Finite Group Databasebeta

← Group #13141061

Character table — Group #13141061

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222224444444466666666121212121212121218181818181818182424242424242424242436363636363636363636363636363636363636363636363672727272
order12442346121224666121212336612121212366612121212888824242424666661212121212244488888812121212242424242424242424246122424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111
χ51111111111-1-11-1-11-1-1111111111111111111111111-1-11-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ61111111111-1-11-1-11-1-1111111111111111111111111-1-11-1-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ71111111111-1-11-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1111111-1-1-1-11111-1-11111-1-1-1-111-1-1
χ81111111111-1-11-1-11-1-11111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-111
χ911-1-1-1111-1-11-1-1111-1-11111-1-1-1-11-11-11-1-11ii−i−iii−i−i11-111-1-11-1-11-1i−ii−ii−i1-1ii−i−ii−iii−i−i11-1-11-1i−i
χ1011-1-1-1111-1-11-1-1111-1-11111-1-1-1-11-11-11-1-11ii−i−iii−i−i11-111-1-11-1-1-11−iii−i−ii-11−i−iiii−iii−i−i-1-111-11−ii
χ1111-1-1-1111-1-11-1-1111-1-11111-1-1-1-11-11-11-1-11−i−iii−i−iii11-111-1-11-1-11-1−ii−ii−ii1-1−i−iii−ii−i−iii11-1-11-1−ii
χ1211-1-1-1111-1-11-1-1111-1-11111-1-1-1-11-11-11-1-11−i−iii−i−iii11-111-1-11-1-1-11i−i−iii−i-11ii−i−i−ii−i−iii-1-111-11i−i
χ1311-1-1-1111-1-1-11-1-1-11111111-1-1-1-11-11-11-1-11ii−i−iii−i−i-1-1-1-1-1111111-1−ii−iii−i-11−i−iiii−i−i−iii-1-1111-1i−i
χ1411-1-1-1111-1-1-11-1-1-11111111-1-1-1-11-11-11-1-11ii−i−iii−i−i-1-1-1-1-111111-11i−i−ii−ii1-1ii−i−ii−i−i−iii11-1-1-11−ii
χ1511-1-1-1111-1-1-11-1-1-11111111-1-1-1-11-11-11-1-11−i−iii−i−iii-1-1-1-1-1111111-1i−ii−i−ii-11ii−i−i−iiii−i−i-1-1111-1−ii
χ1611-1-1-1111-1-1-11-1-1-11111111-1-1-1-11-11-11-1-11−i−iii−i−iii-1-1-1-1-111111-11−iii−ii−i1-1−i−iii−iiii−i−i11-1-1-11i−i
χ172222222222222222222-12-1-1-122-1-1-122-1-1-1000000002-1-1-1-12-1-1-1-122000000220000000000-1-1-1-1-1-100
χ182222222222222222222-12-1-1-122-1-1-122-1-1-1000000002-1-1-1-12-1-1-1-1-2-2000000-2-2000000000011111100
χ19222222222222222222-12-1222-1-1-12-1-1-1-1-1200000000-12-1-1-1-12-1-1-10022002200-1-1-1-1000000000000-1-1
χ20222222222222222222-12-1222-1-1-12-1-1-1-1-1200000000-12-1-1-1-12-1-1-100-2-200-2-200111100000000000011
χ212222222222-2-22-2-22-2-22-12-1-1-122-1-1-122-1-1-100000000-21-111-21-11122000000-2-200000000001111-1-100
χ222222222222-2-22-2-22-2-22-12-1-1-122-1-1-122-1-1-100000000-21-111-21-111-2-2000000220000000000-1-1-1-11100
χ232222222222-2-22-2-22-2-2-12-1222-1-1-12-1-1-1-1-12000000001-2-1111-2-111002200-2-200-1-1-1-100000000000011
χ242222222222-2-22-2-22-2-2-12-1222-1-1-12-1-1-1-1-12000000001-2-1111-2-11100-2-20022001111000000000000-1-1
χ252222-22-222200-200-200222222222-22-2-222-22-22-2222200-20000-20000000000000000-2-2000000000000
χ262222-22-222200-200-200222222222-22-2-222-2-22-22-2-2-2-200-20000-2000000000000000022000000000000
χ2722-2-222-22-2-200200-2002222-2-2-2-22222-2-2-2-22i−2i−2i2i2i2i−2i−2i0020000-20000000000000000−2i2i000000000000
