Finite Group Databasebeta

← Group #13141073

Character table — Group #13141073

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order1244234612122466612121233661212121222443666121212122444444444661212666661212121212246668888121212121212121212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-111-1-1-1-1-11111-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-111
χ51111111111-1-11-1-11-1-11111111111111111111111111111111111-1-11-1-1-1-11-1-1-1-11-1-1-1-1-1-11-1-111111111-1-1-1-1
χ61111111111-1-11-1-11-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-11-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11-1-11-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-111-111-1-111-1111111-1-1-1-1-1-111
χ81111111111-1-11-1-11-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-1-11-1-111-11111-1-1-111-1-1-1-1111111-1-1
χ911-1-1-1111-1-11-1-1111-1-11111-1-1-1-111-1-111-1-111-1-1-11ii−i−iii−i−i11-1-111-111-1-11-1-11-1-111i−ii−i1-1-1ii−i−iii−i−ii−ii−i
χ1011-1-1-1111-1-11-1-1111-1-11111-1-1-1-111-1-111-1-111-1-1-11−i−iii−i−iii11-1-111-111-1-11-1-11-1-111−ii−ii1-1-1−i−iii−i−iii−ii−ii
χ1111-1-1-1111-1-11-1-1111-1-11111-1-1-1-1-1-11111-1-111-1-11-1ii−i−i−i−iii-1-11111-111-1-11-1-1-111-1-1i−i−ii-111ii−i−i−i−iiii−i−ii
χ1211-1-1-1111-1-11-1-1111-1-11111-1-1-1-1-1-11111-1-111-1-11-1−i−iiiii−i−i-1-11111-111-1-11-1-1-111-1-1−iii−i-111−i−iiiii−i−i−iii−i
χ1311-1-1-1111-1-1-11-1-1-11111111-1-1-1-111-1-111-1-111-1-1-11ii−i−iii−i−i11-1-1-1-1-1-1-111111-11-1-1-1−ii−ii111ii−i−iii−i−i−ii−ii
χ1411-1-1-1111-1-1-11-1-1-11111111-1-1-1-111-1-111-1-111-1-1-11−i−iii−i−iii11-1-1-1-1-1-1-111111-11-1-1-1i−ii−i111−i−iii−i−iiii−ii−i
χ1511-1-1-1111-1-1-11-1-1-11111111-1-1-1-1-1-11111-1-111-1-11-1ii−i−i−i−iii-1-111-1-1-1-1-1111111-1111−iii−i-1-1-1ii−i−i−i−iii−iii−i
χ1611-1-1-1111-1-1-11-1-1-11111111-1-1-1-1-1-11111-1-111-1-11-1−i−iiiii−i−i-1-111-1-1-1-1-1111111-1111i−i−ii-1-1-1−i−iiiii−i−ii−i−ii
χ172222222222222222222-12-122-1-10000-1-12-12-1-1-1000000222200002-1-1-1-12-1-1-1-10000000220000000-1-1-1-100-1-1
χ182222222222222222222-12-122-1-10000-1-12-12-1-1-1000000-2-2-2-200002-1-1-1-12-1-1-1-10000000-2-2000000011110011
χ19222222222222222222-12-12-1-1220000-1-1-12-12-1-100222200000000-12-1-1-1-12-1-1-1000002200000-1-1-1-10000-1-100
χ20222222222222222222-12-12-1-1220000-1-1-12-12-1-100-2-2-2-200000000-12-1-1-1-12-1-1-100000-2-200000111100001100
χ212222222222-2-22-2-22-2-22-12-122-1-10000-1-12-12-1-1-100000022220000-21-111-21-1110000000-2-20000000-1-1-1-10011
χ222222222222-2-22-2-22-2-22-12-122-1-10000-1-12-12-1-1-1000000-2-2-2-20000-21-111-21-1110000000220000000111100-1-1
χ232222222222-2-22-2-22-2-2-12-12-1-1220000-1-1-12-12-1-1002222000000001-2-1111-2-11100000-2-200000-1-1-1-100001100
χ242222222222-2-22-2-22-2-2-12-12-1-1220000-1-1-12-12-1-100-2-2-2-2000000001-2-1111-2-11100000220000011110000-1-100
χ252222-22-222200-200-20022222222222222-2-2-2-222-2-200000000222200-20000-20000-2000000-200000000000000
χ262222-22-222200-200-20022222222-2-2-2-222-2-2-2-2222200000000-2-2-2-200-20000-200002000000200000000000000
χ2722-2-222-22-2-200200-2002222-2-2-2-222-2-22222-2-2-2-22-20000000022-2-20020000-200002000000-200000000000000
χ2822-2-222-22-2-200200-2002222-2-2-2-2-2-2222222-2-2-2-2-2200000000-2-2220020000-20000-2000000200000000000000
χ2922-2-2-2222-2-22-2-2222-2-22-12-1-2-2110000-1-1-212-1110000002i2i−2i−2i00002-11-1-1-21-11100000002i−2i0000000−i−iii00−ii
χ3022-2-2-2222-2-22-2-2222-2-22-12-1-2-2110000-1-1-212-111000000−2i−2i2i2i00002-11-1-1-21-1110000000−2i2i0000000ii−i−i00i−i
