Finite Group Databasebeta

← Group #13139195

Character table — Group #13139195

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11112222224444444466666666121212121212121218181818181818182424242424242424242436363636363636363636363636363636363636363636363672727272
order1244234612126881224242424336612121212366612121212224466121261224242424242424242244444468812121212121212121224242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-11-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-11-11-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11
χ511111111111-1-11-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111-1-11-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111111-1-1-1-1-1-1-1-1
χ711111111111-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-11-1-1-111-111-1-1-1-1-1111111111-11-1
χ811111111111-1-11-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-1111-1-1-111-11111-1-1-1-11111-11-11
χ911-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-111-1-111-1-11-11-111-1-1-11ii−i−iii−i−i1-1-11i−ii−i-1i−i1ii−i−iii−i−iii−i−i1-1-11
χ1011-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-111-1-111-1-11-11-111-1-1-11ii−i−iii−i−i-111-1−ii−ii-1i−i1−i−iii−i−iiiii−i−i-111-1
χ1111-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-111-1-111-1-1-11-11-1-111-11ii−i−iii−i−i11-1-1i−i−ii1−ii-1ii−i−i−i−iii−i−iii11-1-1
χ1211-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-111-1-111-1-1-11-11-1-111-11ii−i−iii−i−i-1-111−iii−i1−ii-1−i−iiiii−i−i−i−iii-1-111
χ1311-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-111-1-111-1-11-11-111-1-1-11−i−iii−i−iii1-1-11−ii−ii-1−ii1−i−iii−i−iii−i−iii1-1-11
χ1411-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-111-1-111-1-11-11-111-1-1-11−i−iii−i−iii-111-1i−ii−i-1−ii1ii−i−iii−i−i−i−iii-111-1
χ1511-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-111-1-111-1-1-11-11-1-111-11−i−iii−i−iii11-1-1−iii−i1i−i-1−i−iiiii−i−iii−i−i11-1-1
χ1611-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-111-1-111-1-1-11-11-1-111-11−i−iii−i−iii-1-111i−i−ii1i−i-1ii−i−i−i−iiiii−i−i-1-111
χ172222222222222222222-12-122-1-1-1-12-12-1-1-100000000-1-12-12-1-1-1-1-10202002200000000-1-1-1-100000-10-1
χ182222222222222222222-12-122-1-1-1-12-12-1-1-100000000-1-12-12-1-1-1-1-10-20-200-2-200000000111100000101
χ19222222222222222222-12-12-1-122-1-1-12-12-1-100000000-1-1-12-12-1-1-1-1202022000000-1-1-1-100000000-10-10
χ20222222222222222222-12-12-1-122-1-1-12-12-1-100000000-1-1-12-12-1-1-1-1-20-20-2-20000001111000000001010
χ2122222222222-2-22-2-2-2-22-12-122-1-1-1-12-12-1-1-100000000-1-1-21-211111020200-2-200000000111100000-10-1
χ2222222222222-2-22-2-2-2-22-12-122-1-1-1-12-12-1-1-100000000-1-1-21-2111110-20-2002200000000-1-1-1-100000101
χ2322222222222-2-22-2-2-2-2-12-12-1-122-1-1-12-12-1-100000000-1-11-21-211112020-2-2000000111100000000-10-10
χ2422222222222-2-22-2-2-2-2-12-12-1-122-1-1-12-12-1-100000000-1-11-21-21111-20-2022000000-1-1-1-1000000001010
χ252222-22-2222-200-200002222222222-2-2-2-2222-2-222222-2-20000000000000000-200-20000000000000000
χ262222-22-2222-200-200002222222222-2-2-2-222-222-2-2-2-2-2-2-2000000000000000020020000000000000000
χ2722-2-222-22-2-2200-200002222-2-2-2-22222-2-2-2-222-2-222-2-22-20000000000000000200-20000000000000000
χ2822-2-222-22-2-2200-200002222-2-2-2-22222-2-2-2-2-2-222-2-2222-20000000000000000-20020000000000000000
χ2922-2-2-2222-2-2-22i−2i22i2i−2i−2i2-12-1-2-211-1-1-212-111000000001-12i−i−2ii−i−iii020-200−2i2i00000000ii−i−i00000-101
χ3022-2-2-2222-2-2-22i−2i22i2i−2i−2i2-12-1-2-211-1-1-212-111000000001-12i−i−2ii−i−iii0-202002i−2i00000000−i−iii0000010-1
χ3122-2-2-2222-2-2-22i−2i22i2i−2i−2i-12-1211-2-2-1-11-2-1211000000001-1−i2ii−2i−i−iii20-202i−2i000000−i−iii00000000-1010
χ3222-2-2-2222-2-2-22i−2i22i2i−2i−2i-12-1211-2-2-1-11-2-1211000000001-1−i2ii−2i−i−iii-2020−2i2i000000ii−i−i0000000010-10
χ3322-2-2-2222-2-2-2−2i2i2−2i−2i2i2i2-12-1-2-211-1-1-212-111000000001-1−2ii2i−iii−i−i020-2002i−2i00000000−i−iii00000-101
χ3422-2-2-2222-2-2-2−2i2i2−2i−2i2i2i2-12-1-2-211-1-1-212-111000000001-1−2ii2i−iii−i−i0-20200−2i2i00000000ii−i−i0000010-1
χ3522-2-2-2222-2-2-2−2i2i2−2i−2i2i2i-12-1211-2-2-1-11-2-1211000000001-1i−2i−i2iii−i−i20-20−2i2i000000ii−i−i00000000-1010
χ3622-2-2-2222-2-2-2−2i2i2−2i−2i2i2i-12-1211-2-2-1-11-2-1211000000001-1i−2i−i2iii−i−i-20202i−2i000000−i−iii0000000010-10
