Finite Group Databasebeta

← Group #13139194

Character table — Group #13139194

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111222222444444446666666699991212121212121212181818181818181818181818181824242424242424242424363636363636363636363636363636363636363672727272
order1244234612126881224242424336612121212224436661212121224444444446612126122424242424242424224468812121212121212121224242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111111-11-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1
χ411111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111111111-11-11-1-1-1-1-1-1-1-11111-1-1-1-1-11-11
χ511111111111-1-11-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111111-1-1-1-1-1-1-1-1
χ611111111111-1-11-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-11-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111-1-11-1-1-1-111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11-11-111-11111-1-1-1-11111-11-11
χ811111111111-1-11-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1111111111-11-1
χ911-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-111-1-111-1-111-1-1-11ii−i−iii−i−i11-1-1-11ii−i−iii−i−i11-1-1-1i−i1ii−i−iii−i−iii−i−i11-1-1
χ1011-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-111-1-111-1-111-1-1-11−i−iii−i−iii11-1-1-11ii−i−iii−i−i-1-111-1i−i1−i−iii−i−iiiii−i−i-1-111
χ1111-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-1-1-11111-1-111-1-11-1ii−i−i−i−iii-1-111-11ii−i−iii−i−i1-1-111−ii-1ii−i−i−i−iii−i−iii1-1-11
χ1211-1-1-1111-1-1-1i−i1ii−i−i1111-1-1-1-1-1-11111-1-111-1-11-1−i−iiiii−i−i-1-111-11ii−i−iii−i−i-111-11−ii-1−i−iiiii−i−i−i−iii-111-1
χ1311-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-111-1-111-1-111-1-1-11ii−i−iii−i−i11-1-1-11−i−iii−i−iii-1-111-1−ii1ii−i−iii−i−i−i−iii-1-111
χ1411-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-111-1-111-1-111-1-1-11−i−iii−i−iii11-1-1-11−i−iii−i−iii11-1-1-1−ii1−i−iii−i−iii−i−iii11-1-1
χ1511-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-1-1-11111-1-111-1-11-1ii−i−i−i−iii-1-111-11−i−iii−i−iii-111-11i−i-1ii−i−i−i−iiiii−i−i-111-1
χ1611-1-1-1111-1-1-1−ii1−i−iii1111-1-1-1-1-1-11111-1-111-1-11-1−i−iiiii−i−i-1-111-11−i−iii−i−iii1-1-111i−i-1−i−iiiii−i−iii−i−i1-1-11
χ172222222222222222222-12-122-1-10000-1-12-12-1-1-100000022220000-1-12-12-1-1-1-1-1020200000000-1-1-1-100000-10-1
χ182222222222222222222-12-122-1-10000-1-12-12-1-1-1000000-2-2-2-20000-1-12-12-1-1-1-1-10-20-200000000111100000101
χ19222222222222222222-12-12-1-1220000-1-1-12-12-1-100222200000000-1-1-12-12-1-1-1-120200000-1-1-1-100000000-10-10
χ20222222222222222222-12-12-1-1220000-1-1-12-12-1-100-2-2-2-200000000-1-1-12-12-1-1-1-1-20-2000001111000000001010
χ2122222222222-2-22-2-2-2-22-12-122-1-10000-1-12-12-1-1-100000022220000-1-1-21-2111110-20-200000000-1-1-1-100000101
χ2222222222222-2-22-2-2-2-22-12-122-1-10000-1-12-12-1-1-1000000-2-2-2-20000-1-1-21-211111020200000000111100000-10-1
χ2322222222222-2-22-2-2-2-2-12-12-1-1220000-1-1-12-12-1-100222200000000-1-11-21-21111-20-200000-1-1-1-1000000001010
χ2422222222222-2-22-2-2-2-2-12-12-1-1220000-1-1-12-12-1-100-2-2-2-200000000-1-11-21-2111120200000111100000000-10-10
χ252222-22-2222-200-2000022222222222222-2-2-2-222-2-2000000002222-2-2000000000000-200-20000000000000000
χ262222-22-2222-200-2000022222222-2-2-2-222-2-2-2-2222200000000-2-2-2-2-2-200000000000020020000000000000000