χ3122-2-2-2222-2-22-2-2222-2-2-12-1211-2-20000-1-11-2-1211002i2i−2i−2i00000000-121-1-11-2-111000002i−2i00000−i−iii0000−ii00
χ3222-2-2-2222-2-22-2-2222-2-2-12-1211-2-20000-1-11-2-121100−2i−2i2i2i00000000-121-1-11-2-11100000−2i2i00000ii−i−i0000i−i00
χ3322-2-2-2222-2-2-22-2-2-22222-12-1-2-2110000-1-1-212-1110000002i2i−2i−2i0000-211112-1-1-1-10000000−2i2i0000000−i−iii00i−i
χ3422-2-2-2222-2-2-22-2-2-22222-12-1-2-2110000-1-1-212-111000000−2i−2i2i2i0000-211112-1-1-1-100000002i−2i0000000ii−i−i00−ii
χ3522-2-2-2222-2-2-22-2-2-2222-12-1211-2-20000-1-11-2-1211002i2i−2i−2i000000001-2111-12-1-1-100000−2i2i00000−i−iii0000i−i00
χ3622-2-2-2222-2-2-22-2-2-2222-12-1211-2-20000-1-11-2-121100−2i−2i2i2i000000001-2111-12-1-1-1000002i−2i00000ii−i−i0000−ii00
χ372-22i−2i020-22i−2i0000000022-2-22i−2i2i−2i2-22i−2i2-200002i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i2-22i−2i00000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ382-22i−2i020-22i−2i0000000022-2-22i−2i2i−2i2-22i−2i2-200002i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i2-22i−2i0000000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ392-22i−2i020-22i−2i0000000022-2-22i−2i2i−2i-22−2i2i2-200002i−2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i-22−2i2i00000000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i0000
χ402-22i−2i020-22i−2i0000000022-2-22i−2i2i−2i-22−2i2i2-200002i−2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i-22−2i2i0000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ412-2−2i2i020-2−2i2i0000000022-2-2−2i2i−2i2i2-2−2i2i2-20000−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i2-2−2i2i00000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ422-2−2i2i020-2−2i2i0000000022-2-2−2i2i−2i2i2-2−2i2i2-20000−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i2-2−2i2i0000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ432-2−2i2i020-2−2i2i0000000022-2-2−2i2i−2i2i-222i−2i2-20000−2i2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i-222i−2i00000000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i0000
χ442-2−2i2i020-2−2i2i0000000022-2-2−2i2i−2i2i-222i−2i2-20000−2i2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i-222i−2i0000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
χ45444444444444444444-2-2-2-2-2-2-2-2000011-2-2-2-21100000000000000-2-2111-2-2111000000000000000000000000
χ464444444444-4-44-4-44-4-4-2-2-2-2-2-2-2-2000011-2-2-2-21100000000000000221-1-1221-1-1000000000000000000000000
χ474444-44-444400-400-4004-24-244-2-20000-2-2-42-42-2-2000000000000000020000200000000000000000000000000
χ484444-44-444400-400-400-24-24-2-2440000-2-22-42-4-2-2000000000000000020000200000000000000000000000000
χ494444-44-444400-400-400-2-2-2-2-2-2-2-20000112222110000000000000000-13-300-13-3000000000000000000000000
χ504444-44-444400-400-400-2-2-2-2-2-2-2-20000112222110000000000000000-1-3300-1-33000000000000000000000000
χ5144-4-444-44-4-400400-4004-24-2-4-4220000-2-24-2-42220000000000000000-20000200000000000000000000000000
χ5244-4-444-44-4-400400-400-24-2422-4-40000-2-2-242-4220000000000000000-20000200000000000000000000000000
χ5344-4-444-44-4-400400-400-2-2-2-22222000011-2-222-1-1000000000000000013-300-1-33000000000000000000000000
χ5444-4-444-44-4-400400-400-2-2-2-22222000011-2-222-1-100000000000000001-3300-13-3000000000000000000000000
χ5544-4-4-4444-4-44-4-4444-4-4-2-2-2-2222200001122-2-2-1-100000000000000-2-2-111221-1-1000000000000000000000000
χ5644-4-4-4444-4-4-44-4-4-4444-2-2-2-2222200001122-2-2-1-10000000000000022-1-1-1-2-2111000000000000000000000000
