Finite Group Databasebeta

← Group #13141072

Character table — Group #13141072

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222224444444466666666121212121212121218181818181818182424242424242424242436363636363636363636363636363636363636363636363672727272
order1244234612122466612121233661212121236661212121222446612126666612121212122444446668888121212121212121212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-111-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-11111-1-111
χ51111111111-1-11-1-11-1-1111111111111111111111111-1-11-1-1-1-11-1-1-1-111111-1-1-1-1-1-11-1-111111111-1-1-1-1
χ61111111111-1-11-1-11-1-1111111111111111111111111-1-11-1-1-1-11-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-11111
χ71111111111-1-11-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-11111-1-1-111-1-111-1111111-1-1-1-1-1-111
χ81111111111-1-11-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-111-1-111-11111-1-1-111-1-1-1-1111111-1-1
χ911-1-1-1111-1-11-1-1111-1-11111-1-1-1-111-1-111-1-11-11-111-1-111-111-1-11-1-11-1i−ii−i-111i−ii−i1-1-1ii−i−iii−i−ii−ii−i
χ1011-1-1-1111-1-11-1-1111-1-11111-1-1-1-111-1-111-1-11-11-111-1-111-111-1-11-1-11-1−ii−ii-111−ii−ii1-1-1−i−iii−i−iii−ii−ii
χ1111-1-1-1111-1-11-1-1111-1-11111-1-1-1-111-1-111-1-1-11-11-1-11111-111-1-11-1-1-11i−i−ii1-1-1i−i−ii-111ii−i−i−i−iiii−i−ii
χ1211-1-1-1111-1-11-1-1111-1-11111-1-1-1-111-1-111-1-1-11-11-1-11111-111-1-11-1-1-11−iii−i1-1-1−iii−i-111−i−iiiii−i−i−iii−i
χ1311-1-1-1111-1-1-11-1-1-11111111-1-1-1-111-1-111-1-11-11-111-1-1-1-1-1-1-111111-11i−ii−i-1-1-1−ii−ii111ii−i−iii−i−i−ii−ii
χ1411-1-1-1111-1-1-11-1-1-11111111-1-1-1-111-1-111-1-11-11-111-1-1-1-1-1-1-111111-11−ii−ii-1-1-1i−ii−i111−i−iii−i−iiii−ii−i
χ1511-1-1-1111-1-1-11-1-1-11111111-1-1-1-111-1-111-1-1-11-11-1-111-1-1-1-1-1111111-1i−i−ii111−iii−i-1-1-1ii−i−i−i−iii−iii−i
χ1611-1-1-1111-1-1-11-1-1-11111111-1-1-1-111-1-111-1-1-11-11-1-111-1-1-1-1-1111111-1−iii−i111i−i−ii-1-1-1−i−iiiii−i−ii−i−ii
χ172222222222222222222-12-122-1-1-1-12-12-1-1-1000000002-1-1-1-12-1-1-1-100002200000220000000-1-1-1-100-1-1
χ182222222222222222222-12-122-1-1-1-12-12-1-1-1000000002-1-1-1-12-1-1-1-10000-2-200000-2-2000000011110011
χ19222222222222222222-12-12-1-122-1-1-12-12-1-100000000-12-1-1-1-12-1-1-10022000002200000-1-1-1-10000-1-100
χ20222222222222222222-12-12-1-122-1-1-12-12-1-100000000-12-1-1-1-12-1-1-100-2-200000-2-200000111100001100
χ212222222222-2-22-2-22-2-22-12-122-1-1-1-12-12-1-1-100000000-21-111-21-11100002200000-2-20000000-1-1-1-10011
χ222222222222-2-22-2-22-2-22-12-122-1-1-1-12-12-1-1-100000000-21-111-21-1110000-2-200000220000000111100-1-1
χ232222222222-2-22-2-22-2-2-12-12-1-122-1-1-12-12-1-1000000001-2-1111-2-111002200000-2-200000-1-1-1-100001100
χ242222222222-2-22-2-22-2-2-12-12-1-122-1-1-12-12-1-1000000001-2-1111-2-11100-2-200000220000011110000-1-100
χ252222-22-222200-200-2002222222222-2-2-2-2222-2-22222200-20000-200000000-2000000-200000000000000