χ2722-2-222-22-2-2200-200002222-2-2-2-222-2-22222-2-2-2-22-20000000022-2-22-2000000000000200-20000000000000000
χ2822-2-222-22-2-2200-200002222-2-2-2-2-2-2222222-2-2-2-2-2200000000-2-2222-2000000000000-20020000000000000000
χ2922-2-2-2222-2-2-22i−2i22i2i−2i−2i2-12-1-2-2110000-1-1-212-1110000002i2i−2i−2i00001-12i−i−2ii−i−iii020-200000000−i−iii00000-101
χ3022-2-2-2222-2-2-22i−2i22i2i−2i−2i2-12-1-2-2110000-1-1-212-111000000−2i−2i2i2i00001-12i−i−2ii−i−iii0-20200000000ii−i−i0000010-1
χ3122-2-2-2222-2-2-22i−2i22i2i−2i−2i-12-1211-2-20000-1-11-2-1211002i2i−2i−2i000000001-1−i2ii−2i−i−iii20-200000−i−iii00000000-1010
χ3222-2-2-2222-2-2-22i−2i22i2i−2i−2i-12-1211-2-20000-1-11-2-121100−2i−2i2i2i000000001-1−i2ii−2i−i−iii-20200000ii−i−i0000000010-10
χ3322-2-2-2222-2-2-2−2i2i2−2i−2i2i2i2-12-1-2-2110000-1-1-212-1110000002i2i−2i−2i00001-1−2ii2i−iii−i−i0-20200000000−i−iii0000010-1
χ3422-2-2-2222-2-2-2−2i2i2−2i−2i2i2i2-12-1-2-2110000-1-1-212-111000000−2i−2i2i2i00001-1−2ii2i−iii−i−i020-200000000ii−i−i00000-101
χ3522-2-2-2222-2-2-2−2i2i2−2i−2i2i2i-12-1211-2-20000-1-11-2-1211002i2i−2i−2i000000001-1i−2i−i2iii−i−i-20200000−i−iii0000000010-10
χ3622-2-2-2222-2-2-2−2i2i2−2i−2i2i2i-12-1211-2-20000-1-11-2-121100−2i−2i2i2i000000001-1i−2i−i2iii−i−i20-200000ii−i−i00000000-1010
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−2i0000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
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−2i000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
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-22−2i2i0000000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
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-22−2i2i000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ412-2−2i2i020-2−2i2i0000000022-2-2−2i2i−2i2i2-2−2i2i2-20000−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i2-2−2i2i0000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ422-2−2i2i020-2−2i2i0000000022-2-2−2i2i−2i2i2-2−2i2i2-20000−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i2-2−2i2i000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
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−2i0000000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
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−2i000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ45444444444444444444-2-2-2-2-2-2-2-2000011-2-2-2-2110000000000000011-2-2-2-21111000000000000000000000000
χ4644444444444-4-44-4-4-4-4-2-2-2-2-2-2-2-2000011-2-2-2-21100000000000000112222-1-1-1-1000000000000000000000000
χ474444-44-4444-400-400004-24-244-2-20000-2-2-42-42-2-2000000000000002200000000000000000000000000000000
χ484444-44-4444-400-40000-24-24-2-2440000-2-22-42-4-2-2000000000000002200000000000000000000000000000000
χ494444-44-4444-400-40000-2-2-2-2-2-2-2-200001122221100000000000000-1-100003-33-3000000000000000000000000
χ504444-44-4444-400-40000-2-2-2-2-2-2-2-200001122221100000000000000-1-10000-33-33000000000000000000000000
χ5144-4-444-44-4-4400-400004-24-2-4-4220000-2-24-2-422200000000000000-2200000000000000000000000000000000
χ5244-4-444-44-4-4400-40000-24-2422-4-40000-2-2-242-42200000000000000-2200000000000000000000000000000000
χ5344-4-444-44-4-4400-40000-2-2-2-22222000011-2-222-1-1000000000000001-100003i−3i−3i3i000000000000000000000000