χ37444444444444444444-2-2-2-2-2-2-2-211-2-2-2-2110000000011-2-2-2-211110000000000000000000000000000
χ3844444444444-4-44-4-4-4-4-2-2-2-2-2-2-2-211-2-2-2-21100000000112222-1-1-1-10000000000000000000000000000
χ394444-44-4444-400-400004-24-244-2-2-2-2-42-42-2-20000000022000000000000000000000000000000000000
χ404444-44-4444-400-40000-24-24-2-244-2-22-42-4-2-20000000022000000000000000000000000000000000000
χ414444-44-4444-400-40000-2-2-2-2-2-2-2-21122221100000000-1-100003-33-30000000000000000000000000000
χ424444-44-4444-400-40000-2-2-2-2-2-2-2-21122221100000000-1-10000-33-330000000000000000000000000000
χ4344-4-444-44-4-4400-400004-24-2-4-422-2-24-2-422200000000-22000000000000000000000000000000000000
χ4444-4-444-44-4-4400-40000-24-2422-4-4-2-2-242-42200000000-22000000000000000000000000000000000000
χ4544-4-444-44-4-4400-40000-2-2-2-2222211-2-222-1-1000000001-100003i−3i−3i3i0000000000000000000000000000
χ4644-4-444-44-4-4400-40000-2-2-2-2222211-2-222-1-1000000001-10000−3i3i3i−3i0000000000000000000000000000
χ4744-4-4-4444-4-4-44i−4i44i4i−4i−4i-2-2-2-222221122-2-2-1-100000000-11−2i−2i2i2iii−i−i0000000000000000000000000000
χ4844-4-4-4444-4-4-4−4i4i4−4i−4i4i4i-2-2-2-222221122-2-2-1-100000000-112i2i−2i−2i−i−iii0000000000000000000000000000
χ494-44i−4i040-44i−4i0000000044-4-44i−4i4i−4i4-400004i−4i0000000000000000000000000000000000000000000000
χ504-44i−4i040-44i−4i000000004-2-424i−4i−2i2i-220000−2i2i0000000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ1100000000
χ514-44i−4i040-44i−4i000000004-2-424i−4i−2i2i-220000−2i2i0000000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ1100000000
χ524-44i−4i040-44i−4i00000000-242-4−2i2i4i−4i-220000−2i2i000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11000000000000
χ534-44i−4i040-44i−4i00000000-242-4−2i2i4i−4i-220000−2i2i000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11000000000000
χ544-4−4i4i040-4−4i4i0000000044-4-4−4i4i−4i4i4-40000−4i4i0000000000000000000000000000000000000000000000
χ554-4−4i4i040-4−4i4i000000004-2-42−4i4i2i−2i-2200002i−2i0000000000000000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ1100000000
χ564-4−4i4i040-4−4i4i000000004-2-42−4i4i2i−2i-2200002i−2i0000000000000000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ1100000000
χ574-4−4i4i040-4−4i4i00000000-242-42i−2i−4i4i-2200002i−2i000000000000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11000000000000
χ584-4−4i4i040-4−4i4i00000000-242-42i−2i−4i4i-2200002i−2i000000000000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11000000000000
χ5966666-36-3-3-3-366-3-3-3-3-300000000000000002222-1-1-1-1000000000000000000-122-100000000-1-1-1-10000
χ6066666-36-3-3-3-366-3-3-3-3-30000000000000000-2-2-2-211110000000000000000001-2-210000000011110000
χ6166666-36-3-3-3-3-6-6-3333300000000000000002222-1-1-1-1000000000000000000-1-2-2-10000000011110000
χ6266666-36-3-3-3-3-6-6-333330000000000000000-2-2-2-21111000000000000000000122100000000-1-1-1-10000
χ636666-6-3-6-3-3-33003−3i33i3−3i33i300000000000000002-2-22-1-1-1-1000000000000000000100100000000−i3i3−i3i30000
χ646666-6-3-6-3-3-33003−3i33i3−3i33i30000000000000000-222-21111000000000000000000-100-100000000i3−i3i3−i30000
χ656666-6-3-6-3-3-330033i3−3i33i3−3i300000000000000002-2-22-1-1-1-1000000000000000000100100000000i3−i3i3−i30000
χ666666-6-3-6-3-3-330033i3−3i33i3−3i30000000000000000-222-21111000000000000000000-100-100000000−i3i3−i3i30000
χ6766-6-66-3-6-333-300333−33−3333000000000000000022-2-2-1-111000000000000000000-1001000000003−3−330000
χ6866-6-66-3-6-333-300333−33−33330000000000000000-2-22211-1-1000000000000000000100-100000000−333−30000
χ6966-6-66-3-6-333-3003−333333−33000000000000000022-2-2-1-111000000000000000000-100100000000−333−30000
χ7066-6-66-3-6-333-3003−333333−330000000000000000-2-22211-1-1000000000000000000100-1000000003−3−330000
χ7166-6-6-6-36-33336i−6i-3−3i−3i3i3i00000000000000002-22-2-1-11100000000000000000012i−2i-100000000−i−iii0000
χ7266-6-6-6-36-33336i−6i-3−3i−3i3i3i0000000000000000-22-2211-1-1000000000000000000-1−2i2i100000000ii−i−i0000
χ7366-6-6-6-36-3333−6i6i-33i3i−3i−3i00000000000000002-22-2-1-1110000000000000000001−2i2i-100000000ii−i−i0000
χ7466-6-6-6-36-3333−6i6i-33i3i−3i−3i0000000000000000-22-2211-1-1000000000000000000-12i−2i100000000−i−iii0000
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.