χ2822-2-222-22-2-200200-2002222-2-2-2-22222-2-2-2-2−2i2i2i−2i−2i−2i2i2i0020000-200000000000000002i−2i000000000000
χ2922-2-2-2222-2-22-2-2222-2-22-12-111-2-2-11-1-2211-1000000002-11-1-1-21-1112-20000002-20000000000-1-111-1100
χ3022-2-2-2222-2-22-2-2222-2-22-12-111-2-2-11-1-2211-1000000002-11-1-1-21-111-22000000-22000000000011-1-11-100
χ3122-2-2-2222-2-22-2-2222-2-2-12-12-2-211-1-2-11-111200000000-121-1-11-2-111002i−2i002i−2i00−i−iii000000000000−ii
χ3222-2-2-2222-2-22-2-2222-2-2-12-12-2-211-1-2-11-111200000000-121-1-11-2-11100−2i2i00−2i2i00ii−i−i000000000000i−i
χ3322-2-2-2222-2-2-22-2-2-22222-12-111-2-2-11-1-2211-100000000-211112-1-1-1-12-2000000-22000000000011-1-1-1100
χ3422-2-2-2222-2-2-22-2-2-22222-12-111-2-2-11-1-2211-100000000-211112-1-1-1-1-220000002-20000000000-1-1111-100
χ3522-2-2-2222-2-2-22-2-2-2222-12-12-2-211-1-2-11-1112000000001-2111-12-1-1-1002i−2i00−2i2i00−i−iii000000000000i−i
χ3622-2-2-2222-2-2-22-2-2-2222-12-12-2-211-1-2-11-1112000000001-2111-12-1-1-100−2i2i002i−2i00ii−i−i000000000000−ii
χ37444444444444444444-2-2-2-2-2-2-2-21-21-2-211-200000000-2-2111-2-21110000000000000000000000000000
χ384444444444-4-44-4-44-4-4-2-2-2-2-2-2-2-21-21-2-211-200000000221-1-1221-1-10000000000000000000000000000
χ394444-44-444400-400-4004-24-2-2-244-22-2-4-4-2-220000000000200002000000000000000000000000000000
χ404444-44-444400-400-400-24-2444-2-2-2-4-222-2-2-40000000000200002000000000000000000000000000000
χ414444-44-444400-400-400-2-2-2-2-2-2-2-2121221120000000000-13-300-13-30000000000000000000000000000
χ424444-44-444400-400-400-2-2-2-2-2-2-2-2121221120000000000-1-3300-1-330000000000000000000000000000
χ4344-4-444-44-4-400400-4004-24-222-4-4-2-2-24-42220000000000-200002000000000000000000000000000000
χ4444-4-444-44-4-400400-400-24-24-4-422-24-2-2222-40000000000-200002000000000000000000000000000000
χ4544-4-444-44-4-400400-400-2-2-2-222221-21-22-1-12000000000013-300-1-330000000000000000000000000000
χ4644-4-444-44-4-400400-400-2-2-2-222221-21-22-1-1200000000001-3300-13-30000000000000000000000000000
χ4744-4-4-4444-4-44-4-4444-4-4-2-2-2-222221212-2-1-1-200000000-2-2-111221-1-10000000000000000000000000000
χ4844-4-4-4444-4-4-44-4-4-4444-2-2-2-222221212-2-1-1-20000000022-1-1-1-2-21110000000000000000000000000000
χ494-44i−4i040-44i−4i0000000044-4-44i−4i4i−4i40-4004i−4i00000000000000000000000000000000000000000000000
χ504-44i−4i040-44i−4i000000004-2-42−2i2i4i−4i-20200−2i2i000000000000000000000000000000000000000i6−i66−60000
χ514-44i−4i040-44i−4i000000004-2-42−2i2i4i−4i-20200−2i2i000000000000000000000000000000000000000−i6i6−660000
χ524-44i−4i040-44i−4i00000000-242-44i−4i−2i2i-20200−2i2i00000000000000000000000000000−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ22−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ2200000000000000
χ534-44i−4i040-44i−4i00000000-242-44i−4i−2i2i-20200−2i2i00000000000000000000000000000ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ22ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ2200000000000000
χ544-4−4i4i040-4−4i4i0000000044-4-4−4i4i−4i4i40-400−4i4i00000000000000000000000000000000000000000000000