χ5444-4-444-44-4-4400-40000-2-2-2-22222000011-2-222-1-1000000000000001-10000−3i3i3i−3i000000000000000000000000
χ5544-4-4-4444-4-4-44i−4i44i4i−4i−4i-2-2-2-2222200001122-2-2-1-100000000000000-11−2i−2i2i2iii−i−i000000000000000000000000
χ5644-4-4-4444-4-4-4−4i4i4−4i−4i4i4i-2-2-2-2222200001122-2-2-1-100000000000000-112i2i−2i−2i−i−iii000000000000000000000000
χ574-44i−4i040-44i−4i000000004-2-424i−4i−2i2i0000-220000−2i2i0000002+2i−2−2i2−2i−2+2i00000000000000000000000000−1−i1+i−1+i1−i00000000
χ584-44i−4i040-44i−4i000000004-2-424i−4i−2i2i0000-220000−2i2i000000−2−2i2+2i−2+2i2−2i000000000000000000000000001+i−1−i1−i−1+i00000000
χ594-44i−4i040-44i−4i00000000-242-4−2i2i4i−4i0000-220000−2i2i002+2i−2−2i2−2i−2+2i00000000000000000000000000−1−i1+i−1+i1−i000000000000
χ604-44i−4i040-44i−4i00000000-242-4−2i2i4i−4i0000-220000−2i2i00−2−2i2+2i−2+2i2−2i000000000000000000000000001+i−1−i1−i−1+i000000000000
χ614-4−4i4i040-4−4i4i000000004-2-42−4i4i2i−2i0000-2200002i−2i0000002−2i−2+2i2+2i−2−2i00000000000000000000000000−1+i1−i−1−i1+i00000000
χ624-4−4i4i040-4−4i4i000000004-2-42−4i4i2i−2i0000-2200002i−2i000000−2+2i2−2i−2−2i2+2i000000000000000000000000001−i−1+i1+i−1−i00000000
χ634-4−4i4i040-4−4i4i00000000-242-42i−2i−4i4i0000-2200002i−2i002−2i−2+2i2+2i−2−2i00000000000000000000000000−1+i1−i−1−i1+i000000000000
χ644-4−4i4i040-4−4i4i00000000-242-42i−2i−4i4i0000-2200002i−2i00−2+2i2−2i−2−2i2+2i000000000000000000000000001−i−1+i1+i−1−i000000000000
χ6566666-36-3-3-3-366-3-3-3-3-3000000002222000000002200000000-1-1-1-100000000000000-122-100000000-1-1-1-10000
χ6666666-36-3-3-3-366-3-3-3-3-300000000-2-2-2-200000000-2-2000000001111000000000000001-2-210000000011110000
χ6766666-36-3-3-3-3-6-6-33333000000002222000000002200000000-1-1-1-100000000000000-1-2-2-10000000011110000
χ6866666-36-3-3-3-3-6-6-3333300000000-2-2-2-200000000-2-200000000111100000000000000122100000000-1-1-1-10000
χ696666-6-3-6-3-3-33003−3i33i3−3i33i300000000222200000000-2-200000000-1-1-1-100000000000000100100000000−i3i3−i3i30000
χ706666-6-3-6-3-3-33003−3i33i3−3i33i300000000-2-2-2-2000000002200000000111100000000000000-100-100000000i3−i3i3−i30000
χ716666-6-3-6-3-3-330033i3−3i33i3−3i300000000222200000000-2-200000000-1-1-1-100000000000000100100000000i3−i3i3−i30000
χ726666-6-3-6-3-3-330033i3−3i33i3−3i300000000-2-2-2-2000000002200000000111100000000000000-100-100000000−i3i3−i3i30000
χ7366-6-66-3-6-333-300333−33−33330000000022-2-2000000002-200000000-1-11100000000000000-1001000000003−3−330000
χ7466-6-66-3-6-333-300333−33−333300000000-2-22200000000-220000000011-1-100000000000000100-100000000−333−30000
χ7566-6-66-3-6-333-3003−333333−330000000022-2-2000000002-200000000-1-11100000000000000-100100000000−333−30000
χ7666-6-66-3-6-333-3003−333333−3300000000-2-22200000000-220000000011-1-100000000000000100-1000000003−3−330000
χ7766-6-6-6-36-33336i−6i-3−3i−3i3i3i0000000022-2-200000000-2200000000-1-1110000000000000012i−2i-100000000−i−iii0000
χ7866-6-6-6-36-33336i−6i-3−3i−3i3i3i00000000-2-222000000002-20000000011-1-100000000000000-1−2i2i100000000ii−i−i0000
χ7966-6-6-6-36-3333−6i6i-33i3i−3i−3i0000000022-2-200000000-2200000000-1-111000000000000001−2i2i-100000000ii−i−i0000
χ8066-6-6-6-36-3333−6i6i-33i3i−3i−3i00000000-2-222000000002-20000000011-1-100000000000000-12i−2i100000000−i−iii0000
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).