Finite Group Databasebeta

← Group #13146678

Character table — Group #13146678

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222441212121212121212121212121818181818181818242436363636363636363636363636363636363636363636363636363636363672727272
order12222236666633666666666644441212121266224444448888121212121212121212122424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111-1-11111-1-11111-1-1-1-111111-1-111111-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111-1-11111-1-11111-1-1-1-111111-1-111111-1-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ71111-1-11111-1-11111-1-1-1-111111-1-111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ81111-1-11111-1-11111-1-1-1-111111-1-111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ91-11-11-11-1-111-1111-111-1-1-1-11-111-1-111-1-11-11-11-1i−ii−ii−ii−i1-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ101-11-11-11-1-111-1111-111-1-1-1-11-111-1-111-1-11-11-11-1−ii−ii−ii−ii1-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ111-11-11-11-1-111-1111-111-1-1-1-11-111-1-111-1-11-1-11-11i−ii−i−ii−ii1-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ121-11-11-11-1-111-1111-111-1-1-1-11-111-1-111-1-11-1-11-11−ii−iii−ii−i1-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ131-11-1-111-1-11-11111-1-1-111-1-11-11-11-111-1-1-111-1-11i−i−iii−i−ii-11ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ141-11-1-111-1-11-11111-1-1-111-1-11-11-11-111-1-1-111-1-11−iii−i−iii−i-11−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ151-11-1-111-1-11-11111-1-1-111-1-11-11-11-111-1-1-11-111-1i−i−ii−iii−i-11ii−i−i−i−iii−i−iiiii−i−i-111-1
χ161-11-1-111-1-11-11111-1-1-111-1-11-11-11-111-1-1-11-111-1−iii−ii−i−ii-11−i−iiiii−i−iii−i−i−i−iii-111-1
χ17222222222222222222222222-2-2-2-2-2-2-2-222000000000000-2-200000000000000000000
χ182222-2-22222-2-22222-2-2-2-22222-222-2-2-2-2-2-2-20000000000002200000000000000000000
χ192-22-22-22-2-222-2222-222-2-2-2-22-2-2-222-2-2222-2000000000000-2200000000000000000000
χ202-22-2-222-2-22-22222-2-2-222-2-22-2-22-22-2-222-220000000000002-200000000000000000000
χ214444444444441-2111111-2-2-2100000000-2-200002222000000-1-1-1-1-1-1-1-1000000000000
χ224444444444441-2111111-2-2-2100000000-2-20000-2-2-2-200000011111111000000000000
χ23444444444444-21-2-2-2-2-2-2111-20000000011222200000000000000000000000000-1-1-1-1
χ24444444444444-21-2-2-2-2-2-2111-20000000011-2-2-2-2000000000000000000000000001111
χ254444-4-44444-4-41-211-1-1-1-1-2-2-210000000022000022-2-2000000-1-1-1-11111000000000000
χ264444-4-44444-4-41-211-1-1-1-1-2-2-2100000000220000-2-2220000001111-1-1-1-1000000000000
χ274444-4-44444-4-4-21-2-22222111-200000000-1-122-2-200000000000000000000000000-1-111
χ284444-4-44444-4-4-21-2-22222111-200000000-1-1-2-2220000000000000000000000000011-1-1
χ2944-4-40044-4-4001-2-113-33-32-22-10000000000000000000000003−33−33−33−3000000000000
χ3044-4-40044-4-4001-2-113-33-32-22-1000000000000000000000000−33−33−33−33000000000000
χ3144-4-40044-4-4001-2-11-33-332-22-10000000000000000000000003−33−3−33−33000000000000
χ3244-4-40044-4-4001-2-11-33-332-22-1000000000000000000000000−33−333−33−3000000000000
χ3344-4-40044-4-40044-440000-44-4-400000000000000000000000000000000000000000000