χ262222-22-222200-200-2002222222222-2-2-2-222-222-2-2-2-2-200-20000-2000000002000000200000000000000
χ2722-2-222-22-2-200200-2002222-2-2-2-22222-2-2-2-222-2-222-2-20020000-2000000002000000-200000000000000
χ2822-2-222-22-2-200200-2002222-2-2-2-22222-2-2-2-2-2-222-2-2220020000-200000000-2000000200000000000000
χ2922-2-2-2222-2-22-2-2222-2-22-12-1-2-211-1-1-212-111000000002-11-1-1-21-11100002i−2i000002i−2i0000000−i−iii00−ii
χ3022-2-2-2222-2-22-2-2222-2-22-12-1-2-211-1-1-212-111000000002-11-1-1-21-1110000−2i2i00000−2i2i0000000ii−i−i00i−i
χ3122-2-2-2222-2-22-2-2222-2-2-12-1211-2-2-1-11-2-121100000000-121-1-11-2-111002i−2i000002i−2i00000−i−iii0000−ii00
χ3222-2-2-2222-2-22-2-2222-2-2-12-1211-2-2-1-11-2-121100000000-121-1-11-2-11100−2i2i00000−2i2i00000ii−i−i0000i−i00
χ3322-2-2-2222-2-2-22-2-2-22222-12-1-2-211-1-1-212-11100000000-211112-1-1-1-100002i−2i00000−2i2i0000000−i−iii00i−i
χ3422-2-2-2222-2-2-22-2-2-22222-12-1-2-211-1-1-212-11100000000-211112-1-1-1-10000−2i2i000002i−2i0000000ii−i−i00−ii
χ3522-2-2-2222-2-2-22-2-2-2222-12-1211-2-2-1-11-2-1211000000001-2111-12-1-1-1002i−2i00000−2i2i00000−i−iii0000i−i00
χ3622-2-2-2222-2-2-22-2-2-2222-12-1211-2-2-1-11-2-1211000000001-2111-12-1-1-100−2i2i000002i−2i00000ii−i−i0000−ii00
χ37444444444444444444-2-2-2-2-2-2-2-211-2-2-2-21100000000-2-2111-2-21110000000000000000000000000000
χ384444444444-4-44-4-44-4-4-2-2-2-2-2-2-2-211-2-2-2-21100000000221-1-1221-1-10000000000000000000000000000
χ394444-44-444400-400-4004-24-244-2-2-2-2-42-42-2-20000000000200002000000000000000000000000000000
χ404444-44-444400-400-400-24-24-2-244-2-22-42-4-2-20000000000200002000000000000000000000000000000
χ414444-44-444400-400-400-2-2-2-2-2-2-2-2112222110000000000-13-300-13-30000000000000000000000000000
χ424444-44-444400-400-400-2-2-2-2-2-2-2-2112222110000000000-1-3300-1-330000000000000000000000000000
χ4344-4-444-44-4-400400-4004-24-2-4-422-2-24-2-42220000000000-200002000000000000000000000000000000
χ4444-4-444-44-4-400400-400-24-2422-4-4-2-2-242-4220000000000-200002000000000000000000000000000000
χ4544-4-444-44-4-400400-400-2-2-2-2222211-2-222-1-1000000000013-300-1-330000000000000000000000000000
χ4644-4-444-44-4-400400-400-2-2-2-2222211-2-222-1-100000000001-3300-13-30000000000000000000000000000
χ4744-4-4-4444-4-44-4-4444-4-4-2-2-2-222221122-2-2-1-100000000-2-2-111221-1-10000000000000000000000000000
χ4844-4-4-4444-4-4-44-4-4-4444-2-2-2-222221122-2-2-1-10000000022-1-1-1-2-21110000000000000000000000000000
χ494-44i−4i040-44i−4i0000000044-4-44i−4i4i−4i4-400004i−4i0000000000000000000000000000000000000000000000
χ504-44i−4i040-44i−4i000000004-2-424i−4i−2i2i-220000−2i2i00000000000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000
χ514-44i−4i040-44i−4i000000004-2-424i−4i−2i2i-220000−2i2i00000000000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000
χ524-44i−4i040-44i−4i00000000-242-4−2i2i4i−4i-220000−2i2i0000000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000
χ534-44i−4i040-44i−4i00000000-242-4−2i2i4i−4i-220000−2i2i0000000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000