χ554-4−4i4i040-4−4i4i000000004-2-422i−2i−4i4i-202002i−2i000000000000000000000000000000000000000i6−i6−660000
χ564-4−4i4i040-4−4i4i000000004-2-422i−2i−4i4i-202002i−2i000000000000000000000000000000000000000−i6i66−60000
χ574-4−4i4i040-4−4i4i00000000-242-4−4i4i2i−2i-202002i−2i00000000000000000000000000000−ζ4−ζ14+ζ20+ζ22ζ4+ζ14−ζ20−ζ22−ζ4+ζ14+ζ20−ζ22ζ4−ζ14−ζ20+ζ2200000000000000
χ584-4−4i4i040-4−4i4i00000000-242-4−4i4i2i−2i-202002i−2i00000000000000000000000000000ζ4+ζ14−ζ20−ζ22−ζ4−ζ14+ζ20+ζ22ζ4−ζ14−ζ20+ζ22−ζ4+ζ14+ζ20−ζ2200000000000000
χ5966666-36-3-3-366-3-3-3-3-3-300000000000000002222-1-1-1-1000000000000002200000000-1-1-1-1-1-100000000
χ6066666-36-3-3-366-3-3-3-3-3-30000000000000000-2-2-2-2111100000000000000-2-20000000011111100000000
χ6166666-36-3-3-3-6-6-333-33300000000000000002222-1-1-1-100000000000000-2-200000000-1-1111100000000
χ6266666-36-3-3-3-6-6-333-3330000000000000000-2-2-2-2111100000000000000220000000011-1-1-1-100000000
χ636666-6-3-6-3-3-3003−3i33i33−3i33i300000000000000002-22-2-1-1-1-100000000000000000000000011−i3i3−i3i300000000
χ646666-6-3-6-3-3-3003−3i33i33−3i33i30000000000000000-22-221111000000000000000000000000-1-1i3−i3i3−i300000000
χ656666-6-3-6-3-3-30033i3−3i333i3−3i300000000000000002-22-2-1-1-1-100000000000000000000000011i3−i3i3−i300000000
χ666666-6-3-6-3-3-30033i3−3i333i3−3i30000000000000000-22-221111000000000000000000000000-1-1−i3i3−i3i300000000
χ6766-6-66-3-6-33300-3−3i33i333i3−3i300000000000000002i−2i−2i2i−i−iii000000000000000000000000i−i3−3−3300000000
χ6866-6-66-3-6-33300-3−3i33i333i3−3i30000000000000000−2i2i2i−2iii−i−i000000000000000000000000−ii−333−300000000
χ6966-6-66-3-6-33300-33i3−3i33−3i33i300000000000000002i−2i−2i2i−i−iii000000000000000000000000i−i−333−300000000
χ7066-6-66-3-6-33300-33i3−3i33−3i33i30000000000000000−2i2i2i−2iii−i−i000000000000000000000000−ii3−3−3300000000
χ7166-6-6-6-36-3336-63-3-3-33300000000000000002i2i−2i−2i−i−iii000000000000002i−2i00000000−ii−i−iii00000000
χ7266-6-6-6-36-3336-63-3-3-3330000000000000000−2i−2i2i2iii−i−i00000000000000−2i2i00000000i−iii−i−i00000000
χ7366-6-6-6-36-333-66333-3-3-300000000000000002i2i−2i−2i−i−iii00000000000000−2i2i00000000−iiii−i−i00000000
χ7466-6-6-6-36-333-66333-3-3-30000000000000000−2i−2i2i2iii−i−i000000000000002i−2i00000000i−i−i−iii00000000
χ758-88i−8i080-88i−8i00000000-4-444−4i4i−4i4i20-2002i−2i00000000000000000000000000000000000000000000000
χ768-8−8i8i080-8−8i8i00000000-4-4444i−4i4i−4i20-200−2i2i00000000000000000000000000000000000000000000000
χ7712-1212i−12i0-606−6i6i0000000000000000000000000000−2ζ7+2ζ232ζ7−2ζ232ζ5−2ζ13−2ζ5+2ζ1300000000000000000000000000000000000000
χ7812-1212i−12i0-606−6i6i00000000000000000000000000002ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ1300000000000000000000000000000000000000
χ7912-12−12i12i0-6066i−6i00000000000000000000000000002ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ2300000000000000000000000000000000000000
χ8012-12−12i12i0-6066i−6i0000000000000000000000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ2300000000000000000000000000000000000000

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