Finite Group Databasebeta

← Group #13146561

Character table — Group #13146561

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122222244999912121212121212121212121218181818181818181818181818182424363636363636363636363636363636363636363636363636363672727272
order124423461212612224433666612121212121224444444446612126122244688881212121212121212122424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111-11-1111-1-1-1-1-1-1111-1-1111-1-11111iiii−i−i−i−i-1-1-1-1-1-11-11-11ii−i−i1iiii−i−i−i−iiiii−i−i−i−i1-11-1
χ61111-11-1111-1-1-1-1-1-1111-1-1111-1-11111iiii−i−i−i−i-1-1-1-1-1-1-11-111−i−iii1iiii−i−i−i−i−i−i−i−iiiii-11-11
χ71111-11-1111-1-1-1-1-1-1111-1-1111-1-11111−i−i−i−iiiii-1-1-1-1-1-11-11-11−i−iii1−i−i−i−iiiii−i−i−i−iiiii1-11-1
χ81111-11-1111-1-1-1-1-1-1111-1-1111-1-11111−i−i−i−iiiii-1-1-1-1-1-1-11-111ii−i−i1−i−i−i−iiiiiiiii−i−i−i−i-11-11
χ911-1-111-11-1-11-1-1-111111111-1-1-1-1-1-1-1111-1-111-1-1-1-1111-11-1-11-11-11-1111-1-111-1-111-1-111-1-11-1-11
χ1011-1-111-11-1-11-1-1-111111111-1-1-1-1-1-1-1111-1-111-1-1-1-1111-1-111-1-1-11-11111-1-111-1-1-1-111-1-111-111-1
χ1111-1-111-11-1-11-1-1-111111111-1-1-1-1-1-1-11-1-111-1-111-1-1111-11-1-11-1-11-111-1-111-1-111-1-111-1-1111-1-11
χ1211-1-111-11-1-11-1-1-111111111-1-1-1-1-1-1-11-1-111-1-111-1-1111-1-111-1-11-11-11-1-111-1-11111-1-111-1-1-111-1
χ1311-1-1-1111-1-1-1111-1-1111-1-11-1-111-1-1-11ii−i−i−i−iii11-1-1-1111-1-1-1i−i−ii1ii−i−i−i−iiiii−i−i−i−iii11-1-1
χ1411-1-1-1111-1-1-1111-1-1111-1-11-1-111-1-1-11ii−i−i−i−iii11-1-1-11-1-111-1−iii−i1ii−i−i−i−iii−i−iiiii−i−i-1-111
χ1511-1-1-1111-1-1-1111-1-1111-1-11-1-111-1-1-11−i−iiiii−i−i11-1-1-1111-1-1-1−iii−i1−i−iiiii−i−i−i−iiiii−i−i11-1-1
χ1611-1-1-1111-1-1-1111-1-1111-1-11-1-111-1-1-11−i−iiiii−i−i11-1-1-11-1-111-1i−i−ii1−i−iiiii−i−iii−i−i−i−iii-1-111
χ17222222222222-2-2-2-2222222222222-2-200000000-2-2-2-2220000-20000-200000000000000000000
χ182222-22-2222-2-22222222-2-2222-2-222-2-2000000002222-2-20000-20000-200000000000000000000
χ1922-2-222-22-2-22-222-2-2222222-2-2-2-2-2-22-20000000022-2-22-2000020000-200000000000000000000
χ2022-2-2-2222-2-2-22-2-222222-2-22-2-222-2-22-200000000-2-222-22000020000-200000000000000000000
χ212-22i−2i020-22i−2i002-22i−2i22-200-22i−2i002i−2i001+i−1−i1−i−1+i1−i−1+i1+i−1−i2-22i−2i0000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000
χ222-22i−2i020-22i−2i002-22i−2i22-200-22i−2i002i−2i00−1−i1+i−1+i1−i−1+i1−i−1−i1+i2-22i−2i000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000
χ232-22i−2i020-22i−2i00-22−2i2i22-200-22i−2i002i−2i001−i−1+i−1−i1+i1+i−1−i−1+i1−i-22−2i2i0000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000