χ344-44-44-44-4-444-41-21-111-1-122-2-100000000-2200002i−2i2i−2i000000−i−iii−i−iii000000000000
χ354-44-44-44-4-444-41-21-111-1-122-2-100000000-220000−2i2i−2i2i000000ii−i−iii−i−i000000000000
χ364-44-44-44-4-444-4-21-22-2-222-1-112000000001-12-22-200000000000000000000000000-11-11
χ374-44-44-44-4-444-4-21-22-2-222-1-112000000001-1-22-22000000000000000000000000001-11-1
χ384-44-4-444-4-44-441-21-1-1-11122-2-1000000002-200002i−2i−2i2i000000−i−iiiii−i−i000000000000
χ394-44-4-444-4-44-441-21-1-1-11122-2-1000000002-20000−2i2i2i−2i000000ii−i−i−i−iii000000000000
χ404-44-4-444-4-44-44-21-2222-2-2-1-11200000000-112-2-2200000000000000000000000000-111-1
χ414-44-4-444-4-44-44-21-2222-2-2-1-11200000000-11-222-2000000000000000000000000001-1-11
χ424-4-44004-44-4001-2-1-13-3-33-2221000000000000000000000000−i3i3i3−i3−i3i3i3−i3000000000000
χ434-4-44004-44-4001-2-1-13-3-33-2221000000000000000000000000i3−i3−i3i3i3−i3−i3i3000000000000
χ444-4-44004-44-4001-2-1-1-333-3-2221000000000000000000000000−i3i3i3−i3i3−i3−i3i3000000000000
χ454-4-44004-44-4001-2-1-1-333-3-2221000000000000000000000000i3−i3−i3i3−i3i3i3−i3000000000000
χ464-4-44004-44-40044-4-400004-4-4400000000000000000000000000000000000000000000
χ47666666-3-3-3-3-3-30000000000002222-1-1-1-100000000000000-1-1000000003−33−33−33−30000
χ48666666-3-3-3-3-3-30000000000002222-1-1-1-100000000000000-1-100000000−33−33−33−330000
χ49666666-3-3-3-3-3-3000000000000-2-2-2-21111000000000022221100000000-1-1-1-1-1-1-1-10000
χ50666666-3-3-3-3-3-3000000000000-2-2-2-211110000000000-2-2-2-21100000000111111110000
χ516666-6-6-3-3-3-3330000000000002-2-22-1-1-1-10000000000000011000000003−33−3−33−330000
χ526666-6-6-3-3-3-3330000000000002-2-22-1-1-1-1000000000000001100000000−33−333−33−30000
χ536666-6-6-3-3-3-333000000000000-222-21111000000000022-2-2-1-100000000-1-1-1-111110000
χ546666-6-6-3-3-3-333000000000000-222-211110000000000-2-222-1-1000000001111-1-1-1-10000
χ556-66-66-6-333-3-3300000000000022-2-2-1-11100000000000000-1100000000−i3i3i3−i3−i3i3i3−i30000
χ566-66-66-6-333-3-3300000000000022-2-2-1-11100000000000000-1100000000i3−i3−i3i3i3−i3−i3i30000
χ576-66-66-6-333-3-33000000000000-2-22211-1-100000000002i−2i2i−2i1-100000000−i−iii−i−iii0000
χ586-66-66-6-333-3-33000000000000-2-22211-1-10000000000−2i2i−2i2i1-100000000ii−i−iii−i−i0000
χ596-66-6-66-333-33-30000000000002-22-2-1-111000000000000001-100000000−i3i3i3−i3i3−i3−i3i30000
χ606-66-6-66-333-33-30000000000002-22-2-1-111000000000000001-100000000i3−i3−i3i3−i3i3i3−i30000
χ616-66-6-66-333-33-3000000000000-22-2211-1-100000000002i−2i−2i2i-1100000000−i−iiiii−i−i0000
χ626-66-6-66-333-33-3000000000000-22-2211-1-10000000000−2i2i2i−2i-1100000000ii−i−i−i−iii0000
χ6388-8-80088-8-800-424-40000-22-2400000000000000000000000000000000000000000000
χ648-8-88008-88-800-424400002-2-2-400000000000000000000000000000000000000000000
χ651212-12-1200-6-66600000000000000000023−2323−23000000000000000000000000000000000000
χ661212-12-1200-6-666000000000000000000−2323−2323000000000000000000000000000000000000
χ6712-12-121200-66-6600000000000000000023−23−2323000000000000000000000000000000000000
χ6812-12-121200-66-66000000000000000000−232323−23000000000000000000000000000000000000

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