χ544-4−4i4i040-4−4i4i0000000044-4-4−4i4i−4i4i4-40000−4i4i0000000000000000000000000000000000000000000000
χ554-4−4i4i040-4−4i4i000000004-2-42−4i4i2i−2i-2200002i−2i00000000000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000
χ564-4−4i4i040-4−4i4i000000004-2-42−4i4i2i−2i-2200002i−2i00000000000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000
χ574-4−4i4i040-4−4i4i00000000-242-42i−2i−4i4i-2200002i−2i0000000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000
χ584-4−4i4i040-4−4i4i00000000-242-42i−2i−4i4i-2200002i−2i0000000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000
χ5966666-36-3-3-366-3-3-3-3-3-300000000000000002222-1-1-1-10000000000220000-1-1-10000-1-1-1000000000000
χ6066666-36-3-3-366-3-3-3-3-3-30000000000000000-2-2-2-211110000000000-2-200001110000111000000000000
χ6166666-36-3-3-3-6-6-333-33300000000000000002222-1-1-1-10000000000-2-20000-1110000-111000000000000
χ6266666-36-3-3-3-6-6-333-3330000000000000000-2-2-2-2111100000000002200001-1-100001-1-1000000000000
χ636666-6-3-6-3-3-3003−3i33i33−3i33i300000000000000002-2-22-1-1-1-100000000000000001−i3i300001−i3i3000000000000
χ646666-6-3-6-3-3-3003−3i33i33−3i33i30000000000000000-222-211110000000000000000-1i3−i30000-1i3−i3000000000000
χ656666-6-3-6-3-3-30033i3−3i333i3−3i300000000000000002-2-22-1-1-1-100000000000000001i3−i300001i3−i3000000000000
χ666666-6-3-6-3-3-30033i3−3i333i3−3i30000000000000000-222-211110000000000000000-1−i3i30000-1−i3i3000000000000
χ6766-6-66-3-6-33300-3−3i33i333i3−3i3000000000000000022-2-2-1-1110000000000000000-1−i3i300001i3−i3000000000000
χ6866-6-66-3-6-33300-3−3i33i333i3−3i30000000000000000-2-22211-1-100000000000000001i3−i30000-1−i3i3000000000000
χ6966-6-66-3-6-33300-33i3−3i33−3i33i3000000000000000022-2-2-1-1110000000000000000-1i3−i300001−i3i3000000000000
χ7066-6-66-3-6-33300-33i3−3i33−3i33i30000000000000000-2-22211-1-100000000000000001−i3i30000-1i3−i3000000000000
χ7166-6-6-6-36-3336-63-3-3-33300000000000000002-22-2-1-11100000000002-200001-1-10000-111000000000000
χ7266-6-6-6-36-3336-63-3-3-3330000000000000000-22-2211-1-10000000000-220000-11100001-1-1000000000000
χ7366-6-6-6-36-333-66333-3-3-300000000000000002-22-2-1-1110000000000-2200001110000-1-1-1000000000000
χ7466-6-6-6-36-333-66333-3-3-30000000000000000-22-2211-1-100000000002-20000-1-1-10000111000000000000
χ758-88i−8i080-88i−8i00000000-4-444−4i4i−4i4i2-200002i−2i0000000000000000000000000000000000000000000000
χ768-8−8i8i080-8−8i8i00000000-4-4444i−4i4i−4i2-20000−2i2i0000000000000000000000000000000000000000000000
χ7712-1212i−12i0-606−6i6i0000000000000000000000000000−2i32i323−2300000000000000000000000000000000000000
χ7812-1212i−12i0-606−6i6i00000000000000000000000000002i3−2i3−232300000000000000000000000000000000000000
χ7912-12−12i12i0-6066i−6i0000000000000000000000000000−2i32i3−232300000000000000000000000000000000000000
χ8012-12−12i12i0-6066i−6i00000000000000000000000000002i3−2i323−2300000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.