-111-1-111
χ47333333333333-1-1-1-1-1-1-1-1-3-3-3-3-1-1-1-100000000111111-1-1-1-1111111-1-1-1-1000000000000-1-111-1-111
χ48333333333333-1-1-1-1-1-1-1-1-3-3-3-3-1-1-1-100000000-1-111-1-1111111-1-1-1-1111100000000000011-1-111-1-1
χ4933333333-3-3-3-3-1-1-1-1-1-1-1-133-3-311110000000011-1-111-1-1-1-111-1-1-1-1111100000000000011-1-1-1-111
χ5033333333-3-3-3-3-1-1-1-1-1-1-1-133-3-3111100000000-1-1-1-1-1-11111111111-1-1-1-1000000000000-1-11111-1-1
χ5133333333-3-3-3-3-1-1-1-1-1-1-1-1-3-333111100000000111111-1-1-1-1-1-1-1-1-1-11111000000000000-1-11111-1-1
χ5233333333-3-3-3-3-1-1-1-1-1-1-1-1-3-333111100000000-1-111-1-11111-1-11111-1-1-1-100000000000011-1-1-1-111
χ533333-3-3-3-33i3i−3i−3i-1-1-1-111113-33i−3i−i−iii0000000011-11-1-1-1-111−iiii−i−i−i−iii0000000000001-1-11i−i−ii
χ543333-3-3-3-33i3i−3i−3i-1-1-1-111113-33i−3i−i−iii00000000-1-1-111111-1-1−ii−i−iiiii−i−i000000000000-111-1−iii−i
χ553333-3-3-3-33i3i−3i−3i-1-1-1-11111-33−3i3i−i−iii00000000111-1-1-1-1-111i−iii−i−i−i−iii000000000000-111-1−iii−i
χ563333-3-3-3-33i3i−3i−3i-1-1-1-11111-33−3i3i−i−iii00000000-1-11-11111-1-1i−i−i−iiiii−i−i0000000000001-1-11i−i−ii
χ573333-3-3-3-3−3i−3i3i3i-1-1-1-111113-3−3i3iii−i−i0000000011-11-1-1-1-111i−i−i−iiiii−i−i0000000000001-1-11−iii−i
χ583333-3-3-3-3−3i−3i3i3i-1-1-1-111113-3−3i3iii−i−i00000000-1-1-111111-1-1i−iii−i−i−i−iii000000000000-111-1i−i−ii
χ593333-3-3-3-3−3i−3i3i3i-1-1-1-11111-333i−3iii−i−i00000000111-1-1-1-1-111−ii−i−iiiii−i−i000000000000-111-1i−i−ii
χ603333-3-3-3-3−3i−3i3i3i-1-1-1-11111-333i−3iii−i−i00000000-1-11-11111-1-1−iiii−i−i−i−iii0000000000001-1-11−iii−i
χ6144-4-44i−4i4i−4i00004-44-44i4i−4i−4i00000000-2-222−2i2i−2i2i0000000000000000000000000000000000000000
χ6244-4-4−4i4i−4i4i00004-44-4−4i−4i4i4i00000000-2-2222i−2i2i−2i0000000000000000000000000000000000000000
χ634-4-4444-4-40000-4-4444-4-4400000000-222-2-2-2220000000000000000000000000000000000000000
χ644-4-44-4-4440000-4-444-444-400000000-222-222-2-20000000000000000000000000000000000000000
χ6566-6-66i−6i6i−6i0000-22-22−2i−2i2i2i00000000000000002-2002i−2i-22−2i2i000000000000000000000000000000
χ6666-6-66i−6i6i−6i0000-22-22−2i−2i2i2i0000000000000000-2200−2i2i2-22i−2i000000000000000000000000000000
χ6766-6-6−6i6i−6i6i0000-22-222i2i−2i−2i00000000000000002-200−2i2i-222i−2i000000000000000000000000000000
χ6866-6-6−6i6i−6i6i0000-22-222i2i−2i−2i0000000000000000-22002i−2i2-2−2i2i000000000000000000000000000000
χ696-66-66i−6i−6i6i−6ζ5−6ζ136ζ5+6ζ136ζ7+6ζ23−6ζ7−6ζ232-2-22−2i2i−2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000000000000000000000000000000000000000
χ706-66-66i−6i−6i6i6ζ5+6ζ13−6ζ5−6ζ13−6ζ7−6ζ236ζ7+6ζ232-2-22−2i2i−2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000000000000000000000000000000000000000
χ716-66-6−6i6i6i−6i6ζ7+6ζ23−6ζ7−6ζ23−6ζ5−6ζ136ζ5+6ζ132-2-222i−2i2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000000000000000000000000000000000000000
χ726-66-6−6i6i6i−6i−6ζ7−6ζ236ζ7+6ζ236ζ5+6ζ13−6ζ5−6ζ132-2-222i−2i2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000000000000000000000000000000000000000
χ736-6-6666-6-6000022-2-2-222-200000000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ746-6-6666-6-6000022-2-2-222-20000000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ756-6-66-6-666000022-2-22-2-2200000000000000000000000000002-2-22-222-200000000000000000000
χ766-6-66-6-666000022-2-22-2-220000000000000000000000000000-222-22-2-2200000000000000000000

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