χ574-44i−4i040-44i−4i000000004-2-424i−4i−2i2i0000-220000−2i2i0000002+2i−2−2i2−2i−2+2i000000000000000000000000000000−1−i1+i−1+i1−i0000
χ584-44i−4i040-44i−4i000000004-2-424i−4i−2i2i0000-220000−2i2i000000−2−2i2+2i−2+2i2−2i0000000000000000000000000000001+i−1−i1−i−1+i0000
χ594-44i−4i040-44i−4i00000000-242-4−2i2i4i−4i0000-220000−2i2i002+2i−2−2i2−2i−2+2i000000000000000000000000000000−1−i1+i−1+i1−i00000000
χ604-44i−4i040-44i−4i00000000-242-4−2i2i4i−4i0000-220000−2i2i00−2−2i2+2i−2+2i2−2i0000000000000000000000000000001+i−1−i1−i−1+i00000000
χ614-4−4i4i040-4−4i4i000000004-2-42−4i4i2i−2i0000-2200002i−2i0000002−2i−2+2i2+2i−2−2i000000000000000000000000000000−1+i1−i−1−i1+i0000
χ624-4−4i4i040-4−4i4i000000004-2-42−4i4i2i−2i0000-2200002i−2i000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000001−i−1+i1+i−1−i0000
χ634-4−4i4i040-4−4i4i00000000-242-42i−2i−4i4i0000-2200002i−2i002−2i−2+2i2+2i−2−2i000000000000000000000000000000−1+i1−i−1−i1+i00000000
χ644-4−4i4i040-4−4i4i00000000-242-42i−2i−4i4i0000-2200002i−2i00−2+2i2−2i−2−2i2+2i0000000000000000000000000000001−i−1+i1+i−1−i00000000
χ6566666-36-3-3-366-3-3-3-3-3-3000000002222000000002200000000-1-1-1-1000000000022-1-1-10000-1-1-1000000000000
χ6666666-36-3-3-366-3-3-3-3-3-300000000-2-2-2-200000000-2-20000000011110000000000-2-21110000111000000000000
χ6766666-36-3-3-3-6-6-333-333000000002222000000002200000000-1-1-1-10000000000-2-2-1110000-111000000000000
χ6866666-36-3-3-3-6-6-333-33300000000-2-2-2-200000000-2-20000000011110000000000221-1-100001-1-1000000000000
χ696666-6-3-6-3-3-3003−3i33i33−3i33i300000000222200000000-2-200000000-1-1-1-10000000000001−i3i300001−i3i3000000000000
χ706666-6-3-6-3-3-3003−3i33i33−3i33i300000000-2-2-2-20000000022000000001111000000000000-1i3−i30000-1i3−i3000000000000
χ716666-6-3-6-3-3-30033i3−3i333i3−3i300000000222200000000-2-200000000-1-1-1-10000000000001i3−i300001i3−i3000000000000
χ726666-6-3-6-3-3-30033i3−3i333i3−3i300000000-2-2-2-20000000022000000001111000000000000-1−i3i30000-1−i3i3000000000000
χ7366-6-66-3-6-33300-3−3i33i333i3−3i30000000022-2-2000000002-200000000-1-111000000000000-1−i3i300001i3−i3000000000000
χ7466-6-66-3-6-33300-3−3i33i333i3−3i300000000-2-22200000000-220000000011-1-10000000000001i3−i30000-1−i3i3000000000000
χ7566-6-66-3-6-33300-33i3−3i33−3i33i30000000022-2-2000000002-200000000-1-111000000000000-1i3−i300001−i3i3000000000000
χ7666-6-66-3-6-33300-33i3−3i33−3i33i300000000-2-22200000000-220000000011-1-10000000000001−i3i30000-1i3−i3000000000000
χ7766-6-6-6-36-3336-63-3-3-3330000000022-2-200000000-2200000000-1-11100000000002-21-1-10000-111000000000000
χ7866-6-6-6-36-3336-63-3-3-33300000000-2-222000000002-20000000011-1-10000000000-22-11100001-1-1000000000000
χ7966-6-6-6-36-333-66333-3-3-30000000022-2-200000000-2200000000-1-1110000000000-221110000-1-1-1000000000000
χ8066-6-6-6-36-333-66333-3-3-300000000-2-222000000002-20000000011-1-100000000002-2-1-1-10000111000000000000
χ818-88i−8i080-88i−8i00000000-4-444−4i4i−4i4i00002-200002i−2i000000000000000000000000000000000000000000000000
χ828-8−8i8i080-8−8i8i00000000-4-4444i−4i4i−4i00002-20000−2i2i000000000000000000000000000000000000000000000000
χ8312-1212i−12i0-606−6i6i00000000000000004-44i−4i000000000000000000-22−2i2i0000000000000000000000000000000000
χ8412-1212i−12i0-606−6i6i0000000000000000-44−4i4i0000000000000000002-22i−2i0000000000000000000000000000000000
χ8512-12−12i12i0-6066i−6i00000000000000004-4−4i4i000000000000000000-222i−2i0000000000000000000000000000000000
χ8612-12−12i12i0-6066i−6i0000000000000000-444i−4i0000000000000000002-2−2i2i0000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).