χ242-22i−2i020-22i−2i00-22−2i2i22-200-22i−2i002i−2i00−1+i1−i1+i−1−i−1−i1+i1−i−1+i-22−2i2i000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000
χ252-2−2i2i020-2−2i2i002-2−2i2i22-200-2−2i2i00−2i2i001−i−1+i1+i−1−i1+i−1−i1−i−1+i2-2−2i2i0000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000
χ262-2−2i2i020-2−2i2i002-2−2i2i22-200-2−2i2i00−2i2i00−1+i1−i−1−i1+i−1−i1+i−1+i1−i2-2−2i2i000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000
χ272-2−2i2i020-2−2i2i00-222i−2i22-200-2−2i2i00−2i2i001+i−1−i−1+i1−i1−i−1+i−1−i1+i-222i−2i0000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000
χ282-2−2i2i020-2−2i2i00-222i−2i22-200-2−2i2i00−2i2i00−1−i1+i1−i−1+i−1+i1−i1+i−1−i-222i−2i000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000
χ2944444444444400001-2111-21111-2-200222222220000-2-20000000000-1-1-1-1-1-1-1-1000000000000
χ3044444444444400001-2111-21111-2-200-2-2-2-2-2-2-2-20000-2-2000000000011111111000000000000
χ314444444444440000-21-2-2-21-2-2-2-211000000000000001122220000000000000000000000-1-1-1-1
χ324444444444440000-21-2-2-21-2-2-2-2110000000000000011-2-2-2-200000000000000000000001111
χ334444-44-4444-4-400001-21-1-1-211-1-1-2-2002i2i2i2i−2i−2i−2i−2i0000220000000000−i−i−i−iiiii000000000000
χ344444-44-4444-4-400001-21-1-1-211-1-1-2-200−2i−2i−2i−2i2i2i2i2i0000220000000000iiii−i−i−i−i000000000000
χ354444-44-4444-4-40000-21-2221-2-2221100000000000000-1-12-22-20000000000000000000000-11-11
χ364444-44-4444-4-40000-21-2221-2-2221100000000000000-1-1-22-2200000000000000000000001-11-1
χ3744-4-444-44-4-44-400001-2111-2-1-1-1-1220022-2-222-2-20000-220000000000-1-111-1-111000000000000
χ3844-4-444-44-4-44-400001-2111-2-1-1-1-12200-2-222-2-2220000-22000000000011-1-111-1-1000000000000
χ3944-4-444-44-4-44-40000-21-2-2-212222-1-1000000000000001-12-2-220000000000000000000000-111-1
χ4044-4-444-44-4-44-40000-21-2-2-212222-1-1000000000000001-1-222-200000000000000000000001-1-11
χ4144-4-4-4444-4-4-4400001-21-1-1-2-1-11122002i2i−2i−2i−2i−2i2i2i00002-20000000000−i−iiiii−i−i000000000000
χ4244-4-4-4444-4-4-4400001-21-1-1-2-1-1112200−2i−2i2i2i2i2i−2i−2i00002-20000000000ii−i−i−i−iii000000000000
χ4344-4-4-4444-4-4-440000-21-222122-2-2-1-100000000000000-1122-2-20000000000000000000000-1-111
χ4444-4-4-4444-4-4-440000-21-222122-2-2-1-100000000000000-11-2-222000000000000000000000011-1-1
χ454-44i−4i040-44i−4i0000001-2-13-32i−i3i−3i−2i2i002-2−2i2i2-22i−2i0000000000000000-11i−i-11−ii000000000000
χ464-44i−4i040-44i−4i0000001-2-13-32i−i3i−3i−2i2i00-222i−2i-22−2i2i00000000000000001-1−ii1-1i−i000000000000
χ474-44i−4i040-44i−4i0000001-2-1-332i−i−3i3i−2i2i002i−2i2-2−2i2i2-20000000000000000−ii-11i−i-11000000000000
χ484-44i−4i040-44i−4i0000001-2-1-332i−i−3i3i−2i2i00−2i2i-222i−2i-220000000000000000i−i1-1−ii1-1000000000000
χ494-4−4i4i040-4−4i4i0000001-2-13-32−ii−3i3i2i−2i002-22i−2i2-2−2i2i0000000000000000-11−ii-11i−i000000000000
χ504-4−4i4i040-4−4i4i0000001-2-13-32−ii−3i3i2i−2i00-22−2i2i-222i−2i00000000000000001-1i−i1-1−ii000000000000
χ514-4−4i4i040-4−4i4i0000001-2-1-332−ii3i−3i2i−2i002i−2i-22−2i2i-220000000000000000−ii1-1i−i1-1000000000000
χ524-4−4i4i040-4−4i4i0000001-2-1-332−ii3i−3i2i−2i00−2i2i2-22i−2i2-20000000000000000i−i-11−ii-11000000000000
χ5366666-36-3-3-3-3-322220000000000002200000000-1-1-1-1000000-10000-1000000003−33−33−33−30000
χ5466666-36-3-3-3-3-322220000000000002200000000-1-1-1-1000000-10000-100000000−33−33−33−330000
χ5566666-36-3-3-3-3-3-2-2-2-2000000000000-2-200000000111100000012222100000000-1-1-1-1-1-1-1-10000
χ5666666-36-3-3-3-3-3-2-2-2-2000000000000-2-20000000011110000001-2-2-2-2100000000111111110000
χ576666-6-3-6-3-3-3332222000000000000-2-200000000-1-1-1-100000012i2i−2i−2i100000000−i−i−i−iiiii0000
χ586666-6-3-6-3-3-3332222000000000000-2-200000000-1-1-1-10000001−2i−2i2i2i100000000iiii−i−i−i−i0000
χ596666-6-3-6-3-3-333-2-2-2-200000000000022000000001111000000-10000-100000000−i3i3−i3i3i3−i3i3−i30000
χ606666-6-3-6-3-3-333-2-2-2-200000000000022000000001111000000-10000-100000000i3−i3i3−i3−i3i3−i3i30000
χ6166-6-66-3-6-333-3322-2-20000000000002-200000000-1-111000000-12-22-2100000000-1-111-1-1110000
χ6266-6-66-3-6-333-3322-2-20000000000002-200000000-1-111000000-1-22-2210000000011-1-111-1-10000
χ6366-6-66-3-6-333-33-2-222000000000000-220000000011-1-100000010000-1000000003−3−333−3−330000
χ6466-6-66-3-6-333-33-2-222000000000000-220000000011-1-100000010000-100000000−333−3−333−30000
χ6566-6-6-6-36-3333-322-2-2000000000000-2200000000-1-11100000010000-100000000−i3i3i3−i3i3−i3−i3i30000
χ6666-6-6-6-36-3333-322-2-2000000000000-2200000000-1-11100000010000-100000000i3−i3−i3i3−i3i3i3−i30000
χ6766-6-6-6-36-3333-3-2-2220000000000002-20000000011-1-1000000-12i−2i−2i2i100000000−i−iiiii−i−i0000
χ6866-6-6-6-36-3333-3-2-2220000000000002-20000000011-1-1000000-1−2i2i2i−2i100000000ii−i−i−i−iii0000
χ698-88i−8i080-88i−8i000000-42400-2−4i4i002i−2i0000000000000000000000000000000000000000000000
χ708-8−8i8i080-8−8i8i000000-42400-24i−4i00−2i2i0000000000000000000000000000000000000000000000
χ7112-1212i−12i0-606−6i6i004-44i−4i0000000000000000000000-22−2i2i00000000000000000000000000000000
χ7212-1212i−12i0-606−6i6i00-44−4i4i00000000000000000000002-22i−2i00000000000000000000000000000000
χ7312-12−12i12i0-6066i−6i004-4−4i4i0000000000000000000000-222i−2i00000000000000000000000000000000
χ7412-12−12i12i0-6066i−6i00-444i−4i00000000000000000000002-2−2i2i00000000000000000000000000000000

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